A lot of factors enter into this decision – objectives, bankroll, risk tolerance, spouse, etc. Here I look at only the statistics. To move up you should be confident you are a winning player so the following explains how to determine if you have played enough hands in a
cash game to meet that goal.
Assume you have sample data that indicates you have a positive win rate of W/100 with a standard deviation of S/100. To determine the sample size you need to assure with a specified confidence that you are a winning player, you can use the following formula:
N =100*( Zc*S / W)^2
where Zc is the normal distribution factor corresponding to a one-sided C% confidence interval: Z80 = 0.84, Z90 = 1.28, Z95 = 1.645. Note that N increases with C and S, and decreases with W. On line tracking programs typically provide a standard deviation estimate or you can use a value between 70 and 100 if you don't want to calculate it yourself.
Example: You have an estimated win rate of 5 per 100 hands with a corresponding standard deviation of 75 per 100. To be 80% confident you are a winning player,
N = 100*(0.84*75 / 5)^2 = 16,000 (approx..).
For C=90%, N = 37,000 (approx.) and N = 61,000 for 95% confidence.
The above assumes your win rate is distributed normally (valid by the Central Limit Theorem) and that your win rate and standard deviation are relatively constant over the sample period. If your win rate is not constant but is increasing, then the sample size result can be considered to be conservative.- i.e., it is more than you need.
The following thread discusses sample size requirements for a single table
sit’n’go:
https://forumserver.twoplustwo.com/3...t-rate-1741082