Let's talk MATHS

[SparkyElf-2852]

@Smeet-1144

Quite a few.

@Derkan-2593

The general idea for statistics is that you can start extracting probabilities only when you reach a really large sample size.
Large generaly starts after several thousands.

Bla, bla, bla. Not a single formula! Or even a slightest notion of what ‘large’ etc is, as noted above.

For starters, check something like this out:
https://en.wikipedia.org/wiki/Binomial_distribution
In particular:
https://en.wikipedia.org/wiki/Binomial_distribution#Confidence_intervals
and also
https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval

(WikiDumpster might not be the best or most accurate source, but it’s just a pointer at the proper subject and how these things work in general)

In the posts linked above, I’ve already noted that approximating the (binomial) distribution with the normal one probably isn’t a very good idea here.

It’d be an okay little project for a maths student to implement those formulae in a small program or something like that, otherwise it’d be a bit annoying, that’s why I asked. If you don’t wanna bother, well, for rather large sample sizes (although you’ve likely got no notion what that actually means) you could go with a crude approximation by the Gaussian distribution and use the ‘three-sigma’ recipe I hinted at earlier.

When you grasp at least the basics, we could talk — and the topic-starter has explicitly proposed to talk about MATHS… But, of course, those VERY VOCAL forum participants are eager as ever to contribute their oh-so-valuable clueless ‘opinion’ instead.

@Derkan-2593

The general idea for statistics is that you can start extracting probabilities only when you reach a really large sample size.

@Derkan-2593

And the smaller your probabilities are, the harder it will be to find them back in your statistics.

By the way, you’ve apparetnly got no notion of what ‘statistics’ even means.

For starters:

https://en.wikipedia.org/wiki/Statistic

(Yes, the definition there in the beginning is more or less correct.)

@Schyla-1490

Think of it like a subjective win rate (your personal deck’s win rate) and the objective win rate (the actual real win rate combined of all people using that deck)

Ugh… That’s a… creative way to put it. You might as well go on and tell us there’s no such thing, that a ‘win rate’ is a ‘social construct’ or whatnot. It’s fine and all, everyone is entitled to one’s own opinion, but this isn’t a mathematical approach, if you ask me.

@Schyla-1490

Your subjective win rate will need to be played enough times

The question is: how many?

Sorry for being curt, but you’ve literally said nothing about it, despite being verbose in your post.

@Schyla-1490

to substantiate the deck’s true win rate is X where X = the objective win rate.

That’s the only way.

Thus, you can never use your own deck’s win rate to calculate what the overall win rate of the deck is unless you are the ONLY one playing the deck.

Nope, that’s not how it works.

As said many times, a ‘proper’ way (well, at least one of — there are probably alternative approaches) would be to estimate the confidence interval, for which the player’s own data is as good as any, really, and the amount of data is related to its width — nothing more, nothing less. The ‘objective’ figure still remains one to be estimated.

[Scr0tieMcB-1291]

@Reaver-6716

how many games does a deck need to be played to substantiate it’s true winrate?

This entire question indicates the wrong attitude.

Every sample is less than the entire picture. So no sample is perfect. But some samples are better than others. Maybe it’s because of larger sample size, maybe it’s because one sample doesn’t have a particular bias that another sample has. But there is absolutely no binary line where “true” winrate is established. There are only better samples and worse samples, on a spectrum.

That said, in a world where data websites professionally collect data and for the most part make it available for the low low cost of free with ads, it’s downright silly to consider ANY personal play sample as “good.” It’s competing against samples of thousands or tens of thousands. It’s like trying to build your own car when Toyota exists.

[SparkyElf-2852]

@Scr0tieMcB-1291

Every sample is less than the entire picture. So no sample is perfect. But some samples are better than others. Maybe it’s because of larger sample size, maybe it’s because one sample doesn’t have a particular bias that another sample has. But there is absolutely no binary line where “true” winrate is established. There are only better samples and worse samples, on a spectrum.

