## Archives

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This came up in a 2+2 post, where someone was interested in comparing final pot sizes to the flop type. It turned out to be a little interesting but no big surprises. The original thread with more discussion is here: http://forumserver.twoplustwo.com/15/poker-theory/statistical-analysis-flops-633448/

Here’s the data for a 9-player run and a Heads-Up run, showing the calculated frequency of the flop types, [...]

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In his book Ace On The River, Barry Greenstein gives an example of a card removal effect that he says changes the hand equities significantly (more than 2%):

“In hold’em, with no betting after the flop, all pairs are a favorite over Ace-King offsuit, by at least 52% to 48%. All pairs except Deuces with neither card in [...]

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I ran the scans for a second site with more hands (119 million 9-player), and graphed all the equity boosts for both sites. This graphs shows all the sample sizes, including a baseline for all matching hands (no folds required in front of the bet). Site A shows the results described in the previous post. Site [...]

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This Flop Analysis section is being posted in 7 parts and the final post will contain a detailed statistical analysis of a large number of NLHE flops (hundreds of millions). If you want to jump around click the topic at the top of the page for a list.

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One of the most common complaints about online poker [...]

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Of the removal effects I’ve identified, this one alone is fairly well-known. Players tend to see more flops when holding high cards, and so the board will tend to contain more low cards than high cards. The graphs below show that this effect becomes more pronounced for the turn, and even more pronounced for the river, as player requirements [...]

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Here we examine the card-removal effect that results from players tending to see flops when they hold paired hole cards. This part is a little tedious but it’s necessary to predict what we should see when analyzing an enormous sample of community cards. If you aren’t interested in the math then just skip to the bottom for [...]

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Before we get to the real data, we first need to check our code and our calculations. The input for the run shown below is the set of all possible flops enumerated, rather than real hand data. There are 132,600 possible flops (permutations, not combinations, of which there are 132,600/3! or 22,100), and so we [...]

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Here we look at the effect on the suit distribution of the board according to the suitedness of the hole cards held by players seeing the flop.

Given random hole cards, the flops would break down like this (from full enumeration):

Flops seen: 132600 (100.0%) Known hole cards: [...]

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