Free Fractional to Decimal Odds Converter For Betting

Hey everyone. There's been a lot of questions behind the math of both sides, and I want to break it down into digestible chunks so that most people can understand it. I watch Dream's content quite frequently, so it kind of broke my heart to see that math was being used incorrectly in order to confuse people.

Let me explain basic probability, and then I'll move to explain why the binomial model (used in the mods' paper) is accurate and why the stopping rule should not apply at all, as well as considering what "statistically significant" is supposed to mean.

Flipping a coin ten times, what are the chances of getting ten heads in a row? The fundamental counting rule says to multiply 1/2 ten times, or 1/2 ^ 10. This equates to 1/1024. Hard odds for sure. Most simple things in probability just takes this rule and places it in neat formulas to calculate probabilities with ease given a few variables, instead of having to calculate individual *events* and multiplying them together.

Let's dive a little bit deeper. What are the chances that if you throw a coin ten times, half of them will be heads and the other half are tails? Well, you could calculate the probability of all 5 heads (1/2 ^ 5) and all the tails (1/2 ^ 5) and multiply, right? Multiplying through would get you the same number, 1/1024. But that's not right, because that's the case of getting 10 heads in a row!

What we calculated instead was the probability of throwing exactly 5 heads in a row, and then exactly 5 tails in a row. This doesn't take into the account if we threw 5 tails in a row, then 5 heads in a row. Or if we got a head, a tail, a head, a tail, alternating sequence. Or if we got 4 heads, 5 tails, and then a head on the last flip. Or...

We can see this would take a very long time to find all the different ways to organize 5 heads and 5 tails in a group of ten. Thankfully, we do have another way to solve this. This classic case is called *combinations* and calculates the probability, ignoring the specific order of the events that come in (in this case, coin tosses).

In order to do this, we have to learn about *permutations*. Permutations are something we already covered a little bit with our first coin flipping example. The only difference between permutations and combinations is that order matters in permutations. What do I mean by that?

Permutations would ask questions asking how likely one specific scenario is out of the different ways a race with 10 people can finish in 1st, 2nd, or 3rd, or the exact order of heads and tails on coin tosses (get exactly 2 heads, then 1 tail, then 1 head, then 3 tails, then 2 heads, then 1 tail). The scary looking formula is n!/(n - k)!, where *n* means the *n*umber of objects and *k* means what is being ordered. In the case of the racers, n = 10, k = 3. In the case of that exact set of coin flips, n = 10 and k = 10 as well.

Maybe you don't trust this formula. That's fine, you can look it up yourself, you can read *why* in works here, or any other site if you don't like wikipedia.

All this is doing is the counting rule in a nice formula. In the case of the racers, there's 10 ways any one of them can come in first, 9 of the remaining 9 comes in second (because someone is already first and can't be second at the same time) and 8 of the remaining 8 (because 2 people are already first and second and can't be third at the same time). This gives us 10 * 9 * 8, or 720 ways 3 racers can come in 1st, 2nd, and 3rd. Out of a list of boring people A thru J, the chance of B comes in 1st, F comes in 2nd, and A comes in 3rd is only 1 possible way of those 720 outcomes, giving a probability of 1/720.

I hope so far it's been making sense. Do let me know if it does not, because I can point you in the right direction for more resources, or try my best to explain it myself.

The way it works with the formula is that n! is equal to 10 * 9 * 8 * 7 * ... * 1. The ! is a shortcut of all the numbers multiplied counting down to 1, starting from n. We take this ungodly large number 10! and divide it by (10 - 3)!, or 7!. You can run it through your own calculator, but doing 10! and then dividing by 7! doesn't really show how the counting rule works. What we can see instead is that when we do this:

10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
--------------------------------------------------
7 * 6 * 5 * 4 * 3 * 2 * 1

We can cross cancel everything from the 7 onwards, giving us just

10 * 9 * 8
-------------
1

This is exactly the same as the counting rule, because the scary formula n!/(n! - k!) was derived from the counting rule, not vice versa. Place a 1 on top of that number, and that's your chance of getting some arbitrary 3 people getting 1st, 2nd, and 3rd. 1/720. The same answer we got when using the counting rule.

Cool. So going back to our original example of combinations, we gotta figure this out without the order. What are the chances of the top 3 finishers being people BFA, in no particular order?

Thankfully, in a group of 3, things are much easier to calculate. It could be ABF. Or AFB. Or BAF. Or BFA. Or FBA. Or FAB. Six ways.

Kinda hard to do with 5 heads in 10 tails to count everything out though, right? There's a shortcut.

We can organize these top three runners in their own little group. How many ways can we get 1st 2nd and 3rd in a group of 3? Using the counting principle, there's only 3 options for 1st place, 2 options for 2nd place, and only 1 for 3rd place. 3 * 2 * 1. 6 ways to organize a team of 3. So out of the 720 ways, there are 6 ways to organize a group of three, giving us the number 6/720, or 1/120.

That was a mouthful. Thankfully, there's another function for combinations, which is n! / (k! * (n - k)!). Don't take my word for it, you can find it here or any other site if you don't like wikipedia. N is again the number of objects/events, k is again the number of things being sorted. If you are really astute, you can see that combinations formula is only an additional k! in the denominator of the fraction. In the case of the racers, it was that 3! for organizing 3 people teams. The formula bakes up to get us 120, and so the chances of people BFA being chosen in A thru J would be only 1 out of 120 ways. The same exact answer we derived from using permutations only. 1/120. This is not a coincidence, again, but a formula to save time.

Let's go back to the coins example of 5 heads and 5 tails in 10 coin flips. Well, you'd get 10! / (5! * (10 - 5)!). Plugging this into a calculator gets us the cool value of 252. Well, that's the number of ways to organize 5 heads and 5 tails in all the possible orders. We still have 1024 ways to get coin flips. To calculate probability, we just put the number of wanted events over the number of all events, which gets us 252/1024. You can search up the answer yourself if you don't believe me. Run through a calculator.

That's combinations. Let's jump into the binomial theorem.

Geosquare's video does a wonderful job explaining *when* to use the binomial theorem, and in the case of blaze rods and ender drop barters, it's quite accurate. The binomial theorem is used to answer questions like "out of some number of trials, what are the chances that we got some number of successes?" In the case of our coin flips, it's 5 heads out of 10 coin flips. In the case of piglin barters, it's Dream's 42 successful ender pearl trades out of 262 barters. Cool.

The formula already given by Geosquare is already out there, but it's nCx * p ^ x * q ^ (1 - x). Reddit formatting fails me here, but I can explain it. nCx is just a shorthand way of writing the combinations equation, with N attempts and X successes (10 flips, 5 heads). P is the probability of a success (1/2 chance of heads) and Q is the probability of a fail (otherwise known as 1 - P, or 1 - 1/2, or 1/2, or the chance of a tails). For our 10 coin flips example, we have all the information we need to plug in everything we need. You can follow along with any calculator, or check wikipedia or any other site for the math.

We get the same answer, in case you were too lazy. 252/1024 if you kept the number as a fraction, or about .246 if you didn't. This binomial equation was created stemming from the very same counting principle we started this entire crash course with. We just organized the 5 heads and 5 tails in 10C5 ways. I hope you're still with me, because we're at the final stretch.

Let's move on to dream's ender pearl trades. The known rate of a success is 4.73%, or .0473, the number of successes is 42, the total number of trials is 262. All of these are numbers from the 6 streams that happened after Dream's short speedrunning hiatus, or rates from the Minecraft wiki.

Try it yourself using a website that does it for you, like this first search result or anything else you can scrounge from the internet. If you have a graphing calculator, there's probably a built-in formula that does it for you. If not, you can still do it with the combinations formula, and the simple exponents.

The number is low. Very low. So low that the site I linked cannot find the significant digits. So low that the second search result gets a number of 0. This is not a mistake. The mod team has received this number in their own calculations.

But to be fair, we shouldn't be calculating the odds of getting *exactly* 42. We should be calculating the odds of getting 42 *or more* trades, since we're looking for the odds of getting Dream's luck or better. Doing this the long way is simple enough, if not tedious. We calculate the odds of getting 42 successes, then add it with the odds of getting 43 successes, and then 44... all the way up to 262 out of 262. Thankfully, there's another formula to do it for us. It's called Cumulative probability, and it does nothing but add up binomial theorems over and over again until a given value. If you have a graphing calculator, then it should be an option next to binomial probability. Otherwise, you can search up a site that does it for you like this.

The cumulative theorem starts at 0 and add binomial formulas until a given stop point. So in order to calculate the odds of getting Dream's luck or better, we just subtract 1 by the cumulative formula, since the odds of 100% minus the odds of getting 0 to 41 successes should get us 42 to 262 successes. All I'm doing is finding the *opposite* chance of something since it's easier to calculate. For example, for calculating odds of finding 1 or more heads out of 10 coin flips, it's easier to find the probability of getting 0 heads, and then subtracting with 1; rather than finding the chance of exactly 1 head, then exactly 2 heads, etc.

The number is still very grim. For reference, in AP stats we consider anything lower than a .05 chance to be statistically significant, although this is a random number. Other fields may field a different *p* value, as it is called.

Dream's chances for pearls alone are .00000000000565, a number which borders on completely improbable. My math is done via this Wolfram Alpha widget. Plug in X > 41, n as 262, and p as .0473. This number is incomparable to most real life scenarios, as most people have memed about. Could it happen? I suppose it could. The thing is with numbers of this scale, we can only conclude that either

congratulations, the odds have been beaten to an incomparable degree or

there was another factor that had been introduced that wasn't previously calculated, or any of these plugged in values were wrong. It's a simple matter to check all of the values via his streams and the value in the Minecraft wiki, with zero margins for error, so the values can't possibly be wrong. The only explanation is that something went wrong in this system because the probability of Dream's droprates is very significantly low. Either the Java random generator bugged out (unlikely, see Geosquare's video why this is not possible) or the drop rates had been changed.

Do zombie baby villagers with enchanted diamond armor and an iron sword on a chicken exist? Sure, by some fraction of some decimal with 34 trailing zeroes. The problem is that this sample size is large. 262 trials make this number incredibly difficult to replicate. For reference, getting 8 straight ender pearl trades is easier than Dream's odds. More samples make this number difficult to believe.

So that's the math. Now I'll explain why a "stopping rule" is not a valid way to throw out the binomial model. Thanks for reading if you got this far. I only want to get the numbers straight. I'm not informed on jar files, code editing, or anything else. Do comment if you have any questions or concerns about the numbers, I'd be happy to explain it.

—

The "stopping rule" is valid in cases where in any given trial, you "stop" on a success. This leads to the average trial having more "successes" than failures. This is best explained by, again, heads and tails. You succeed on a day when you flip heads, but you keep flipping on tails until you get heads.

Some days you'll get just one head. Great! But that would mean that you'd have runs where you get 100% heads, no? And that's not very accurate to the coin's 50-50 rates.

This is *supposed* to skew the data against Dream, because it unfavorably makes the odds worse for him, because there are "less trials" because the speedrunner stops trading after receiving their final success. The problem with this "stopping rule" is that it doesn't change the base chance of success. If you run this heads and tails simulation, you aren't going to magically have a more than 50% of head drops because you stopped on heads. The coin is still 50-50. You run the heads-stop, tails-keep going game for a month, and you'll see that about half of flips are still heads.