Yep, that’s more or less it, as said above.

Biases apart, it’s not so much about a ‘spectrum’, but rather about how wide the confidence interval for the estimated ‘true’ win rate is.

In the example linked above, I provided an estimate that it’s roughly proportional to the inverse square root of n (number of data points) in this case.

@Scr0tieMcB-1291

That said, in a world where data websites professionally collect data and for the most part make it available for the low low cost of free with ads, it’s downright silly to consider ANY personal play sample as “good.”

Not if you’re testing the theory of the game’s being rigged, for example. In this case, if you average this over a large amount of players, any such effects would be cancelled out.

Besides, one should still be mindful of things like ‘the average body temperature in a hospital’ (some patients have high fever, others are already cooling off in the fridge, but we are seriously using this ‘metric’ as an indicator of patient health on average), to begin with some silly and basic examples, or Simpson’s paradox, if you look at something slightly more advanced and mathematical, rather then pure common sense.

[Scr0tieMcB-1291]

@Schyla-1490

The way you prove the game is rigged is by making a claim, and then proving demonstrably that the claim is backed. The key word here is demonstrably

The issue here is that you can’t really prove a negative with data. I mean, I have said that the data shows that the game is 95+% not rigged, and that this is objective fact. And I stand by that statement… but the 95% part is pretty crucial. If the output is random and we have high confidence in its conclusions based on sample size, then we can pretty much say random output proves randomish method and no widespread rigging. But if a few dozen games out of the hundred thousand are rigged, well, there’s really no way to detect that with data. There is no such thing as a 100% confidence interval.

It’s kinda like Bigfoot. I can’t prove that Bigfoot doesn’t exist. But if you’re trying to tell me that Bigfoot is commonplace, well that would be objectively false. Similarly, I can’t prove that zero rigging exists, but it is an objective fact that it’s not common.

[Scr0tieMcB-1291]

@SparkyElf-2852

it’s not so much about a ‘spectrum’,

It’s absolutely entirely about a spectrum. Confidence interval is just a way of measuring how far along that spectrum you are, and 100% confidence doesn’t exist.

@SparkyElf-2852

if you average this over a large amount of players, any such effects would be cancelled out.

This is essentially a claim of unfalsifiability, which immediately makes it scientifically invalid. If you can’t perform some test of the output in such a way that you get one result in the data if rigged and another result of not rigged, then your hypothesis is untestable and that’s not science, that’s religion.

If the output matches random, then it’s not rigged, because any rigging that doesn’t effect results isn’t rigging at all.

[SparkyElf-2852]

@Scr0tieMcB-1291

It’s absolutely entirely about a spectrum.

‘Spectrum’ as a mathematical term means an entirely different thing (suddenly reminded be of the ‘standard variance’ incident, which was apparently an erroneous conflation of ‘standard deviation’ and ‘variance’, by the way). If you’re trying to explain ideas in your own words, that’s fine, but let’s just not confuse it with (mathematical) terminology.

@Scr0tieMcB-1291

100% confidence doesn’t exist

By the way, technically, it does — the entire domain of the distribtution function. Not that it’s very useful practically, of course…

Anyway, since you’ve mentioned it again — that by itself is not necessarily a problem, including mathematically rational decision-making (all that Bayesian ‘magic’ and whatnot… I think we’ve touched the subject slightly already).

@Scr0tieMcB-1291

This is essentially a claim of unfalsifiability

No, it’s not. I’m merely pointing out that, on the most trivial level, in a zero-sum game like this, ‘positive’ and ‘negative’ riggings for many players would cancel out, and you wouldn’t see the effect; moreover, amalgamation of sets might introduce a new ‘bias’ (have you taken a look at the aforementioned Simpson’s paradox? I’d highly recommend it if you’re not familiar, it’s a good one), so simply having ‘bigger data’ might not necessarily make your results better — sometimes, in fact, quite the contrary, that was my point.

