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firstly, i think it is beautiful that we're discussing whether the 25 hands is a 1 in 100,000 event, or a 1 in 10billion event.

to clarify, you would need to have 100,000 sets of 25 hands to presumably replicate it.

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Now, if we have other reasons to think somebody's cheating (which we do here, of course), that becomes the hypothesis. Then somebody comes along and says "Hey, dude, he might have just happened to fold exactly those times AA-JJ came up." Then we say, "No way, dude, that's 1 in 10 billion."

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i think that's the difference - my hypothesis is:
"what are the chances that villain makes the 'right' decision <u>given</u> the cards that were dealt?"

i think your hypothesis is:
"what are the chances that villain makes the 'right' decision <u>and</u> the cards are dealt in that way?"



i prefer my hypothesis because i don't care about the luck of the cards falling in that particular way. i'm only interested in looking at the chances of the villain responding as he did.

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No, that's not it at all.

You can't examine the hypothesis "Villain doesn't know the cards" and then look at the cards.

What you do is say "What are the chances that Villain plays perfectly preflop, where perfectly given his style is defined as folding only when an opponent has AA-JJ, over a 25-hand stretch?"

Then you run it.

THEN you pull open the data to see how he did.

I mean, maybe think about this intuitively. 1/100,000 doesn't even begin to capture the unlikeliness.

Or think about a single hand. OK, we're dealing the cards. What are the chances he folds AND somebody has a premium pair? 1/100 with my numbers. Oh, shnap, that's what happened. I mean, if you just use 1/10, that's just his chance of folding, and so what? Then the question you are answering is something like "What is the chance that Villain demonstrates the follwing pattern: CCCFFCCCCCFCCC..." etc. and who cares about cards, and that's 1/100,000 or whatever you got. The whole point is to account for the cards.