Sample Size Question

[twomarks]

I know that the bigger the sample the better, and I know from reading posts on here that a sample size of 10k hands is just the beginning of obtaining a meaningful sample size. So...here's my question:

How many 10k hand samples diverge from the results of a 20 - 30k hand sample? And then from an even larger sample?

What I'm trying to find out is, while the larger the sample, the closer to reality the results are, just how far can a 10k sample be off percentage wise?

Ex: You have 1 million hands that show you are winning 5 BB/100 hands. If you take any consecutive 10k hand sample, how many sets would be truly divergent of the average?

I'm not the most statistically gifted person in the world so please take spirit of this question to heart as opposed to its letter.

Thanks in advance,

twomarks

[gaming_mouse]

Let's say you have a win rate of 2BB/100. The standard deviation for your win rate (for most players, anyway) will be between 15 and 18 BB/100. Let's just call it 15 for sake of argument.

After 10,000 hands, you will have played a set of 100 hands 100 times. The standard error for win rate becomes:

15/sqrt(100) = 1.5

Therefore, a set of 10,000 hand is normally distributed with mean = 2 (your true win rate) and sigma = 1.5.

You can then calculate various probabilites using the normal curve. For example, the chance that your total winnings are less than or equal to 0 is just over 9%.

HTH,
gm

[twomarks]

I guess what I'm asking is this:

Taken over a large sample size - what percentage of 10K hand sets would significantly deviate from the mean?

I'm trying to get a handle on why I could consider myself a winning player, or losing player, at the moment I reach 10K hands.

Thanks,

twomarks

[gaming_mouse]

[ QUOTE ]
Taken over a large sample size - what percentage of 10K hand sets would significantly deviate from the mean?

I'm trying to get a handle on why I could consider myself a winning player, or losing player, at the moment I reach 10K hands.


[/ QUOTE ]

You have define what you mean by significantly. That's why I gave the example of being down or even after 10K hands, which happens only 9% of the time. That should give a decent idea.

Nothing magical happens at the 10K mark. It's a spectrum. After 20K, you will be even more unlikely to still be even if you are indeed a winning player. 10K is just taken by convention among the poker community as a significant marker. But wheather or not you choose to take it as one is just a matter of personal preference. Some people like to be more sure than others.

Personally, if I am beating a game at 2BB/100 after 10K hands, I'll be feeling pretty confident -- but keeping a small reservation in mind. Likewise, if I am down or even after that long, I'm going to look at my game and assume that it was not simply bad luck -- but keeping in mind that there is that possibility.

[twomarks]

Ok - thanks mouse

twomarks