In the streams, piglin barters don't stop. Perhaps gold is not further traded for that particular run, but the ender pearl rate is still .0473. New runs are made regardless. On a personal best record, maybe on a run with 3 pearl drops out of 10 gold is earned, and Dream shuts off a stream after a good run. That doesn't change the fact that there are more streams to continue and the ender pearl drop rate is unchanged and will continue to be .0473. In the case of the last stream, unless he got ungodly luck on only the last run of the last stream would this "stopping rule" be implemented. And only then would the stopping rule apply. But this luck was consistent across all 6 streams.

Saying that the stopping rule is relevant is like saying that in our heads-stop tails-keep going example, the probabilities should be adjusted. Sure, maybe if we're looking at a single run *only*, where we could flip a single heads and call it a day. The rate of heads isn't 100%, after all. But when we look across literally *all* of the streams after his hiatus, stopping rule is being used inappropriately to change the data.

The six streams in question were all watched and tabulated after Dream's short hiatus. There was no specific stream the moderators picked and chose, but simply all of them. The added streams should not have been calculated in the result because you're changing the sample. Introducing new data in light of the improbable is misleading.

Even then, the stopping rule and added data went so far to decreasing the 11 leading zeros to... 7 leading zeros. For reference, statistically significant is still .05. 1 in 10 million odds is still unquestionably difficult. Someone has calculated already how many alternate universes it would take for every man, woman, and child playing a stream's worth of runs a day since Minecraft came out to attain his luck.

As for Dream's point that statistics are biased...

Yes, they're inherently biased. But most of this comes from data sampling. It's incredibly time and resource consuming to literally survey *everyone* in the world to see how much they like the newest brand of Coke. Or how much they like their current salary. Or how much pizza they eat on any given week. If someone isn't careful in how they pick and choose to study a small group in order to get a good survey explaining everyone, then this leads to skewed statistics.

We're not working with biased data sampling here. We have the time and resources to manually go through his streams and find the exact numbers. Statistics works based off the fact that we *don't* have easy numbers to just plug into equations. We *don't* know the percentage of the entire world who likes the newest brand of Coke. Or their salary. Or their pizza consumption. So we have to figure that out using the formulas at our disposal to find them, given unbiased sampling of the entire population.

This level of math is a practice problem in an AP Statistics class. It does not require college or university. We've been spoon-fed all the data nice and neat and all we have to do is plug in the information. There is no bias in math. Nobody can claim the numbers are wrong because of calculations, as Dream has mentioned multiple times. They are wrong because of how the data was taken. And as far as I know, everyone is on the same page with the same values given the streams and datamined values.

Now I'm incredibly disappointed, first and foremost. There are skeletons in everyone's closet. I have my own, and so do many. But please don't try to the basis of all facts by obfuscating the math. What happens when people use it to their own advantage, and there's no trust remaining in them? People lose faith in them, and go off uninformed opinions.

Maybe you don't agree with this side comment about the stopping rule and the added streams. That's fine. I just implore you all to do the math, and understand that there are some things which shouldn't be lied about, like math and facts which everything else relies on.

Edit: fixed links, cleared up some ambiguous syntax.

I'm challenging myself to make my girlfriend a midpoint calculator for her sewing class but having an issue with float()

