Winrate, standard deviation and spin size

[precogmiles]

Winrate = amount won/ amount bet

I have just done a little calculation using a sample size from the MPR leaderboard. The criteria were players that had between 180 to 220 spins.  I found the mean was 0.98 and the standard deviation was 0.1

Which is fairly accurate representation of a larger sample.

Given such a small sample size how many standard deviations above the mean would it take to be convinced that variance was no longer a major factor in the results?

For example would a Winrate of 1.2 be sufficient?

[precogmiles]

Let's also assume the sample bets are all flat bets.

[Joe]

The criteria were players that had between 180 to 220 spins.  I found the mean was 0.98 and the standard deviation was 0.1

How many players met the criteria? Assuming the sample size is adequate (it's needs to be at least 30), 4 standard deviations above the mean is certainly significant, and in fact the standard significance level is usually taken to be 5% which corresponds to less than 3 SD above the mean.

Let's also assume the sample bets are all flat bets.

I highly doubt that assumption is warranted.

And I thought you didn't believe in probability? 

[Steve]

None of the players in mpr have statistically significant samples.

I've seen many losing systems beat 10k spins. Just repeat the test and sometimes it will profit.

I hope to release the new video soon to show what i mean. The last video didnt go into enough detail about it.

And what std deviation is acceptable? There's no specific value. You can never be 100% sure. You on my approach 100%

[Joe]

None of the players in mpr have statistically significant samples.

That doesn't even make sense. And you seem to think that the only criteria for being statistically significant is a huge sample size. While an adequate sample size is important, it doesn't mean that smaller sample sizes can't be significant in the statistical sense.

I've seen many losing systems beat 10k spins. Just repeat the test and sometimes it will profit.

If you test a system over and over, then sure, you're going to occasionally find that it beats a sample, even if that sample is 10k spins or even more. But just because it's possible for a system to beat 10k spins doesn't mean that this is likely or probable in a one-off test.This is what you're not understanding.

And what std deviation is acceptable? There's no specific value. You can never be 100% sure. You on my approach 100%

Again this is totally missing the point. The only 100% guaranteed way to be sure is to test the whole population of spins, which is impossible. The purpose of inferential statistics is to make inferences 'beyond reasonable doubt' using samples from the population. If you could sample the whole population then statistics wouldn't be needed, but it's is rarely possible.

You seem to think that if it can't be done, no inference is possible, or if it is, it's not certain, and therefore useless. This is a very naive and impractical interpretation of statistical inference. In fact you seem to be saying that probability is pointless, and unless we have complete certainty any inference can be ignored. That's a very strange point of view from someone who sells roulette systems and computers.

And even though I don't know exactly how the score is calculated on MPR, it doesn't matter because if the sample is large enough (> 30) the Central Limit Theorem says it approximates to a Normal distribution, so you can use all the standard statistical tests.

link:s://statisticsbyjim.com/basics/central-limit-theorem/

[Steve]

Joe, you're not understanding. The next video i do might clarify a few things

[Joe]

lol, that's what you always say when someone disagrees with you.

I would like to buy one of your computers, but you must guarantee that I will never lose a session, otherwise your computers are useless. 

[Steve]

Joe, i dont have time so I'll address only a few points.

With a random system, maybe 1 in 50 players will beat 50,000 spins. Or maybe 3 in 10 will beat 10,000 spins. Does it mean the system "works"?

I will never be convinced a system works, from 10k, 50k,100k or 1m spins alone. Why? Because I've seen losing system beat that many spins, then lose big over more spins. So yes, no players on mpr have statistically significant spins. But i should clarify the context. I mean no account's positive results mean anything to rave about. Its not my opinion. Its just basic statistics.

Still i find it peculiar when some people lose on mpr, so criticize it and use rs or parx where lots of people win play money.

Convincing and viable proof needs much more. 

And "proof" is a combination of quantity and quality of data. Systems are wins and loses, with no substantiating data, so they rely solely on numbers. That's why many more spins are needed as validation.

