I think there is a fundamental misunderstanding here by some posters--even though others got it right, let me try to rephrase this.

Most certainly it's true that the random variable, let's call it X, that describes the outcome of a single game is not normal (e.g., if we're not playing HU, the maximum loss is your buy-in, but the maximum profit is larger than the buy-in, assuming everybody has equal stacks; so, unlike a normal, X's distribution is asymmetric).

However, that doesn't matter for the winrate at all, if the winrate is calculated as the average win/loss over a sequence of realizations of that random variable X (say, over 100 realizations). Asymptotic theory tells us that those averages over samples of size 100 are approximately normal, even if X is not, that's the beauty of it.

So that's not a problem. However, the fact that each game is different (position, your opponents, possibly even the same opponents endogenously switching their strategy in response to your actions), we potentially cannot observe more than one realization of X; the next game likely a different random variable.

For practical purposes, however, I don't think that matters like these are terribly important for several reasons:

1.) Yes, position matters a LOT in a single game but there are only 9 different positions. Without trying to make a precise statistical argument here, think about doing the OPs experiment, done separately for each position. Well, if each of those stats is approx. normal, I would wildly guess that there is a theorem out there telling us that the average over those 9 sample stats is approx. normal as well.

2.) At the micros, there is a constant influx of new players (and exit of old players), which may be one of several types, but, in practice, there are only so many non-trivially distinct types. So my hunch is the fact that opponents are changing will average out as well. Also, my guess would be that your endogenous response to the kind of table you are facing (loose, tight, etc.) and other players' endogenous response to your play should average out over a number of sessions.

3.) Yeah, maybe over the first 20K or 50K hands or so you play (not sure about a reasonable number here), the changes in your own strategy should probably be visible. But after that (caveat: I am a total n00b), changes in your strategy should be pretty much low-frequency and I doubt it'll matter much if other factors are held constant (e.g., we don't move up levels)

Now, you could argue, due to these factors we need huge samples. I doubt it. Yes, it's true that we need quite a few more observations than if we were to observe realizations of X repeatedly, but nowhere near the 30k-50k that ppl here and the literature are suggesting.

So are they wrong? No, of course not. What is left then? I would argue, the *decisive* factor, and I think one poster above mentioned it, is the fact that when playing Hold'em, we have a large number of hands that are of second order for the winrate (because we fold those hands early). On the other hand, a good part of our winrate and its SD are driven by tail events (doubling up, stacking off,...). From all the econometrics I know, it is usually *much* harder to estimate using data from a distribution with fat tails. Roughly speaking, you need a lot more data before approximations from asymptotic theory become useful. All my intuition tells me that this is what necessitates the large sample sizes we need.

I'm just a beginner, just my naive take here. Experts, correct me if I'm wrong...

In 100 hands of Texas Holdem NL, there is no gain limit.

If you want to be exact, then, if you double your stack in every hand, then there is a maximum on 2^100 BB in a 100 hands row, assuming you beat a single villain each time.

2^100=1.267651e+30, which is a high amount, higher than expected for a normal-modelled variable.

corp

I checked, I found no explanation on it...

If you have the link, I'd appreciate to share it with me.

corp

holdem, how do you interpret the SD for 100 hands?

The SD of a 100 hand sample only OR
The SD of gains in 100 hands, using all the data??

corp

Pretty dense. You can't double your stack every time because your opponent cannot rebuy for more than 100bbs

I didnt say that you beat THE SAME opponent in EVERY hand, you can beat a different person every time, a person with enough stack, of course. But: Is it possible? YES, it is possible. Is it probable? No, it isnt. That's why it makes no sense to tell a variable in nature to reach -Inf/+Inf.

As some users had already tell you, no normality is needed for using the Central Limit Theorem.

You seem pretty sure of what you are saying (correct or not), so, are you statistic or something?

corp

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This post may be too old but this post will bring attention to it.
http://forumserver.twoplustwo.com/78...onally-538033/

Is it possible for someone to create a simple excel sheet to easily plug in the variable to figure out a win rate?

I tried to do this in excel but did not see a way to upload the excel document. Below represents the excel information and formulas for each number. Please let me know if this is correct?

Great post, OP

Great bump Cherufe and great thread OP.