Yang vs Tifa: An Examination and Critique. Also featuring DB Critique

So, as the title says, this will be an examination and critique of the episode Yang vs Tifa, and a bit of a critique on DB as a whole. Yes, this is an essay. A lengthy one. I put more effort into this than I did most of my college assignments, so get comfortable and bring some snacks. Enjoy it or don’t, either way is fine. I’m not expecting everyone to agree with me, but I think I bring up some valid points. This is by no means meant to be an exhaustive account, but instead my interpretation of the episode and DB as a series. Here we go!
DB has the honor and privilege of using characters from other franchises, representing them as they see fit to create their own show. Therefore, they should handle this privilege with reverence and responsibility. Because these characters mean so much to the fans and people that are invested in them. If they forego this obligation, I think it can be harmful, considering DB’s influence, reach, and popularity. Without the great amount of characters they have at their disposal, Death Battle wouldn’t be possible in the first place. So, misrepresenting and disrespecting them does the characters and fans of those characters, a great disservice. The characters are essentially the biggest component of Death Battle, so they deserve respect no matter what your personal opinion on them is.
As the leading authority in character debates (like it or not) I think most would agree it is important for DB to represent characters accurately and get the correct outcome as many times as possible. But why is this important you ask? It’s simple: to avoid fandom toxicity and backlash. The more correct outcomes they achieve, and the more thorough in their representations they are, the less likely fandoms are to display toxic behavior. As many people consider DB as the word of God and infallible experts of vs debates, it is important they have high standards in the matchups they choose, the research they perform, and conclusions they come to.
Nothing is worse when a fanbase thinks their character is somehow superior just because they defeated the losing character in a DB. And people rubbing the result in the face of the fan of the losing character is childish, demeaning, and disrespectful. DB plays a big part in the spawning of this type of behavior, and that is perhaps my biggest criticism towards the show. Yes, this type of behavior would still exist without DB, but DB magnifies it to a great extent and propagates it out into the world for large-scale consumption. Franchises, and fans of said franchises, that would coexist in peace, respect, and appreciation are suddenly at odds with one another, causing a rift to grow between them. DB, by its very nature, causes a lot of divisiveness and bitterness. I, myself, have bitterness towards certain franchises that I otherwise wouldn’t have because of DB. I think other people, whether or not they want to admit it, feel the same way. I created a poll some time ago, that asked if DB was more divisive or unifying, and the divisive option was chosen by a landslide.
DB, themselves, can mitigate this negative behavior, and I think it is their responsibility to do so. Accomplishing this by: Doing thorough, exhaustive research, and effective application of said research. Making sure there are no glaring holes in their argument when reaching a conclusion for the victorious character. DB researchers that spend weeks analyzing these characters shouldn’t have their research completely dismantled by someone who did research in a fraction of that time. They should hype up and give the losing character just as much love and attention to detail as the victorious character. They should assume their fanbase, the audience of DB, is intelligent and well informed. If someone from the community tries to refute their research and conclusions, they should be willing to engage in a conversation, and not belittle and laugh at them for reaching a different conclusion than they did, especially when that conclusion holds merit. Here is a big one: They should be willing to admit that they are wrong. I have never outrightly seen them admit that they were wrong about an episode. This is baffling because everyone makes mistakes. If they admitted that they were wrong, it would humanize them and make them more reputable. Admitting that they are wrong about an episode could potentially reduce fandom toxicity, because if the toxic fans realize that DB, the authority figure, can be wrong, then that could make the toxic fans realize that they can be wrong too. It can challenge their way of thinking. I truly believe that DB isn’t deliberately trying to make people angry and alienate fanbases, but at times, this is what happens when they make serious oversights.
I think most people would agree that they don’t mind if their preferred or favorite character loses the fight. I personally don’t mind either, as long as a few things are achieved: There isn’t some ulterior motive for the fight (ex. promoting one character at the expense of another), the fight is objective, the characters are represented accurately, they are researched thoroughly, and they aren’t degraded in the process. There are plenty of instances, where my favorite has lost, but they have met the above mentioned criteria. So, I wasn’t upset in the slightest. But there is one fight that stood out to me the most for not adhering to many, if any, of these criteria. This fight is Yang vs Tifa. In my opinion, the prime example of what not to do when creating a DB. Below is my “case study” of this DB.
Out of all the DB's, this is the only one that upsets me. That bitterness I mentioned? This is the one that caused it. To me, it felt more like an advertisement than a DB, and an unequal representation of franchises. There are several things I have against this DB, I'll explain them below.
Ok, so I said that this fight felt more like an advertisement than an actual fight. It felt disrespectful towards Tifa. I'll explain why. Ben and DB say that DB is a celebration of the characters, well it seemed like Yang was way more "celebrated" than Tifa was in this fight. Sure the fight took place Tifa's bar, the 7th Heaven, but she died brutally to a psychopathic Yang who would seemingly kill the entire staff just for a drink. I don’t watch RWBY, and never will, but I know enough about it to know that this isn’t how Yang would act. Tifa was mostly just a boob joke during her entire analysis. But to be fair, she did get her iconic wall pose, like the one in Advent Children, and she got to fade into the lifestream (FF7's afterlife) after her death. But that's literally all the references she had.
So let's see what Yang gets. She gets her own theme song during the fight (a great indicator of her eventual victory). She gets the superior 3D model. At least Yang's model somewhat resembled her as opposed to Tifa. Yang gets her original VA. She gets the superior character analysis, but I'll get to that later. She wears the "deal with it" glasses after her victory, which Yang's VA actress owns. This begs the question to deal with what? Were DB and RT already expecting backlash for this fight? And to top it all off, the banner promoting the tournament arc for RWBY season 3 unashamedly being on display after the fight's conclusion. There's even an interview with Yang and her voice actress sometime after the fight, gloating on how great Yang is as a character. Tifa gets no such treatment, nothing to celebrate her character. Nor does any other character for that matter, perhaps apart from Goku and Superman. Let’s be honest, if anyone deserves a little extra care in their treatment as characters it’s those two. Just like Chun Li made characters like Tifa possible, Tifa made characters like Yang possible. No admiration for that, no respect.
And now to address this whole RT and DB merger and bias argument. I think this episode coming out during the merger was more than a coincidence. There are just too many factors to suggest otherwise. For me, it seemed like a tryout of sorts. RT seeing how DB could represent their flagship product. A representation in the form of a DB that served as an advertisement. This whole DB is unbiased argument I see floating around is ridiculous. Everyone has bias towards something, to suggest that you don't is arrogant. I have bias, you have bias, the creators of DB have bias as well. But DB have something far more glaring than bias to alter the outcome of this fight, they had incentive. Ben and Chad never played FF7, so of course the proposition for more stability, better resources, and potentially better income from merging with RT would be more than tempting to let the RWBY character be displayed more favorably than Tifa, to which they have no attachment towards. Yes, there is the Weiss vs Mitsuru fight to serve as a counterargument of them not having bias. But just because there wasn’t bias in that one, doesn’t mean there wasn’t bias in Yang vs. Tifa. You can argue that there is bias in that one as well, as Weiss had, by far, the tamest death in the entire series. If anything, Mitsuru vs Weiss was a way to make up for the negative backlash they received from this fight. And don’t let Yang vs Tifa’s seemingly positive reception and like to dislike ratio fool you-- for those who can look below the surface, beyond the flashy kicks and punches, this result was egregious. The fight has aged poorly, and many people who were satisfied when it first came out have since changed their opinions.
Even on the DB Wiki it states that this fight was to commemorate RWBY's 3rd season. A lot of people say that started watching RWBY after this fight, but not me. I never watched RWBY because of this episode. They tried so hard to make Yang and RWBY seem like these awesome characters instead of letting them stand on their own merit, and that turned me off to RWBY entirely. In another reality, where DB didn’t use this episode as a promotional tool, I might’ve been a RWBY superfan. And Yang could have been one of my favorite characters, but like I stated before, now all I have is bitterness.
Tifa was Yang's biggest character design inspiration in terms of fighting style, and without Tifa, odds are Yang wouldn't exist in her current state, maybe not at all. Also, I've heard somewhere that Remnant was heavily inspired by the world of FF7. The mixture of magic with technology is very FF themed, and dust is very similar to materia. A magical substance put inside a weapon to enhance it? Sounds an awful lot like materia to me. Instead of celebrating Tifa, they just deconstructed her, in order to bring up Yang. Using the more established, popular character, to introduce a less popular one. Then have that less popular character defeat the popular one for clout and to display how much "better" this one is compared to the older one. I think RT just doesn't like the Tifa character. She lost this DB and her DBX when she should have won the first and was probably just killed out of spite for the second. Also, Miles Luna, the co-creator of RWBY called Tifa a prostitute. No, I'm not joking. If you're curious I can find it for you. There’s also another person, a head writer for RWBY who refers to Yang as his waifu. Do you think people who are so integral to RT’s biggest property—one who hates Tifa, and another who loves Yang to a strange level—are going to allow Yang to lose? And it’s not like RT is the biggest example of integrity. The company is infamous for the number of allegations and confirmed cases of inappropriate behavior leveled against it. So, what’s using a DB fight as promotional material when compared to that?
Now for the analysis and why I think this fight is incorrect. Told you this was going to be a long post. Thanks for staying with me thus far.
There are numerous holes all throughout this argument. I kind of feel sorry for it, it’s going to look like a pincushion after I’m done. Their research just felt lazy, and I find it difficult to believe that all the researchers unanimously agreed with this verdict.
They say Tifa's defense and speed are somewhat lacking. They say she's a glass canon. They say this, but they don't use anything to back it up. No actual math. It's just a vague statement based on gameplay stats that they briefly show. They just account for her stats, not the feats she’s been shown performing. It felt like vague statements to make it so they wouldn't actually have to research them. I find this strange, since they took so much effort into figuring out Yang's durability but not Tifas. Even though Tifa has took hits from Sephiroth and his remnants. And if you want to consider this canon or not, has actually taken a hit from a supernova. Even without the supernova feat, her durability is still greater than Yangs. They don't even mention any of this. And in terms of speed, she has been able to keep up with Sephiroth, his remnants, and the likes of Bahamut.
In the feats section of her analysis, they say she helped defeat Weapons, Sephiroth(which they spelled incorrectly btw), and can throw giant monsters like it's nothing. They even show her picking up the Emerald Weapon and throwing it. So, if they’re going to mention these feats, all of which are incredibly impressive, why not use them as evidence as to why she would win this fight? Throwing Weapons and mechs and defeating Sephiroth are all more impressive feats strength wise than her throwing Cloud fast enough to break the sound barrier. A feat, for some reason, they deem her greatest showing of strength, but when referencing the very feat section they gave to her, it is clearly not. Like what?
It seemed like they use gameplay stats only when it favors Yang. Like I said before, they use Tifa’s in game stats to say she is slow and weak defensively. But they won't use gameplay stats to account for Tifa's strength. Like the multipliers added to her strength when she uses her limit breaks. They don't account for that powerful strength increase when it could benefit Tifa, but account for her weak defense and slow speed, when it can be used against her. Totally feels like cherry picking. They did say her gloves give her a 7x strength increase, but didn't use that to account for her total power when using it with the Cloud sound barrier feat. And if you're going to say her weapons increase her strength output which is a gameplay mechanic, but you're not going to say that her limits increase her power, which is also a gameplay mechanic, how does that make any sense? It's very inconsistent, and again feels like cherry picking.
The FF7 guidebook states that her Final Heaven is similar in power to a nuke going off. The calculations from the power of her Cloud sound barrier feat, plus strongest weapon, plus the multiplier from her limit break, can corroborate and back up that Final Heaven does have nuclear-level striking capacity. But they fail to mention this, even though it is from a credible source and is line with her power output. But, in the Vergil vs Sephiroth fight, DB used the Crisis Core strategy guide to validate supernova, Sephiroth’s most powerful attack, but not Tifas Final Heaven. They could use that strategy guide to validate one feat, but not another strategy guide to validate another. Just seemed like another convenient omittance.
Now for materia. All combatants are supposed to be at their strongest in DB, but they just give Tifa ice and fire materia, two of the weakest and most basic materia in the game. I know its difficult to determine exactly which materia to use since there’s a lot of variability, but fire and ice is definitely not letting Tifa be at her strongest.
For this segment we’re going to apply the math that DB gives us, not the full gameplay feats, and scaling that would give her a conclusive edge. The pillar feat, and supposedly Yang's biggest durability is 1400 tons. That is a pretty definite calculation for Yangs durability. But as for Tifa's best display of strength, we're left in the dark. DB should have provided a definitive formula to calculate Tifa’s strength but they do not do this. We have to put the pieces together ourselves as the viewer. They say that Tifa's "best feat" of throwing Cloud to break the sound barrier is 153 tons. But they said that her Premium Heart gloves give her a strength boost of 7x which would put her strength output to 1071 tons. But they leave the viewer to make that connection for themselves, it isn’t clearly explained. This is to why, in my opinion, Yang has the better analysis.
Now for the inclusion, or should I say exclusion of limit breaks. They show Tifa performing her limit breaks and mention them in the rundown and feats sections, but they don't attribute any sort of power boost for them. Like I said before, if they're going to give her a strength multiplier for her gloves then they should for her limits as well. By DB's logic, since she doesn't show any type of strength similar to when she uses her limits outside of battle, then they don't count. Even though she's capable of throwing Cloud fast enough to break the sound barrier without them or any gloves, which is a very impressive feat showing she does have great natural strength. They said in her feats section that she can pick up giant monsters. Well, she performs this feat when she does her limit breaks. Limit breaks aren't just for show in the game, they actually have a purpose. Otherwise what's the point in their inclusion in the first place?
Her strongest limit break, Final Heaven, according to the FF7 guide book, increases her strength by 2.5x her normal output. This would give her a power output of 2,677 tons of force when combined with her Premium Heart gloves, nearly doubling Yangs durability threshold. Again, I guess they chose to not account for the power of limit breaks because it would totally change the outcome of the fight. And, like I mentioned before, if they use in game stats to highlight her weakness, then they should use them to highlight her strength. But they never did this. DB only used the stats they wanted when it was convenient for them.
Now to elaborate on the claim that Tifa shouldn’t be allowed to use her limit breaks to her full potential, that is, attribute any actual power toward them, because she can’t use them naturally. In canon, she learns these techniques from her teacher Zangan, so that she can use them when she needs them. Depriving her of her most powerful techniques is an absurd handicap. That’s the equivalent of not giving Yang her semblance/aura. They’re not a natural ability? How are they not? They’re perfectly fine with letting Sonic and Mario use their powerups, which are in no way natural for the characters, but do not let Tifa use her limit breaks which she gains from training and experience?
There’s also another important factor DB glossed over. Sephiroth. When determining how strong a character is, the most powerful opponent that character has faced should play a critical factor in determining their strength. You know Sephiroth, the guy who tried to absorb all of the planet’s energy for himself in order to become a god? The guy who overpowered Jenova’s will inside him, because he was stronger. For those who don’t know, Jenova is an alien like being who travels from planet to planet eradicating all life until moving on to the next one. And it is canon that Sephiroth is stronger than that. And yes, I know that Tifa didn’t defeat him by herself, but she did play a part. So if Sephiroth isn’t the best indicator of her power, then someone else is.
That someone is Loz, one of the three remnants of Sephiroth. Loz is the physical embodiment of Sephiroth’s strength. It is important to note that the remnants aren’t equal manifestations of Sephiroth’s power. As in, one’s strength and and specialties aren’t the same as another. Since Loz is the embodiment of Seph’s strength, then that obviously means he is the most potent in terms of physical prowess of the three. And Loz is the remnant who fought Tifa 1 v 1. Yes, Tifa did technically lose to Loz, but that is nothing to be ashamed of, and doesn’t diminish her capableness. She fought him while having to protect Marlene or without having any special weapons or materia. And, finally, she wasn’t at her peak when fighting. Tifa herself says that the crew have gotten rusty and aren’t as powerful as their OG FF7 counterparts.
But let’s talk about how strong Loz actually is. As determined by Sephiroth vs Vergil, Sephiroth has a striking force of 3.5 billion newtons, which translates to 393,415 tons of force. Yes, you read that number right. Feel free to translate it yourself. Since Loz is a physical manifestation of Sephiroth’s strength, that means Tifa is potentially tanking hits that are 281 times the strength of Yang’s durability. Even if you lowball it and say that Loz is literally 1/3 of Sephiroths power, that means Tifa is still taking 131,000 tons of force. So even if Yang could take Tifa’s power and use it against her, according to Tifa’s durability, she still wouldn’t be harmed. Yet, DB states that Tifa is a glass cannon. So what does that make Yang, exactly? A glass BB gun?
And do you know where DB calculated Sephiroth’s strength from? Crisis Core, a game that came out in 2007. Yet they didn’t even mention it in Tifa’s analysis for determining how strong and durable she is. Again, just felt like they were being sneaky and omitting sources for Tifa that could contribute to her victory.
Also, in Vergil vs Sephiroth, they state that Sephiroth tanked a 1600 ton strike from Cloud. He did so with one hand, and didn’t appear to be trying. So that would mean that 1600 tons is nowhere near Seph’s durability threshold, which would also mean it wouldn’t be close to Loz’s either. And Tifa is seen damaging Loz, so her normal strikes should be around that same 1600 ton range. And this is without any special weapons or limit multipliers.
Using the above mentioned Sephiroth and Loz discussion, I think it was a detriment to not give Tifa any scaling in this fight. Since they extracted her feats from very selective gameplay mechanics, they could have at least given her some scaling. If we scale her logically, she should be at least 1/3 of Sephiroths power. Since it took a party of three to take him out in the OG FF7 and, like I mentioned before, she holds her own with Loz, a remnant of Sephiroth, who is, you know 1/3 of Sephiroths power. Even scaling her close to Cloud is enough to take Yang out. As he can casually cut buildings in half. If they’re going to cherry pick gameplay stats like they did in her analysis, then she is shown to have the second highest strength stat behind Cloud, the dude who, again, can cut buildings in two.
I’m going to expand on the use of gameplay mechanics a little more. Do you know which characters get to use gameplay mechanics to compose their feats in their respective DB’s? Literally every other video game character up to that point besides Tifa. Knuckles gets to use gameplay mechanics. So does Donkey Kong, so does Link, so do does Zelda, so does Mario, Luigi, Tails, etc. You get my point. Every other video game character gets to keep their ridiculous feats, yet Tifa doesn’t. She literally picks up a monster the size of a building, twirls it in her hand, and throws it to the ground. Way more impressive than the Cloud sound barrier feat, but they limit her to Advent Children even though it isn’t technically her source material. They contradict themselves by putting feats like her picking up and throwing monsters in her feats section, but she doesn’t get to use them from that very same feat section they listed. And most of those characters I mentioned have animated shows as well as video games from which they are allowed to draw their feats from. But Tifa is exempt from that for some reason.
Without gameplay mechanics, and scaling all you leave her with is maybe 10-15 minutes total in Advent Children to where she is fighting and showing off feats that they deem appropriate to use to calculate her strength. Yet another severe handicap.
DB states that they primarily take characters’ feats form their source material, and every other source is used as supporting evidence if it aligns with the feats and power levels displayed within that source material. Well, guess what Tifa’s source material is for her? The original FF7. That means Advent Children is technically supporting evidence, but they decided to use AC to represent the feats they wanted her to have. Again, DB say they use characters when they are at their strongest. Well, OG FF7 is when she is at her strongest. Where she is at her max level, and isn’t rusty from time off not fighting. Where she has free reign to use the most powerful and useful materia, and where she uses limit breaks to decimate colossal monsters.
There are other DB’s that are incorrect, sure, but never has a DB been so incorrect and inconsistent that its own analysis can be used as supporting evidence to prove why it’s wrong. No complex calculations need to be performed, no lofty analysis. There are so many blaring holes, that it can dismantled in minutes, by using only a little bit of critical thinking. Now to summarize why the fight is incorrect. DB cherry picked the gameplay mechanics Tifa could use, gave her superior feats other than the Cloud sound barrier feat but don’t let her use them, gave her no scaling to the monsters, people, and threats she’s faced, deprived her of limit break power because they say it’s not a natural part of her arsenal even though they are, say she’s weak defensively and speed wise even though there is definitive supporting evidence to suggest otherwise, limiting her to the most basic of materia, and not using her true source material where she is at her most powerful.
And that pretty much concludes why this is my least favorite DB of all time. Felt like a huge conflict of interest and a disservice to Tifa. This post isn’t an indictment towards DB. There are some aspects that I greatly enjoy about DB, but that doesn’t mean it’s exempt from criticism. Helpful criticism is the only way something is going to improve. DB has improved considerably over the years, and I think they are more conscious about representing characters and franchises accurately. Feel free to add to the discussion. As for me, I’m going to keep trying to let this fight go, but I think a little bitterness will still always be there. For those who stuck around and read the entire thing, thank you.

