Poker-AI.org

Hey all

Just wondering how many HU NL tourneys you'd reckon a GTO bot needs to play on average to average to get an idea of whether it's actually a winning bot or just getting lucky? And what % of tourneys would you expect it to be winning at the micro/low stakes?

It depends.

For HU tourneys you can do a binominal test. Let's say you need to win 55% of your tourneys to break even after rake. Then you choose H_0: p_0 = 0.55. Now say you played 200 tourneys and won 120. Then p-hat = 120/200 = 0.6.
Now do a right-tailed hypothesis test: http://www.wolframalpha.com/input/?i=te ... 2C+n%3D200
And look at the p-value (0.06731 in this example). It means that we can say with 1-0.06731 = 93% confidence that our winrate is over 55%.

You can also calculate a confidence interval for your winrate. Use google to figure out how to do this.

Edit: Or be lazy and use this link: http://www.wolframalpha.com/input/?i=confidence+interval+for+binomial