As a reference, even this would do:

https://en.wikipedia.org/wiki/Simpson%27s_paradox

A side note: I’ve been berating this dubious ‘source’, and for a good reason — if you look at anything even slightly sensitive, political etc, that WikiDumpster looks heavily curated at least or utter totalitarian propaganda at worst, so I wouldn’t trust it one bit, but a number of purely technical articles in the US version have apparently been written by students, enthusiasts etc citing actual decent books and literature, thus some material isn’t that bad there (and not that it’d interest many people but ‘nerds’ anyway, so there’s no point in machinations there) — in fact, it can occasionally be useful.

PS One more thing… Can’t believe I’m saying it, but I’m really glad it’s you who showed up in this topic. On the personal level, you might be… you , but at least you can operate with facts and rational arguments (when not trolling and such, that is) — there’s that, and I do like conversations of this kind.

[Schyla-1490]

@Scr0tieMcB-1291

The issue here is that you can’t really prove a negative with data.

I didn’t say you would prove a negative. My example wasn’t to show how to prove the game isn’t rigged. That’s the negative. My example was to show how it is rigged, which isn’t a negative.

“prove the game isn’t rigged” = proving a negative claim
“prove the game is rigged” = proving a positive claim

So I don’t even know what you’re talking about when you reply to me saying the issue here is that you can’t really prove a negative with data. Yeah, I know. That’s why I didn’t say anything about proving a negative.

@SparkyElf-2852

The question is: how many?

I said how many. Until your subjective data matches the objective data. Which is essentially meaningless because…

@SparkyElf-2852

Nope, that’s not how it works.

Yes, it is.

…your single deck experience will never be enough to make an overall case for the deck. Thus, you can’t take a single iteration of data within a whole to determine what the whole is.

So if you want a number, it’s whatever number matches the overall data. For some deck iterations it will be 100 games. For some deck iterations it will be 1000. For some it won’t get there even with 1,000,000 games. So it could be a number you reach and it could be a number you never reach.

This is basic statistics.

Given a pool of 1,000,000 participants (or whatever number you choose), some participants aren’t going to experience the average participant experience.

So asking “how many games until I see ______” Is like asking how many games does a participant have to play to see the average participant experience. There is no number. And asking for a number is just being unknowledgeable in how statistics work. You may as well be asking for what number do I count to in order to get to infinity.

And if you understand how statistics works and why this is the way it is and continue to say “The question is: how many”? then you are being dishonest. I’m going to assume you’re not dishonest and instead assume you’re just lacking understanding.

[SparkyElf-2852]

@Schyla-1490

I said how many.

Nope.

No formula, only empty words and assertive self-repetitions.

@Schyla-1490

This is basic statistics.

No, it isn’t.

I dunno, get a decent university degree, take some courses or whatever… There are even books after all, although it might be hard for a layman to navigate through this rather complex subject.

@Schyla-1490

And if you understand how statistics works and why this is the way it is and continue to say “The question is: how many”?

Then it’s a perfectly reasonable question in terms described above.

In practice, such a question is raised, perhaps implicitly, all the time. “We’re seeing a peak in the spectrum here [talking about an example from particle physics again] at ‘three sigmas’, could that really be it? — Well, let’s gather data for ‘five sigmas’, then we’ll see whether it disappears or we’ll claim a discivery”, something like that.

[Kassadin-21130]

@Schyla-1490

…your single deck experience will never be enough to make an overall case for the deck. Thus, you can’t take a single iteration of data within a whole to determine what the whole is.

With enough games, it can be a pretty good measure of how that deck operates under certain conditions.

For example, you state your rank, how variable that rank is (average deviation, let’s say, not to try to dabble with exact terminology - means how much does it oscillate around your current rank) and a couple of more variables just in case (server of play, your usual finishes) which can under some circumstances impact the rank of winrate (for example fresh account/server = a lot of bots, not fresh account on old server = more precise)…

…and then you can be sure of your data more than what you read from aggregate data websites, because they’re not collected under those specific conditions only, but other conditions which impact the data’s precision.