ANSWERS TO ALL THE QUESTIONS THE MOD WILL ALLOW ABOUT DICK SIZE. Revised to adhere to the rules 100% Please stop taking my post down. I feel very discriminated against and like I'm trying to be silenced. To the detriment of all who could take something from it.😤👍🏼

Average means that the majority of men have the same size (5.1") or less in their pants. First of all, it's a scientific/mathematic term. It means, if we measure 10 people, and the numbers are: 4½", small 5", low avg 5⅛", scientific avg 5¼ slightly above avg 6" " *"Nice" *the start of an actual category 6⅛" nice 6½" nice 7" *Big *the start of an actual category. 7½" big *hits the avg cervix in a fully aroused female 10" way outside of average, and bigger than most men on the planet, abnormally long vaginas and ones that have been stretched consistently and regularly by a 10" or larger penis can take it all (this stretching takes time and patience but is possible). ....then we add those numbers up,(these numbers probably represent all who read this or atleast a close enough approximation) we get 63 as a total, we then, divide that number by the number of participants in the study group 63÷10= 6.3. Now, keep in mind that the 4½" guy brought the overall avg down, however the 10" brought the average "way" up ..... The actual average size of a human male penis is 5.1" this is slightly less than 5⅛"=(5.125) although you see slightly different numbers here or there, this is a pretty safe average. And you will never see it leave from inside a standard deviation. I wont explain standard deviations, but you can look at them as the left and right ends of a "category". Now in my personal and private life, I work with multiple sex shops in 2 states, and I design dildos. I won't give info on who or which ones.... just suffice it to say, there are people that dont know dick😉, and then there's me. I have more data,empirical,practical, hands on, and conversational, than anyone who will take time to explain to a customer base (the public). This can apply to all dicked, human beings but is written from the point of view shared with me by countless heterosexual women, some homosexual women that use dildos and/or strap ons for penetration, and multiple reliable studies where medical,or "women's health" professionals took the measurements and entered them into a database. I have both participated and done surveys, never with less than 10, but usually 100 to 10s of thousands of participants. I wont answer questions about that either due to privacy. But the numbers are accurate in all these studies, unless they breach the 6" barrier and really, the 5.5" barrier for an average. Once they break that invisible line, it means that a very small group, like ours☝🏽,was measured or that there are a majority of larger than average participants,like ours☝🏽, or both, like ours☝🏽. The low numbers in a study group will almost always be higher than the high numbers quantitatively. In our small group I took measurements from the penises on rate my cock, reddit. While the less endowed guys do show up, not nearly as many of them do as should, this creates a false narrative that says, "well 99% of guys I see on the internet are larger than me, and by this logic, I'm small😭". This is the furthest thing from the truth..... most average guys confuse average with small. They, in turn, dont post as much as guys that are more comfortable with their size. That, in turn, puts nearly every dick on rate my cock and sites like it at around +or- 7". This almost, artificially ofcourse, pushes the percieved avg up to 7". In fact most men that aren't afraid of talking to another man about dick size, sees atleast 7" as what a man needs. This is in no way true. But perception is often the law of the land... even if it's a myth based on incorrect assumptions and internet science. This, in turn, is repeated by women, who as a rule, and like most men in the millenial group, dont know how to use a measuring tape, let alone measure by eye, or estimate with any kind of accuracy. (If this doesn't apply to you and you are a woman or millennial, good for you. I'm a millennial, and I'm very good at measuring by eye, but most arent.) Because women dont typically know or care about measurements, they dont use them in practice, and they cant typically look down and accurately "appraise" the size of your penis.
Many men take advantage of this fact. They use trick photography to make a 6½"-7" dick look much bigger. With this, it all comes down to ratios. It has to be a certain girth range that meshes well with the length at certain angles. But it is very common and an expert, can usually spot it much easier than most that dont know dick😉.
These same guys and a few others take advantage of women's lack of measurement knowledge by telling them false measurements. Girl: " How big is it?" Dishonest guy: " 7".... and sometimes 7½"... Girl: Wow,( I read) that's pretty big...😀. Now this proverbial young lady is not that experienced, doesn't know how to read a tape measure, and finds the penis of her dishonest partner to be nice looking, and it looks like it might hurt a little or feel fan-fucking-tastic, she takes his word that, that is what a 7"-7½ dick looks like. She enjoys the sex and he enjoys the fact that she will brag to her friends about his 5½" dick, telling her girlfriends that its 7-7½". Then she sees a guy who is 5½" on the web, asking if he's enough to please a woman, she says I dont think so. That's 2" smaller than my bf, and while he's great, I've heard below that is trash"..... First of all this bitch is savage. Lol. But the guy shes talking to is the exact same size as her bf, but shes just cut his ass down like a slow samurai. And all based on misinformation. Many guys feel suicidal about their size. Propagating these myths about dick size is literally killing people. It's a quiet,but substantial problem. And one that the sex industry and insecure dishonest males is creating. Shame on them. And to all that read this and have considered suicide, please dont. Its definitely not worth it. Having a small penis is not a reason for self harm. If you dont think you can please a woman, try and see. You most likely will do fine. If you still fall a bit short there are sleeves and extensions that you can buy or order and have any dick size you want. Women are into you, not your dick. Now, you do need to please her sexually,as well. This is where novelty items come into play. Many guys are uncomfortable with dildos because they are worried that the dildo is going to steal their girl....😑. If an implement can steal your girl, you're probably a shitty guy and she just doesn't want you around anymore. If you're a good guy, size truly doesn't matter, but dont deny her the pleasures that you cant give her because of the cards you were dealt. Have a conversation. Communication or an unplanned couples visit to a sex shop is a good way to to make a good thing great. Dont limit her or you will lose her. Some women perfer to shop alone. If so, that's good, she needs to feel comfortable when buying something thats going inside her. Sex and partnership are separate but equal things in a woman's mind. 90+% is about how she feels. It's a mind game for them. For guys its 90+% about our dicks. That's a shame, but it's TRUE. If you dont understand that women are not like us in this way, you're probably not a very good lover. Again, communication is key. All the sex shops I work with, report that 5"-6" dildos are their top selling items when it comes to women. Gay men tend to buy bigger dildos. One reason for this is that the rectum is not as elastic as the vagina and tends to stay "roomier" much longer. Also, there is a natural larger capacity once you get past the anus, and pressure on the Pspot (prostate) is what causes the male anal orgasm. Another and more frequent reason, is the stigma and myths about small penises. Gay men are just as susceptible to falling for the bullshit line that porn, some novelties,and the internet propagate, and once they have stretched themselves out,and are looking for an actual dicked human being to have sex with, they often times feel like they do need bigger and bigger and bigger, until no human can fill that void. This is a small group of men and also women who are addicted, sometimes unhealthily so, to stretching their orifices. But they cause waves across all lines with their obsession with the "bigger is better" culture and propaganda. Half of "size queens" on both sides( male and female) are actually scared of "Big" dicks. Period. The other half was born with a larger than average canal( male and female),or have been continuously and regularly stretched and "worked out" by a guy or toy, with an abnormally large penis. Now all canals will eventually shrink back down near original size, or the size that best fits their partner, with rest and healing. For different people this happens at different rates. Some hours, some days, some weeks, and some months. Real size queens that do perfer larger penises are then cut in half again.... one half likes big dicks because that's all they've ever had. This is usually based on 1-2 guys. 1 long term relationship, or a girl that just happened up on 2 abnormally large dicks. It then seems logical that less dick is lesser. Not necessarily true, but once shes made up her mind, it is so. The other group are more experienced and or experimental, they are size queens, but if an average guy comes along that they want to ride into the sunset.... they do and they enjoy it and feel powerful while taking the whole thing without having to work up to it ,and if the guy ever makes them mad some of them will tell him how small his dick is compared to what she's had in the past, or will look for in the future. This is mainly to hurt you, and while some of it may be true, you have to ask yourself, "Is she saying this because I told her she had picked up some weight....🤔😑. A good woman will never cut down a good man for no reason. So if she does, one of you is probably an asshole. And people often times say hurtful things when they are upset. If she had sex with you more than once you fall in a category that women call "Fuckable " ("F"). As it has been explained to me, men do the 1-10 scale. Women do fuckable or not fuckable ("NF"). And that scale can be over laid on the following info. Tried and true confirmed by women without knowing the actual measurements(this cuts out the bias of hearsay and myths and propaganda) of dick shaped objects chart. [These are erect bp lengths] 1. Micropenis <2.75" 2. Tiny penis 3" the length of a finger 3. Small penis 4" usable, * ld point out here that many top selling toys are 4" insertable these are the ones that dont have a penis shape and tend to boast the ergonomic Gpot shape but not the length.... these are typically the ones that look like crab claws and are beloved by all who buy them. 4. Low avg penis 5"- literally this much shorter than "Average" ( lll ). This size is highly sought after in all the sex shops I work with. Most guys on the planet, and therefore most guys she's got access to are somewhere around here by sheer statistic probability. Women also choose based on how it looks like it will feel. 5" looks big enough for pleasure, without any pain. They have twice the amount of nerves down there than we do.... Mmmm or Ouch, is a much bigger deal for them than us. 5. "Nice" sized penis 6" this size is highly sought after in all the sex shops I work with. And women say ,"Nice", in this instance, like a guy would about a fish, a gun, or a car. Not a measly meh nice.... 6. "Big" penis is 7" . In reality, in a room of 1000(yes one thousand) random men, you're larger than the vast majority, 52 or so are projected to possibly be larger. When real data is looked at and studied, and blind test are done, nearly everyone that worries about size is worried about a non-issue. Copy and paste the site below for an accurate look at data found by one company with a slightly larger than usual "avg" but still inside the acceptable parameters of the standard deviation. Put in your length and girth and it instantly tells you where you stand in a room of 1000 "swinging dicks"👍🏼. If you dont know how to get the decimal value, its easy, use your calculator app by putting the fraction in and it gives you the decimal value. A kindergartener can do it. [Examples ] 1÷8 is the same as ⅛" and equals .125 ....¾"= .75 etc.... https://bl.ocks.org/abovethemean/raw/9395398/ Since I wrote the original article, I was contacted,privately by a man who has a 4½" penis. He and his wife both enjoy sex with one another and they have an open relationship as well. He doesn't feel in any way slighted by the data, or his open relationship. He has found someone to love and be loved. And he puts in the time and effort to make his partner happy. More men and women should follow his lead. Not groan and complain and put one another down....but educate, love, and be loved. Its not easy for anyone to find "The One", but if you dont have confidence through education, the odds are stacked against you. Self Acceptance, Confidence, Education and Memorable Execution of skills learned through education and communication, are the only things you need going forward. It's all women need you to have. If you didnt have it before reading this article, you do now. Or atleast a seed for self-acceptance and confidence and a lot clearer picture of the truth of dick size, contrary to all the misinformation and skewed internet science. Everytime you put someone down because of dick size, it hurts not only them, but whomever else it may concern. Unless someone is into SDH or SPH, a pointed or harsh word should never defile your lips. Its causing Suicide, Lack of confidence, despair, and Erectile Dysfunction (*some cases). Noone deserves that. Noone needs to lose a son or erection quality due to an adult internet bully. My reason for writing this article is because I nearly lost a friend who is 6.3" to suicide,because of this matter. We have to stop this silent killer. We have to stifle our tongues and use them for raising people up..... not cutting them down. You are responsible for your own words and actions and their consequences..... Someone who is in a constant state fear of rejection, feeling like they can never please a woman, despair, sleeplessness, constant negative bombardment, and being shit on all day every day by their peers, bullies, SPH people (who strangely don't mean any harm???), women that believe and buy into the prejudicial info that's out there and propagate it, May Not Be. If someone rejects you, they weren't for you. Move on with your head held high until you find the one that you will spend the rest of your life with. They are out there. Most people don't find them.... they settle. Some do, and it was worth the years of looking. Be her missing part....She will be yours. Good luck my friends. Good luck my brothers. Help me spread this message by liking it, commenting, crossposting it, or however you see fit, short of writing a book and plagiarizing my article...contact me for that😁👍🏼