[Steve]

And i said wait for the video because you'll see what i mean. It's not an opinion.

[Joe]

With a random system, maybe 1 in 50 players will beat 50,000 spins. Or maybe 3 in 10 will beat 10,000 spins. Does it mean the system "works"?

I will never be convinced a system works, from 10k, 50k,100k or 1m spins alone. Why? Because I've seen losing system beat that many spins, then lose big over more spins.

The standard of what constitutes 'proof' that a system works depends in part on what the consequences are. So supposing someone says they have a system which wins and they want to claim your $100k. Obviously you want to hit that system with millions of spins and not take even the smallest chance that it might turn out to be a loser.

And what std deviation is acceptable?

This is the key to it, because there comes a point where luck runs out, and the number of spins needed depends on the edge which the system has.

Here's an example of what I mean. Suppose you try out a system betting on 5 numbers, for a hundred spins, and it wins. The win rate is actually more like 6/37 when in theory it should be 5/37. Now assuming that the system really doesn't have an edge (the result is due to variance) the observed win-rate of 6/37 is less than one SD from the mean (actually 0.79).

You keep testing, and after 1000 spins the win rate is staying steady at 6/37 (remember,  you're only betting 5 numbers so it should be 5/37). Is this result statistically significant? Not really, because it's still only 2.5 SD's from the mean, which means it could happen once every 100 samples, just by luck.

You continue to test, and after 5000 spins the win rate is still 6/37, and this represents 5.6 SD's from the mean. Now this is starting to look 'significant', because only in the rarest of cases does any system perform this well for 5000 spins. You're at the edge of luck at this point.

After 10,000 spins the win-rate is steady at 6/37, which is nearly 8 SD's from the mean. Now you can definitely say that the result is statistically significant. You haven't necessarily 'proved' beyond all doubt that the system works, but you can rule out the results as being due to variance. And after all, that's what precogmiles wanted to know.

Obviously, the smaller the edge, the more spins it will take for the SD to get high enough for you to judge significance. And usually by that stage you will have abandoned the system anyway because the return is too low.

[Joe]

because only in the rarest of cases does any system perform this well for 5000 spins.

I should have qualified this by adding that it depends on the expected win-rate. I'm not suggesting that to have a higher than expected win-rate over 5000 bets is very rare for EVERY system; of course it isn't.

So  anyway, the take-home message is that although sample size is a factor, the main one is the number of SD's from the mean.

The problem is that most systems use progressions, which magnify the variance. In practice the best way to test these is to write a simulation, and having done that you might as well test over 10 million spins because it's as easy as testing over 10,000.

But what about testing precognition or AP systems where it's just not practical to test for millions of spins? In that case you will have to make do with as many as you can get, and more is always better. But that doesn't mean the result of the test means nothing.

[precogmiles]

Thanks Joe that makes sense to me. A Winrate of between 3  to 4 standard deviations above the mean, for something like precognition, would count as sufficient proof from a statistical point if view.

[Moxy]

Thanks Joe that makes sense to me. A Winrate of between 3  to 4 standard deviations above the mean, for something like precognition, would count as sufficient proof from a statistical point if view.

Not biased at all.  Perfectly impartial.

[pepper]

Not biased at all.  Perfectly impartial.

R u gonna change ur passionate attitude bout precog roulette gamers?
Do u think they r just deluding themselves cuz it's easy to say, "see, I predicted that"
If u think telekinesis is easier than predicting/influencing the future, than just say so. I do. It's much more practical; u r actually affecting the physical object. That's just my two cents.

[Moxy]

R u gonna change ur passionate attitude bout precog roulette gamers?
Do u think they r just deluding themselves cuz it's easy to say, "see, I predicted that"
If u think telekinesis is easier than predicting/influencing the future, than just say so. I do. It's much more practical; u r actually affecting the physical object. That's just my two cents.

I believe in all those.  Telepathy, TK, Precog.  It's his snobby-ness that irks me.