If I can hit, for example, top 200 with sludgelock with a winrate of 59% consistently on more servers (obviously I can’t, not anymore), that means that everyone under those circumstance can switch to sludgelock and reach that same statistic with enough games, and unchanging circumstances (no meta shifting).

That’s also, btw, why I always include my rank when I talk about stuff. It’s not because I like to flex, but because I feel like those are neccessary additions to explain under which circumstances that’s possible.

I mean I do like to flex, but I rather open a new thread to do it, rather than use other topics.

[SparkyElf-2852]

@Kassadin-21130

With enough games

@Kassadin-21130

under certain conditions.

Ugh… Again, how many exactly and so on?

Am I the only one here dealing in terms such as the binomial distribution and so on, rather than vague and vacuous verbal equilibristics?

[Kassadin-21130]

@SparkyElf-2852

Am I the only one here dealing in terms such as the binomial distribution and so on, rather than vague and vacuous verbal equilibristics?

Nothing vague and vacuous here, this is practical, it’s not theoretical.

You’re continuously trying to apply actuarial mathematics in a place where it has no business to be. This is some basic statistics, and it’s actually useful, unlike your failed attempts of what you clearly don’t understand if it brought you the idea that the game is rigged.

You can feel flattered I even replied to you. It won’t happen again.

[SparkyElf-2852]

@Kassadin-21130

You’re continuously trying to apply actuarial mathematics in a place where it has no business to be.

Lo and behold: some anonymous guy on the forum has just claimed to have brought down the entire progress of humanity in this particular discipline, which deals exactly with problems such as this one. Well, how do I put it: I don’t think so.

@Kassadin-21130

You can feel flattered I even replied to you.

Ha! ’ Remember this day, for you are graced with my presence.’

@Kassadin-21130

It won’t happen again.

Here comes this promise… again.

[Schyla-1490]

@Kassadin-21130

With enough games, it can be a pretty good measure of how that deck operates under certain conditions.

Don’t fall for the trap. There isn’t a set number. You saying “with enough games” is hinting a specific number exists. No such specific number exists statistically, and that’s what he wants you to give.

This is why I’m now avoiding this discussion further with this individual now. They are either purposefully dishonest or stubbornly ignorant. Despite giving the benefit of the doubt earlier, I’m no longer certain which now.

It’s asking an unanswerable question similar to asking someone to tell you the exact person in history that started speaking Italian. No such person exists even though the start of Italian existed. And when you say no such person existed, the person acts like they win the argument because you can’t answer it because the answer doesn’t exist. It’s one of the most lamest tactics in debates and that’s exactly what he’s doing.

It’s dishonest. There is no set number statistically.

Just ignore and move on.

[Scr0tieMcB-1291]

@Kassadin-21130

If I can hit, for example, top 200 with sludgelock with a winrate of 59% consistently on more servers (obviously I can’t, not anymore), that means that everyone under those circumstance can switch to sludgelock and reach that same statistic with enough games, and unchanging circumstances

The biggest of these circumstances is that you are you, and very few if any people are like you. It is a critical error to simply assume that oneself is normal, and that therefore one’s experience can be generalized as normal. You need to first investigate what normal is, and see to what extent you match it.

@SparkyElf-2852

Am I the only one here dealing in terms such as the binomial distribution

You can’t just assume that something conforms to a bell curve. I’d imagine that if everyone played the same number of games, then a random win-loss record per player would fit such a distribution… but players do not play the same number of games, so I don’t see where there’s a binomial distribution to be had.

[Kassadin-21130]

@Scr0tieMcB-1291

The biggest of these circumstances is that you are you, and very few if any people are like you. It is a critical error to simply assume that oneself is normal, and that therefore one’s experience can be generalized as normal. You need to first investigate what normal is, and see to what extent you match it.