Ndad abused me using mathematics - any similar experiences?

Struggling to understand this boolean algebra question.

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About the general probability for scoring that sweet relic that you want on a new banner in FFRK. This may be helpful for people who are having trouble deciding whether or not to pull on a banner... It also may make you want to think twice about ever spending money to summon on a normal banner...

tl;d(w)r: Don't spend money on Gacha games unless you are ready to be disappointed or break the bank to get what you want. The data below might also make it a bit easier for you to decide about what banners to pull on, and what banners to avoid.
\ahem**
I haven't seen this topic for a long time, so I thought it might be fun to do a probability breakdown of 11-pulls, and pose a question for any math whiz out there who might be able to clarify/confirm the actual chances of these things happening. I'm ready to make a fool out of myself on the internet once again, so here is my attempt to breakdown the chances of getting a specific relic on a banner. Even if these probabilities are not 100% accurate, hopefully it will illustrate the point I am out to set: Gacha games are evil and you should never, ever spend money on regular pulls.
Overview:
(1) I will be using the in-app rates published in accordance to Japanese Mobage law on the most recent Japanese banner (the one with Shadow's new Synchro). They are as follows:
Total Relics in Pool

Rarity	On Banner	Off Banner	Total
7-star	1	1	2
6-star	10	22	32
5-star	3	28	31
4-star	0	46	46
3-star	0	89	89
Total	14	186	200

Rates for all relics in Pool

Rarity	On Banner (per relic)	Off Banner (per relic)	Overall Pool Rate	Advertised Rates
7-star	1%	0.00078%	1.00078%	1.00078%
6-star	1%	0.00078%	10.01716%	10.01725%
5-star	1%	0.00078%	3.02184%	3.02196%
4-star	0%	0.54347%	24.99962%	25.00000%
3-star	0%	0.68494%	60.95966%	60.96000%

Note: I am assuming that the advertised rate is slightly different on the stipulation that DeNa calculated their overall rate based on a fraction rather than a percentage that was rounded to 5 decimal places. I will be basing the probabilities on DeNa's Advertised rates, as they are most likely more accurate. I don't know the rates for Global, but I assume they are pretty similar.

(2) I have no idea how to factor in the guaranteed 5 star or higher, as I have no idea when the game draws this relic. I would assume that the game is programmed as "if no 5-star or higher drops in one 11-pull, then another roll from a pool of only 5, 6, or 7-star relics will be performed and replace a relic of the lowest rarity". If the FIRST relic drawn is guaranteed to be a 5-star or higher, the probabilities of getting a certain relic will change slightly... Though I doubt it will make much of a difference. If anyone has any idea how this actually functions, please chime in.

(3) This will assume that 50 mythril = 11 pulls. Calculations will not be provided for 5 mythril single pulls or 15 mythril 3-pulls. 11 for the price of 10 means the rates will be slightly higher overall, but the difference should be negligible.

(4) I suck at math and am lazy, so I will be using this online probability calculator to derive the percentages. The section on the page titled "Probability of a Series of Events" allows you to input numbers for both drop rates and number of times you roll. I will be focusing on "Probability of A occurring", "Probability of B occurring", and "Probability of A, but not B occurring" unless otherwise noted.

Probability Breakdowns:
(1) General probability of any specific relic on this banner. (1% per relic, 11 times per pull)

Total pulls	Total Cost (Total Relics)	Probability
One 11-pull	50 mythril (11 relics)	10.466%
Two 11-pulls	100 mythril (22 relics)	19.837%
Three 11-pulls	150 mythril (33 relics)	28.227%
Ten 11-pulls	500 mythril (110 relics)	66.897%
Twenty 11-pulls	1,000 mythril (220 relics)	89.042%

Note: Since every relic on this banner has the same rate of dropping, this probability pertains to getting any specific relic on the banner whether it is a 5-star, 6-star, or 7-star.

(2) General probability of getting at least one of any 6 star or higher on this banner. (11% per relic, 11 times per pull)

Total Pulls	Total Cost (Total Relics)	Probability
One 11-pull	50 mythril (11 relics)	72.248%
Two 11-pulls	100 mythril (22 relics)	92.298%
Three 11-pulls	150 mythril (33 relics)	97.863%

(3) General probability of getting only one 5-star on the banner but not a 6 or 7-star. (3% per relic, 11 times per pull, and not 11% per relic, 11 times per pull)

Total Pulls	Probability
One 11-pull	7.901%
Two 11-pulls	0.624%
Three 11-pulls	0.049%

Note: I didn't know how to generate an accurate probability for more than one pull, so I took the probability derived from one roll and used that percentage with "Probability of A Occurring x Time(s)" for consecutive pulls.

(4) General probability of getting no 5, 6, or 7-star relics out of all relics in the pool, initiating a guaranteed relic pull. (14.04% for a 5, 6, or 7-star relic, 11 times per pull)

Total Pulls	Probability
One 11-pull	18.935%
Two 11-pulls	3.585%
Three 11-pulls	0.679%

Note: In this case, A = 85.96% and B = 14.04%, so the chance of NOT getting B, but getting A will yield the probability in question. Same factors were applied from point 3 to derive rates for more than one 11-pull.

(5) General probability of getting any relic of a specific rarity in a guaranteed 5-star or higher pull. (65 relics total, 14 on-banner, 51 off-banner)

Rarity	On-banner relic	Off-banner relic
7-star	7.123%	0.006%
6-star	71.226%	0.122%
5-star	21.368%	0.156%

Note: With 14 relics @ 1% chance (14\1 = 14), and 51 relics @ 0.00078% chance (51*0.00078 = 0.03978), the overall weighted percentage for each relic would be (14/14.03978) for relics on the banner, and (0.03978/14.03978) for relics not on the banner. I'm not really confident that I've gone about this the right way, but it was the best my feeble brain could think up.*

(6) I really like Shadow. Should I pull on this banner in hopes to get one of his new relics? Shadow has 5 relics on this banner, 3 of which I want.

Total Pulls	Probability of Getting a Shadow Relic	Probability of Getting a Relic I Want	Probability of Not Getting a Relic I Want
One 11-pull	43.120%	28.470%	71.530%
Two 11-pulls	67.647%	48.834%	51.166%
Three 11-pulls	81.597%	63.401%	36.599%

Note: Going all-in for me would be three pulls, and I really don't want to blow all my mythril right now... So I'll stop there.

Overall Noteworthy Conclusions
(1)
Chances of landing one specific relic on the banner are extremely small. Even after ten 11-pulls the chance is just a little more than a coin toss.

When considering whether to pull or not on a banner, if there is only one relic you want/need, you should ALWAYS skip it. The odds are just way too low to make it worth it.
This is especially important to keep in mind for Synchros, or banners with only one AASB on them. Sure, that new relic looks shiny, but 9 times out of 10 you won't get it after one pull.
Think of how amazing your luck was if you actually did land one in a single 11-pull, or better yet, on a 5-mythril pull! Relish these moments even more now that you know JUST HOW RARE they are.

(2)
Chances of you getting at least one 6-star or higher are very strong now that the banners are featuring more high rarity relics.

Conversely, getting a 5-star to drop is considerably more difficult now with this distribution. Most people will see this as a blessing, but if you have your aims set on a specific legend materia, good luck...

(3)
Good news, having only a single 5-star drop on a banner is incredibly low!

Bad news, this probably happened to you anyway. Better luck next time!

(4)
Chances of getting NO 5-star or higher equipment is still surprisingly high with the banners. However, not really high enough to statistically pose a threat if you do more than one pull.

Really makes me wonder if this "Guaranteed 5-star or higher" tag is significant overall... Is it better, sure, but it may not be as relevant as it seems.

(5)
If you get an off-banner relic... Seriously, just laugh about it. The odds are so small that it is seriously worth a guffaw.

Continuing from my point from 4), is this really as good as it seems (or even beneficial), from a probability sense? If anyone knows how to factor in the guaranteed relic draw, we could better shed light to this question. I'm still feeling like the guaranteed 5-star or higher, or guaranteed two 5-stars or higher are not as beneficial as they may seem...

(6)
If I blow all 150 mythril I have right now, I still have a sizable chance of not getting even one of the relics I want. Annnd I really didn't want to pull more than once anyway... :<<<

Sorry Shadow - you rule and those relics look super sweet, but I have to pass this time around. ;___; RIP ;____;

Anyway, I looked into this specifically to help myself decide whether or not to pull on Shadow's new banner. This helped me understand that even getting one of the relics that I wanted would not be worth the cost. However, if you follow this train of thought, you probably won't pull on anything but Fest banners... I'm a believer that this is the way to go anyway, but... A cheeky pull every now and again won't break anyone. ;) Just don't blow it all on one non-fest banner... Your chances of getting better stuff down the road go down every pull you make. :D :D :D

I've just released my bet tracker with a lot of features

The most common types of football bets

(CH2) The whole transcendance mechanic needs to be cleaned up, plus RNG issues. Again.

Demystifying Memory Overclocking on Ryzen: OC Guidelines and Explaining Subtimings, Resistances, Voltages, and More!

Edit: thanks to RaptaGzus, spikepwnz, darkomax, dragontamer5788, sillyvalleyserf. New section and updated several timings. I don’t have enough characters!
This post by Mrfrizzl and this post inspired me to write a guide on what the different timings, resistances, voltages, and other memory settings on Ryzen do, and to detail how and when to change them.
That means this post is really long, as I will cover basically every setting in Ryzen DRAM Calculator and Ryzen Timing Checker. I would add more, but I’m at the character limit ¯\_(ツ)_/¯. I’ll be discussing DRAM somewhat technically, so if you only want high frequency and tight timings, I included my personal method for tightening all timings.

