[Silent A]

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On season 1 and 2 running it three times meant that one player will scoop the whole pot. That's how I understood it. This was explained by Eli Elezra in one of the episodes where they ran it twice. Running it twice was better according to Eli has it gave to "even it out". I guess I understood the concept wrong.


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This doesn't make much sense to me. If you deal three times, each one should be for 1/3 of the pot. That seems like the best way to minimize the variance.

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It actually makes no sense at all unless it's exactly a 50/50 proposition. If it's not, and you make it a best of 3 proposition, the guy who's ahead has an even better chance of scooping.

For example, if we assume PA has a 75% chance of winning on each river, and they go for a best of 3, then PA wins 54/64 (84%) and JG wins 10/64 (16%).

Which means it's a really good way to go if you're ahead and your opponent is bad at math.

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FAIL

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I dare you to try to explain how what I said was wrong.

Just so that we're clear, we're talking about a scenario where you run it three times and whoever wins 2 or more scoops the whole pot.

If you still think I'm wrong, then ... well, let's just say that people like you make poker fun.

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Your calculations are correct, but wrong. When dealing rivers, the hits change the propabilites for the next river cards, so your constant odds analogy is wrong for this purpose.

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It was an approximation. The small changes due to the effect of hits is relatively trivial.

If you still doubt it, using the exact numbers in my above post ...

Conventional running the three times:

PA scoops 34*33*32/(44*43*42) = 35904/79464
PA wins twice 3*34*33*10/(44*43*42) = 33660/79464
JG wins twice 3*34*10*9/(44*43*42) = 9180/79464
JG scoops 10*9*8/(44*43*42) = 720/79464

PA's equity = 35904/79464 + (2/3)*33660/79464 + (1/3)*9180/79464 = 61404/79464 = 34/44 (77.3%)

Weird, probable misunderstanding of Elezra method, where PA scoops if he hits 2/3 and busts if he hits 1/3:

PA's equity = 35904/79464 + (3/3)*33660/79464 + (0/3)*9180/79464 = 69564/79464 = 38.52/44 (87.5%)