Seven-Card Hands

[FF] “Stan, what’s the average hand in Hold ‘Em on the river?” queried Figaro the Fish.

[SS] “Well, the average hand that sees the river depends a lot on the players in the game, but if you mean the average hand, including all the mucked hands, then it’s just a pair”, responded Stan the Stat.

[SS] “Since you asked about the flop hands last time, I was ready for this followup. About three-sevenths (43.82%) of all 7-card hands are just pairs. Two pairs comes next at 23.50% then no pairs at 17.41%. The rest of the hands appear less than one-sixth of the time total (Three of a Kind: 4.83%, Straight: 4.62%, Flush: 3.03%, Full House: 2.60%, Four of a Kind: 0.17%, and Straight Flush: 0.031%).”

[SS] “But so much depends on the betting that this information is almost useless, except for one important point. Beginners have a bad habit of getting over-enamored of their overpairs. Even without any clues from the betting, an overpair is beaten by almost two-fifths of all hands. Top pair is even worse than that. So if someone who isn’t totally crazy keeps betting (or even just calling your bets) with no obvious draws, you can lay down your overpair on the river with no regrets.”

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