Contents:

Introduction
My Methodology
TL;DR of DRAM
Primary Timings
Secondary Timings
Tertiary Timings
Impedances & CAD_BUS Setup
Voltages
Other (Important!) Memory Overclocking Features

Introduction:
I constantly see questions about Ryzen memory overclocking on this subreddit. Many commenters say, “Just put in the values from Ryzen DRAM Calculator, it just works!!!”, but for some people this doesn’t work, and others are left curious as to why it works. What do all those settings...do? There should be lots of data out there explaining what the values mean, right? Well a guide like this one may already exist...Ryzen’s been out for a while, and there’s an active Ryzen memory overclocking community...but I’ve never seen it. A lot of this information is out there, sure, but not all in one place, and not necessarily in places that are easy to find!
Like others on this sub, when I was overclocking my own memory a couple of months ago, I had a lot of trouble finding any detailed, comprehensive sources for this information. I tried googling all the timings, and often I was met with ancient, useless threads. I want to keep others from struggling like I did, and I want to share what I’ve found so that there’s at least one decent post out there.
(With that said, I will not really cover die-specifics, for that go that here)
Disclaimer: I’m NOT the most knowledgeable person for this, and (most of) my information comes from

my own findings from overclocking every timing on my kit (TLRED416G3000HC16CDC01)
my BIOS’s timing descriptions
browsing many forum threads for anecdotes/data from other Ryzen owners
official blog posts from AMD
publicly available DDR data sheets

Also, there are several thing I have not tested myself, and of course this is overclocking so YMMV.
Any input or corrections would be GREATLY appreciated if I made any mistakes. I don’t want to spread misinformation!

If you just want to make the numbers smaller, here’s my personal Ryzen memory overclocking method (though I'd still recommend reading this!). It’s adapted from this chart accompanying DRAM Calculator, but changed to essentially redo some steps so you find your kit’s sweet spot. It's imperfect, and the calculator presets bad timings on some dies. However, my approach should mitigate this, since it doesn’t rely on these values and involves changing every timing one by one instead of hoping the calculator just works. (Fair warning though, this process is very time-consuming, depending on your stress test/how much you tighten timings at a time.)

TL;DR of DRAM: a bunch of arrays, or banks, of tiny capacitors. Every bit of data, or address, is just a capacitor that’s 1 or 0.
Sidenote: “Bank” isn’t well-standardized but it’s used to refer to either a layer of a memory die or a logical unit of organization as determined by your memory controller that can be spread across multiple dies.
[Paraphrase of dragontamer5788] Unfortunately, one issue with DRAM is that reading cells destroys their data, so for all reads and writes, data must be copied into circuits called sense amplifiers (“Opening a Row”), where it can be read (“Column Read”) and written to (“Column Write”) safely. To read a new row, the sense amplifiers must copy the data back where it came from (“Precharge”).
For more check this article out.

For the following: some of these settings can only be changed on high-end motherboards, while others cannot be manually changed. If I can not verify information, I’ll make a note. Also, there’s a few things that you probably won’t ever need to change, but they exist.

First: what do primary timings do? How do they impact memory performance? (There’s plenty of information on these out there, but just so we’re on the same page...)
tCL: Column Access Strobe (CAS) Latency, the delay in clock cycles between when the IMC activates a column of memory for reading and when the address in the column is actually read. Essentially, this is how fast the sense amplifiers work. This is supposedly the most important timing because the CAS, i.e. the strobe capacitor, activates last (kinda), and so only when that happens can data be read. Thus lower tCL means less cycles between when the CPU asks for data and the data is actually read.
Overclocking guidelines? : Go as low as your kit allows, balancing high frequency with low true CAS latency (tCL / frequency in GHz) to optimize bandwidth with latency.

tRCDWR: Row Address Strobe (RAS) to Column Address Strobe (CAS) Delay (Write). The delay between when a row address is activated and when a column address is activated for writing. This is how fast data from the RAM transfers to the sense amplifiers. The reason for why this timing is important is pretty similar to tCL: it’s the amount of cycles between when a row is activated and when a column is activated, so lower tRCDWR means less delay before writes.
Overclocking guidelines? : Same as above.

tRCDRD: RAS to CAS Delay (Read). The delay between when a row address is activated and when a column address is activated for reading. Basically tRCDWR but for read operations.
Overclocking guidelines? : Same as above.

tRP: Row Precharge Time. The amount of time it takes to deactivate (precharge) one row of memory and activate a new row of memory (on the same rank). This is how fast data is transferred from sense amplifiers back to the cells. You can think of this as essentially the “cooldown” between memory operations on the same rank, or side, of a DIMM. (Sidenote: it’s not necessary true that rank = side, especially for 4 or more DIMMs. If you’re interested, here’s buildzoid’s video about memory ranks).
Overclocking guidelines? : Same as above.

tRAS: RAS Active Time. The minimum time between a row of memory being activated and precharged. This is the amount of cycles that a row of memory can be accessed for reading/writing. Just like the name suggests, it’s how long the RAS capacitor stays active once it receives a signal from the IMC.
Overclocking guidelines? : Hearsay says that a good starting point is something near tCL + tRP. The specific value you can reach depends on the die. For example, a Micron B-die kit like mine can run tRAS very tight. I have it set to 21 (lower than tCL + tRP = 28), the lowest my BIOS allows.

CR: Command Rate. The amount of consecutive clock cycles that commands must be sent to the DRAM to ensure that the command is executed. If this is 1T, the IMC sends each command the memory once; if it’s 2T, then the IMC sends each command twice in a row. Thus, it should be pretty intuitive that a command rate of 2T can help OC stability: if there is any kind of issue with the memory not receiving/executing the command sent in the first signal, it has a second chance.
Overclocking guidelines? : Set to 1T ideally, but 2T may improve stability, especially with 4 or more DIMMs. As a sidenote, AMD recommends disabling Geardown Mode (covered later) for 1T.

Now for the secondary timings. Unfortunately I don’t have as much information on them as I do for primary timings, but it is still enough to understand what they do.
tRC: Row Cycle Time. The minimum amount of time between activation commands to the same memory bank. Just like the name suggests, this is the amount of cycles that the IMC has to wait before it can send another activation signal to a bank of memory.
Overclocking guidelines? : By definition, the lowest this can go is tRAS + tRP. The reason is as follows: tRAS is the number of cycles from activation to precharging, and tRP is the number of cycles between precharging and the activation of another row. Thus, tRAS + tRP is the number of cycles between activating one row of memory and activating another. If you’ll think back one paragraph, that’s exactly what tRC is for.

tRCPage: Page Time Line Period. EDIT: As mentioned in this patent, is the number of activate commands that can be sent to a row within a predetermined window of time.
Overclocking guidelines? : This timing defaults to 0 in my BIOS, so it’s probably not worth changing.

tRRDS: RAS to RAS Delay, Different Bank Group. The delay between two row activations across different bank groups. Once a row is activated in one bank group, the IMC has to wait this many cycles before a row can be activated in another bank group.
Overclocking guidelines? : On my kit this timing went as low as my BIOS allows (4), but this may not be true for other kits.

tRRDL: RAS to RAS Delay, Same Bank Group. The delay between two row activations within one bank group. As you probably can guess, this is the same as tRRDS, but regarding a single bank group instead of multiple bank groups.
Overclocking guidelines? : On my kit this timing went as low as my BIOS allows (4), but this may not be true for other kits.

tFAW: Four Activate Window. The amount of time in which four row activations can occur within the same rank. Pretty self explanatory, if the IMC needs to access four different rows of memory within one rank of a DIMM, it will take tFAW cycles to do so.
Overclocking guidelines? : This timing isn’t hearsay! According to AMD, the minimum for this timing is 4 * tRRDS (lower actually does nothing), but if that isn’t stable, it may be worth trying 5 * tRRDS, 8 * tRRDS, or higher.

tFAWDLR: All I know is that it’s related to tFAW.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

tFAWSLR: See tFAWDLR.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

tWTRS: Write to Read Delay, Different Bank Group. The delay between a successful write command and a read command across different bank groups. Once a write command has been finished on a memory address, this is the amount of cycles before a read command can be executed on a row in a different bank group.
Overclocking guidelines? : On my kit this bottomed out at the lowest value my BIOS allows (2), but this may not be true for other kits.

tWTRL: Write to Read Delay, Same Bank Group. The delay between a successful write command and a read command within one bank group. Just like with tRRDS and tRRDL, the only difference between this and tWTRS is which bank groups are involved.
Overclocking guidelines? : On my kit this bottomed out at the lowest value my BIOS allows (7), but this may not be true for other kits.

tWR: Write Recovery Time. The delay between a successful write command and the active bank being precharged. Once a write command to a memory address has finished, it takes this many cycles before the bank (not just the row) containing that address is deactivated.
Overclocking guidelines? : Hearsay says to try setting this to tRAS - tRCD, but my kit went lower; even values should be more stable as well. According to AMD, the lowest this should be set to is 8, as any lower will cause data corruption.
Now the next 8 are all very similar, but have some slight differences between them, so I’ll format this differently.

tRDRD _ _ (_): Read to Read Delay. The delay between two read commands. Self explanatory, the number of cycles that must pass after the IMC sends a read command before it can send another. There are 4 variants of this:
tRDRDSC: tRDRD, Different Bank Group. Involves two rows in different bank groups.
tRDRDSCL: tRDRD, Same Bank Group. Involves two rows within one bank group. This one is notable as it has a large impact on bandwidth.
tRDRDSD: tRDRD, Different Rank. Involves two rows in different ranks of a DIMM.
tRDRDDD: tRDRD, Different DIMM. Involves two rows on different DIMMs.
Overclocking guidelines? : From what I’ve heard these should all go down to 1 or 2 on most kits; on my kit these all are stable at 1. However, tRDRDSCL does not need to go this low, especially at higher frequencies, where lowering it past a certain value (even as high as 4 or 5) may bring no tangible gains nor impact stability.

tWRWR _ _ (_): Write to Write Delay. The delay between two write commands. Think tRDRD but with two write commands instead of two reads. Again, there are 4 variants:
tWRWRSC: tWRWR, Different Bank Group. Involves two rows in different bank groups.
tWRWRSCL: tWRWR, Same Bank Group. Involves two rows within one bank group. This one is notable as it has a large impact on bandwidth, like tRDRDSCL.
tWRWRSD: tWRWR, Different Rank. Involves two rows in different ranks of a DIMM.
tWRWRDD: tWRWR, Different DIMM. Involves two rows on different DIMMs.
Overclocking guidelines? : See tRDRD set.

