100,000 hands

[shawny boy]

I'm studying statistics and I understand how increasing sample size reduces std error, but what is the basis for using 100,000 hands as a statistically significant sample?

[pzhon]

People incorrectly believe there is some magic threshold below which results have no meaning, and above which they are meaningful. 100,000 is a guess at that imaginary magic threshold.

For some purposes, such as determining whether you are a winning player, you usually don't need 100,000 hands. For others, such as determining your win rate precisely, you usually need more. Of course, uninformed people confuse the two, and say 100,000 fits all problems.

[indianaV8]

Since some time I'm arguing that 100000 is not always good, and you need 200000 hands. Good that it's finally confirmed by authority.

[jogsxyz]

No amount of hands is sufficient. Your game is constantly changing. The level of play of the opposition is changing.
Those who win are constantly moving up in level. No one has a fixed win rate over time. The net difference between your ability and that of each table opponents is not fixed.
The stats are just approximations or estimates.

[Al Mirpuri]

[ QUOTE ]
No amount of hands is sufficient. Your game is constantly changing. The level of play of the opposition is changing.
Those who win are constantly moving up in level. No one has a fixed win rate over time. The net difference between your ability and that of each table opponents is not fixed.
The stats are just approximations or estimates.

[/ QUOTE ]

QFT.

[shawny boy]

um, okay I guess I'm looking for something a little more mathematical. if you want to claim a win rate of 5ptbb/100 hands then your expectation per hand would be .05ptbb/hand but maybe 95% of the time your deviation from expected value of up to plus or minus 50ptbb's. if there is a normal distribution around the true mean with a 2 standard deviation range to 50ptbb's (100 BBs) then the standard deviation is going to be huge (surprise, surprise) but to say that your true mean is to the right of 0 with a high degree of certainty you need a huge number of samples (100,000 anyone?).

I understand the concepts and the reason for the large sample size, but what I'd like to see is the actual math and what underlying assumptions (or empirical data, or whatever) drive the formula.

[pzhon]

The standard deviation for live limit play is usually expressed in BB/hour, which technically should be BB/sqrt(hour). For online limit games, the standard deviation is usually expressed in BB/(100 hands).

After n independent periods, the standard deviation of your result is sqrt(n) times as great. The standard deviation of your observed win rate per period is smaller byb a factor of sqrt(n).

So, if your standard deviation is 15 BB/100 (a typical figure for online limit full ring), then after 10,000 hands the standard deviation of your total result is about 150 BB, and the standard deviation of your observed win rate is about 1.5 BB/100.

The main assumption is independence, that your results in this batch of 100 hands tells you nothing about how you will do in the next 100. This is not necessarily true if you tilt, but tilt is not a rational phenomenon. So, it is usually ignored.