I can explain to anyone how I play sludgelock and why, and people can repeat it.

That’s basically what coaching does xD

Jesus. Imagine all that wall of text for literally nothing of practical importance? You really want back on ignore list?

[Scr0tieMcB-1291]

@Kassadin-21130

I can explain to anyone how I play sludgelock and why

I don’t doubt this.

@Kassadin-21130

and people can repeat it.

I doubt that they could do so consistently.

But hey, I’m just speculating. Try coaching five people — preferably with a different deck, given the meta — and see how many of them can match your achievements. I’m guessing one in five, but I’d be happy to be wrong.

In every field where coaching is a thing, the majority of those coached fail to be exceptional. I mean nothing personal against you specifically.

[Derkan-2593]

@SparkyElf-2852

Bla, bla, bla. Not a single formula!

Nothing in OP’s post requires a formula.
They are asking a generic beginner question about math.
Throwing formulas at their face without explaining the link with their question would not serve any purpose unless you try to make yourself look more intelligent than you are.

@SparkyElf-2852

Or even a slightest notion of what ‘large’ etc is, as noted above.

You literaly quote the notion of large in my reply.

@SparkyElf-2852

But, of course, those VERY VOCAL forum participants are eager as ever to contribute their oh-so-valuable clueless ‘opinion’ instead.

That link is a message of your own, none of the previous persons of this current thread have replied to the topic you linked, beside yourself. Are you the very vocal participant with clueless opinion ? Because I fail to understand the purpose of devaluating your own messages.

@SparkyElf-2852

By the way, you’ve apparetnly got no notion of what ‘statistics’ even means.

And you’ve apparently got no notion of what a discussion should look like.
If you tell me I’m wrong, the least would be to elaborate why I’m wrong.

@SparkyElf-2852

(Yes, the definition there in the beginning is more or less correct.)

You either talk about mine and contradict yourself, or talk about the wikipedia one, your own source, and don’t make sens.

If I were to explain the difference betwene statistics and probabilities to a beginner, it would look like
“Probabilities are the real odds of an event to occure, given beforehand.
Whereas statistics are the data you collect after the event has occured.
From statistics you can try to deduce the probabilities, since on the long run they should align with the probabilities”
But you’re not the type of user that tries to explain things

You may have great information on the subject, but you have absolutely no will to help beginners understand anything, you’re just here to shove your knowledge (or at least your google search skill) in the face of people. You don’t care about the level of the person you’re talking to, you don’t adapt and you just expect any one to have your level of comprehension of the topic. Talk about being vocal.

[Elchar-11130]

You sound a little silly rattling off stats textbook terms…

[NeonGhost-111963]

@Elchar-11130

You sound a little silly

Reading their posts, they come off as pretty unbalanced. There is little good to come out of engaging with unbalanced people.

@Schyla-1490

Don’t fall for the trap.

… of replying to sparky at all.

[Aggrevane-1126]

no way calls to action to ignore someone when they werent befuddled with your other tactics of trying to shame and confuse them with wordsalads wordbuffets and wordtroughs…

Gosh I guess my deck tracker was lying when it showed the last 8 priests all illuminated on 1… get Neptulon on 5 and res res res.

Same exact plays over and over and over until I quit playing again.

Like the 12 giants on t4…

over and over and over until I quit.

Hellya on 4

Brann on 6

OVER AND OVER AND OVER AND OVER…

30 CARDS DOESNT MATTER 40 NO BIG DEAL.

Play RENO DECK… see plagues.

Change to slow deck get aggro change back get combo…

Try another deck…

Priest 0 mana discover t1

Neptulon for 5

OVER AND OVER AND OVER…

Deck Tracker shows the truth.

“Bro there is no number of games you can play to show anything you dont know how statistics works bro”

“Everyone ignore this one who knows maths armed with vocabulary”