Returning to previous formatting, here are the last 6 secondary timings:
tRFC: Refresh Cycle Time. The amount of time between a refresh command and an activation command being executed by the DRAM. Refresh commands are what make DRAM special, and are when a section of memory is read and then the data there immediately rewritten to the same addresses. Refreshing a section of memory prevents it from being physically lost by way of leakage. Anyway, this is the amount of cycles after a refresh command has been issued before a row of (that section of?) the memory can be read again.
Overclocking guidelines? : Hearsay says to start by setting this to around 8 * tRC or 8 * tRC + 8. (4 * tRC applies to DDR3 only). Use the true latency of tRC for this calculation for accuracy's sake (i.e. convert tRC to ns, calculate tRFC, convert back to timing).

tCWL: CAS Write Latency. The delay between when the IMC activates a column of memory and when a write command is executed. Although not in the timing abbreviation, tCL specifically controls read operations; this timing, then, is just tCL but for write operations. (I’m not sure why it’s not as important as tCL...) According to AMD, this timing greatly impacts stability, which again makes sense, as it is related to the famous tCL.
Overclocking guidelines? : According to the previously linked AMD “Let’s Talk DRAM!” post, tCWL should be set to tCL or tCL - 1, and is much more stable at even values. My kit has this stable as low as 10 (with CL13), but any lower absolutely refused to POST.

tRTP: Read to Precharge Delay. The delay between a read command and a row precharge in the same rank. This is the minimum amount of cycles between a row of memory being read and a different row in the same memory rank being deactivated.
Overclocking guidelines? : Go as low as you can.

tRDWR: Read Write Command Spacing. The amount of turn-around clocks between a read command and a write command on the same rank. I’m not entirely sure what a turn-around clock is, but I believe it refers to tRDRD/WRWR timings. Anyway, this is the amount of those cycles that must pass after a read command is sent to a memory address before the IMC can send a write command to a different address on the same rank of a DIMM. According to AMD this timing has a large effect on throughput.
Overclocking guidelines? : According to some users (and myself), this timing is somewhat tied to tWRRD, in that only one of the two can be set to a very low value, while the other must be set to a higher value. One approach to tightening these two timings is to set one to auto, lower one all the way, and then take the other off auto and manually tighten it.

tWRRD: Write Read Command Spacing. The amount of turn-around clocks between a write command and a read command on the same rank. This is basically tRDWR, but after a write command and before a read command instead of vice versa. According to AMD this timing has a large effect on throughput.
Overclocking guidelines? : See tRDWR.

tCKE: Clock Enable Time. The minimum amount of time it takes for a CKE pulse to occur. This one is one of the more technically involved timings here, so I may not have this exactly correct. From what I can tell, a CKE pulse changes a DIMM’s power state. There are two kinds: CKE LOW and CKE HIGH. CKE LOW causes the DIMM to enter powerdown mode for the duration of a clock cycle, while CKE HIGH causes the DIMM to exit powerdown mode for the rest of a cycle. CKE LOW prevents the memory from receiving unwanted commands (i.e. puts it in an idle state), whereas CKE HIGH allows the memory to receive all commands from the IMC (i.e. puts it in an active state).
Overclocking guidelines? : According to at least one overclock.net user, lowering tCKE allows for further tightening of some timings, although that needs testing and data for verification. I could only lower this timing slightly before my system stopped POSTing.

tRPPB: Row Precharge Time, Per-Bank/Single Bank. I believe this is the minimum amount of time between a row of memory being precharged and another row in the same bank being available for reading. It may be the number of extra cycles in addition to tRP that must pass between two row precharges, though I’m not sure, since the sources I found only discuss this in regard to LPDRAM. For LPDRAM, the data sheets I found say tRC = tRAS + tRPPB. However I don’t know that that applies to SDRAM.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

tRCPB: Row Cycle Time, Per-Bank/Single Bank. I couldn’t find anything whatsoever on Google, so this name is only an inference based on my findings for tRPPB. I presume this is also something related to LPDRAM specifically.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

tRRDDLR: I have no idea.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

tRDRDBAN: Read to Read Timing Ban. Once a CAS has been activated for a read operation, the CAS is banned (i.e. blocked) from receiving another read activation signal until a certain number of cycles (corresponding to the Ban #) has passed. The different settings are as follows:
Ban 0 - no ban, control of signal traffic done by tRDRDSDSC, tRDRDSDDC, and tRDRDDD.
Ban 1 - bans tRDRD for one clock cycles.
Ban 2 - bans tRDRD for two clock cycles.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to Ban 2 for me.

tRDRDSCDLR: I have no idea.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

tWRWRBAN: Write to Write Timing Ban. Basically tRDRDBAN, but regarding write operations.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to Ban 2 for me.

tWRWRSCDLR: I have no idea.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

tWRRDSCDLR: I have no idea.
Overclocking guidelines? : Cannot be changed in BIOS, and is locked to 0 for me.

Now for tertiary timings. I had great difficulty finding anything on these, with the exception of tREF. I can’t change any of them in my BIOS, so no overclocking guidelines here. This is exclusively for those curious about what these timings are called/do. I’d appreciate input if anybody knows anything about these timings.

tREF: Refresh Time. The amount of cycles between memory refreshes. Self explanatory. The higher this is, the more cycles between refresh command executions, i.e. the data is guaranteed to be stored for longer, but at the risk of degradation.
tMOD: MRS (Mode Register Set) Command to Non-MRS Command Delay. From what I can understand, DRAM modules contain a section of memory called the mode register, and it seems to have something to do with power states. At the very least, this timing seems to be related to tCKE, ProcODT, and RTT_NOM. To be more specific, it appears that the CKE state (LOW/HIGH) will only change if certain parameters are satisfied for at least tMOD + tMRD clock cycles.
tMODPDA: MRS (Mode Register Set) Command to Non-MRS Command Delay, Per DRAM Addressability Mode. Same as above regarding tMOD. Per DRAM Addressability Mode, or PDA, seems to save a single MRS value across a DIMM, which seems to have something to do with preventing data degradation.
tMRD: Mode Register Set Command Cycle Time. See tMOD.
tMRDPDA: Mode Register Set Command Cycle Time, Per DRAM Addressability Mode. See tMODPDA.
tSTAG: Subrefresh Staggering Delay. Seems to be related to tREF, in that it involves staggering memory refresh commands to minimize the amount of memory addresses that are being refreshed at any given moment.
tSTAGLR: It’s obviously related to tSTAG somehow, that’s all I know. It’s disabled for me, which may suggest it’s some kind of offset.
tPHYWRD: I believe this is related to a digital-to-analog microcontroller called a PHY chip found in the Ryzen SoC. This timing also appears to be related to writes.
tPHYWRL: Same as above.
tPHYRDL: Same as the two above, but related to reads.
tRDDATA: Probably related to data...wow.
tWRMPR: I have no idea.
[The aforementioned “Let’s Talk DRAM!” post mentions a couple other timings, namely tMAW and tMAC, but Ryzen Timing Checker only shows the ones above to me. My research also shows that there’s some other obscure timings, but they’re all very technically involved and you can’t change them anyway, so I don’t feel the need to spend my time deciphering those].

That’s all the timings! Now for the termination resistances/impedances (as well as a couple timings related to one set of them). In general you should need to change these only when you’re having serious issues getting a certain frequency/set of timings stable. For example: not POSTing, instant BSODs, or constant memory errors.
Termination Resistances:
ProcODT: Processor On-Die Termination Impedance. The resistance which a memory signal travelling to the CPU terminates at. This reduces signal noise and lowers how much the signal over- and undershoots the voltage that the signal should be sent at. From what I understand, going too low can allow signal noise to send faulty signals to the memory, but going too high can actually cause a signal to be absorbed and not reach the processor. This defaults to 53.3Ω.
Overclocking guidelines? : This is probably the most important value to change in this section to improve overclock stability. Notice I only said change, as it is generally accepted that RAM kits have different “preferences” for this value; that is, higher is not necessarily better. The overclocking community recommends keeping this in the range of 40Ω-80Ω, while AMD recommends 60Ω-96Ω. (However, for values of at least 80Ω, you should ensure that your memory is receiving some airflow.) As a rule of thumb, dual rank memory requires this value to be higher than single rank memory, but this does not mean that single rank memory cannot benefit from higher values.

RTT_PARK: Park On-Die Termination Impedance. The resistance at which signals sent to a memory die will terminate when ODT is low. I believe this is related to CKE LOW/Powerdown Mode. From what I can decipher, when RTT_NOM is disabled/off, this value seems to take over. This resistance can help prevent signal integrity loss to dies in which the memory is not executing write commands. The values for this are measured in terms of fractions of RZQ, which is a reference 240Ω resistor.
Overclocking guidelines? : To be honest I’m not really sure exactly how to tune this, but theoretically (and as corroborated by Ryzen DRAM Calculator) a higher value for this may be necessary to stabilize an overclock, as it should help signal integrity. However, like with ProcODT, too high of a resistance probably causes instability by way of signal absorption. Furthermore, several users have reported lower values working better. According to one Micron data sheet, this should be disabled for single-rank DIMMs and enabled for dual-rank DIMMs, but I have not tested this myself.

RTT_NOM: Nominal On-Die Termination Impedance. For high ODT, this is the termination resistance for signals sent to a memory die not being written to, but which is connected to one that is being written to. I believe this is related to CKE HIGH pulses. This resistance can help prevent signal integrity loss when the memory is not executing write commands. The values for this are also measured in terms of fractions of RZQ.
Overclocking guidelines? : See RTT_PARK.

RTT_WR: Dynamic/Write On-Die Termination Impedance. This is the resistance at which signals sending write commands to a memory die will terminate at. This resistance can help prevent signal integrity loss when the memory is executing write commands. The values for this are also measured in terms of fractions of RZQ.
Overclocking guidelines? : Like the previous two I don’t personally know how to tune these, and simply used DRAM Calculator values, but in theory higher can improve stability. Though again, several users have reported lower values working better. The aforementioned data sheet says that memory rank does not impact whether this should be enabled or disabled, so changing this may be purely trial and error and something of a matter of kit “preference.”

CAD_BUS Resistances:
ClkDrv or CLKDrvStr(en): Clock Drive Strength/Impedance. The resistance on the MEMCLK (memory clock) drive pins on the CPU (or memory controller?). This adjusts the strength of the signal that controls memory clock. I believe this should have some effect on stabilizing memory frequency, and theoretically higher values may improve signal quality to the corresponding pin.
Overclocking guidelines? : The minimum value of 20Ω is recommended, but higher settings (to a point) may aid in stability.

AddrCmdDrv or AddrCmdDrvStr(en): Address/Command Drive Strength/Impedance. The resistance on the following CPU (or memory controller?) pins: address, RAS, CAS, WE, bank, parity. Theoretically, then, raising it can increase stability of tight timings. However, I have not tested that specifically.
Overclocking guidelines? : See ClkDrv.

CsOdtDrv or CsOdtDrvStr(en): Chip Select/On Die Termination Drive Strength/Impedance. The resistance on the CS and ODT pins on the CPU (or memory controller?). This adjusts the strength of the signals controlling Chip Select (which is self explanatory) and ODT (which in this context is related to CKE and DRAM powerdown state). As before, raising might be helpful, but isn’t necessarily.
Overclocking guidelines? : See ClkDrv.

CkeDrv or CKEDrvStr(en): CKE (Clock Enable) Drive Strength/Impedance. The resistance on the CKE pins on the CPU (or memory controller?). This adjusts the strength of the CKE signal, which I discussed previously. As before, raising might be helpful, but isn’t necessarily.
Overclocking guidelines? : See ClkDrv.

CAD_BUS Timings:
AddrCmd(Setup): Address/Command Setup Time. The setup time for the address and command pins of the CPU (or memory controller?) with respect to a memory clock. Essentially, this prepares the address and command pins a fraction of a memory clock before a read or write command must be sent. If set to 0, then the pins will set up 1/2 of a clock before the command is sent for CR=1T or 1 1/2 clocks before the command is sent for CR=2T. If set to 1, the number of clock cycles for setup will equal your command rate.
Overclocking guidelines? : You shouldn’t need to change this, and should leave at 0 ideally, but 1 might improve stability. However, I have not tested this myself.

