Organizing a project to determine which sites are legit or rigged

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Unless you suspect that the rigged aspect takes pot size into consideration then you shouldn't use money at all. The test should only compare the outcomes with no regard to funds vs the expected results. Once you include money you no longer have a reference distribution.

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No, the rigged aspect would not take pot size into consideration. And I can't see why an EV vs Actual result comparison wouldn't suffice.

If the all in EV calculation says you should've made 1,000,000 over 100,000 hands and you have only made 750,000 there is a problem. I don't see where the room for error is here.

It's the same as flipping coins. If you got $1 for every time you called a flip correctly your EV would be $500,000 over 1,000,000 flips. What is the difference between that and the poker allins scenario.