CsOdt(Setup): CS/ODT Setup Time. The setup time for the CS and ODT pins of the CPU (or memory controller?) with respect to a memory clock. If set to 0, the pins will set up 1/2 of a clock before a read or write command is sent. If set to 1, they will set up 1 clock before.
Overclocking guidelines? : See AddrCmd(Setup).

Cke(Setup): CKE Setup Time. The setup time for the CKE pins of the CPU (or memory controller?) with respect to a memory clock. See CsOdt(Setup) for behavior.
Overclocking guidelines? : See AddrCmd(Setup).

Now if you’re still with me after all of that, let’s talk about what the different voltages do. For the sake of completeness I will include the trivial ones as well (VDIMM and VSOC). Most of these I cannot change in my BIOS, so I don’t have any personal information on the non-trivial ones.
VDIMM: DRAM Voltage. The voltage fed directly to your memory through the memory VRM. Different memory kits scale with VDIMM differently, so depending on your die this will impact memory stability differently.
Overclocking guidelines? : It is generally accepted that this can go as high as 1.45V or 1.5V, but some kits do not need/like it so high. See the overclocking DDR4 guide for more information.

VSOC: System on a Chip Voltage. The voltage sent through the SoC VRM; the SoC contains various interfaces and controllers, including the memory controller.
Overclocking guidelines? : More VSOC can improve stability, notably when pushing higher memory frequency. Ideally this should be kept low, somewhere in the range of 1V-1.15V, but this can be set up to 1.2V safely (though it’s in question as to whether this much voltage does much).

VTT_DDR: DDR Termination Voltage. Controls memory bus impedance. Apparently this voltage is useful for maintaining signal integrity, and is likely related to termination resistances.
Overclocking guidelines? : My BIOS doesn’t have this, but you should keep this around half of VDIMM, though raising it by a few millivolts can help stability at high frequencies.

VPP: Programming Power Voltage. Used to activate word line transistors. This rail is used to power the DRAM during precharge as a means to reduce power consumption. Default is 2.5V.
Overclocking guidelines? : I’m not sure what to do for this voltage as my BIOS does not have it, but DRAM Calculator suggests that either raising or lowering this by about 20-30 millivolts can improve stability.

PLL Voltage: Phase-Locked Loop Voltage. The voltage supplied to the PLL circuit. The PLL circuit essentially prevents the desynchronization of certain signals from one another, as well as mitigating certain delays. From what I understand, it can be important in maintaining stability at high frequencies. Default is 1.8V.
Overclocking guidelines? : As with VPP, I’m not sure what to do for this voltage as my BIOS does not have it, but DRAM Calculator suggests that either raising or lowering this by about 30 millivolts can improve stability.

CLDO_VDDP: DDR4 PHY Voltage. The voltage supplied to the SoC PHY chip. Changing this require a cold restart (shutdown, unplug PSU for a few seconds, and then restart). Tweaking this voltage can resolve memory holes. A memory hole is a specific range of frequencies that your memory won’t run. For example, a kit may boot fine at 3400 or 3600, but near 3466 it will fail to POST.
Overclocking guidelines? : Tweak this voltage a little lower or higher (but not above 1050 mV) to resolve a memory hole. Supposedly VDIMM - 100mV is a good value to try.

VDDP: DDR4 PHY Voltage. The voltage supplied to the SoC PHY chip, but from an external current monitor. Basically CLDO_VDDP but (I would think) a little higher, as this value does not account for some Vdroop.
Overclocking guidelines? : Update your BIOS, this no longer exists on BIOSes using the AGESA 1.0.0.6 firmware.

Last but definitely not least, I will cover some of the other miscellaneous settings.
Spread Spectrum: This setting reduces the electromagnetic interference (EMI) produced by your VRM. The point of this is to quite literally spread out the spectrum of frequencies that your memory runs at. Thus, your memory will run at a slightly wider range of frequencies than what you set in BIOS.
Overclocking guidelines? : Some have reported that this sometimes improve overclock stability, but others warn against it since the frequency variation can drastically reduce stability. It may be worth trying to turn it on, but you theoretically should keep it off unless you live somewhere where there’s a lot of EMI for whatever reason.

Geardown Mode: Overrides CR and runs some timings off an internal ½-frequency clock when storing certain values. Recall that DDR means double data rate because the effective memory clock is double the actual memory clock. What this means, then, is that all timings will be rounded up to the nearest even number, since your memory will skip half of the effective clock cycles. To further clarify why this is, if you’re running your memory at... let’s say 3000CL13, then enabling Geardown would run it at ~~1500CL6.5~~ except you can’t have decimal timings, so it would actually run it at 1500CL7, which has the same latency as 3000CL14.
Overclocking guidelines? : This lowers performance slightly for CR=1T, but according to AMD it *may** run better than CR=2T, depending on your timings.* This should be used if you’re having difficulty stabilizing a certain memory clock, while using odd timings, and if your issues are not serious enough to warrant changing things like termination resistances.

Powerdown Mode: Lowers VDIMM when the system is at idle. This can save a little bit of power, but it reportedly can cause issues with stability, and slightly increases DRAM latency.
Overclocking guidelines? : It’s off by default, so keep it off.

BankGroupSwap: Changes how applications are assigned to memory locations. According to the same AMD post linked just a couple paragraphs ago, this essentially optimizes performance for synthetic workloads (like benchmarks or compute applications) when enabled, or games when disabled.
Overclocking guidelines? : Well AMD pretty much explained it for me. Disable it for gaming, enable it otherwise.

Memory Interleaving: Controls the mode by which memory is interleaved (shockingly). Memory interleaving is a method of increasing memory bandwidth by organizing memory blocks across multiple memory banks to prevent what are essentially “stutters” in memory access. One motherboard manual suggests that it has the following modes: Auto, None, Channel, Die, Socket.
Overclocking guidelines? : I don’t know as it does not appear in my BIOS. I believe this defaults to channel mode, and DRAM Calculator recommends keeping it at that. Apparently it is a setting that is mainly important for Threadripper and Epyc, though I would like further verification of that.

Memory Interleaving Size: Controls the memory interleaving size (another big surprise) and changes at which bit at which interleaving begins. One motherboard manual suggests that it has the following values: Auto, 256B, 512B, 1KB, 2KB.
Overclocking guidelines? : I don’t know as it does not appear in my BIOS. DRAM Calculator suggests a value of 2KB, but one overclock.net user claimed he saw improved stability and bandwidth with 256B. Apparently it is a setting that is mainly important for Threadripper and Epyc, though I would like further verification of that.

Channel Interleaving Hash: Controls hashing of address bits when memory interleaving mode is set to channel. I don’t know what this does, though.
Overclocking guidelines? : I’m clueless. This may also be something that’s more important for Threadripper and Epyc, but again I don’t know.

DRAM R1/R2/R3/R4 Tune: I have no idea.
Overclocking guidelines? : These settings only exists on the Crosshair VI Hero and Crosshair VI Extreme, and I don’t have either of those boards so I don’t know what to do. According to the creator of DRAM Calculator, 63 is the default for these settings, with 40 potentially improving overclock stability.

L1/L2 Stream HW Prefetcher: Control whether the CPU prefetches data from memory that may be accessed soon. If disabled, then (I believe) your CPU will simply not prefetch, which is, well, a bad thing for performance.
Overclocking guidelines? : I believe these settings only exists on the Crosshair VI Hero and Crosshair VI Extreme. If your BIOS shows them, keep them on.

Super I/O Clock Skew: I have no idea, but my reading about DRAM leads me to believe that clock skew is something to be corrected. The logical extension of that, then, is that this setting should be left off.
Overclocking guidelines? : As corroborated by DRAM Calculator, keep it off.

Opcache: Controls whether instructions recently decoded by the CPU are stored, so as to prevent them from being re-decoded. The purpose of this is to essentially prevent the CPU from doing extra work, i.e. save power. This could also improve the efficiency and performance of the CPU in certain workloads.
Overclocking guidelines? : Supposedly enabling it increases performance, but I have not tested that. At worst, your system draws slightly less power with it enabled.

Memory Clear: Zeroes out all bits of memory upon boot...maybe.
Overclocking guidelines? : I don’t know.

And that’s all! If you read all the way through then hopefully I helped you gain a better grasp for how DRAM works and how to go about the very complicated thing that is memory overclocking. Once again, if you have any feedback or corrections on this information please let me know, I don’t want to spread inaccurate information.

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Fractional and decimal odds. To convert fractional odds to decimal odds, you need to turn the fraction into decimal form and then add 1. To convert a fraction to a decimal, you simply divide the numerator (the number left of the divider) by the denominator (the number right of the divider). Let’s say you want to convert fractional odds of 1/5 into decimal format. There are two steps to convert decimal odds into a fraction. Step 1) Convert decimals odds into a fraction by subtracting 1, and using 1 as the denominator. Example: 3.40 – 1 = 2.40. This creates the decimal odds of 2.40/1. While this is a perfectly good fraction, bookmakers never use numbers with decimal points in fractionals. That is why we need step two. Fractional odds are sometimes known as ‘Traditional’ or ‘British’ odds. The price quoted by the bookmaker about an outcome is quoted as a fraction, hence the name fractional. One difference between decimal and fractional odds is that the stake is not displayed in the quote price for fractional odds. Decimal odds Decimal odds is an odds format typically used in Australia. Fractional odds is an odds format typically used in the UK. To be able to convert from Decimal to Fractional odds you first have to enter a decimal.Converting Decimal Odds to Fractional Odds can be confusing to begin with because of the different ways they are displayed. The only thing you need to know is that the decimal odds value stands as a multiplier for your wager – Your bet stake x Odds = Payout. The lower the decimal multiplier is, the higher the implied probability of a wager to be successful. For example on odds 2.50 – a 100 euro bet will return potential winnings of 250 euros – with net winnings of 150. American odds. Their even more widely used name is Moneyline odds. If the odds convertor calculator isn’t your cup of tea then there is also an odds convertor table available. Much like the calculator, this simply displays a list of popular odds offered with each and every other format aligned. For example, looking for fraction odds of 8/1 will display the decimal, American, and probability odds too. How to Use the Fractional to Decimal Odds Calculator. Using this converter is easy. Simply enter the fractional odds into the box that states Fractional Odds. Fractional odds look like 2-1 0r 13/5. Press convert and the decimal odds will be shown in the Decimal Odds Box. more. How to Convert a Repeating Decimal to a Fraction. Repeating decimal numbers require a slightly different process to convert to a fraction. A repeating decimal is a decimal number that continues infinitely, such as 1.1787878. These numbers are usually expressed in a rounded form, such as .788, or with an over-bar like this: 1.1 78. Decimal odds are widely used around Europe and are the display format of choice for the betting exchanges around the world. They are also incorporated in Asian Handicap betting which is quickly becoming a popular way of gambling on football and other events, and, to many, decimal odds are the most straightforward representation of probabilities. Decimal - 1 divided by the decimal odds, multiplied by 100 to give a percentage e.g. decimal odds of 2 = (1/2) * 100 = 50%. Fraction - 1 divided by (the fractional odds plus 1), multiplied by 100 to give a percentage. e.g. fractional odds of 3/1 = (1 / ( (3/1) + 1)) * 100 = 25%. American:

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