Poker News

Richard Burke

Fred stood from his $4-8 Hold’Em game and stumbled over to the row of chairs where I was working on a crossword puzzle and slumped into a chair. Why him, he wailed. He had raised with pocket Deuces in late position in an unraised pot, got a few callers and this beautiful flop, As-7h-2d.

It was checked around to him. He bet, the Small Blind folded and the Big Blind raised. The others folded. Fred re-raised and the Big Blind capped it. Fred’s pretty wary, so he just called the Big Blind’s bets on the Turn and River because his Set didn’t improve. The Big Blind’s Set of Sevens spanked him for $40. Fred, I told him, it’s still a nice sunny day in late fall. Take a walk outside and cool off for a bit before returning to your game. I’ll have some answers for you tomorrow.

There were three Sevens and three Aces that could make a Set for Fred’s opponents. If none or only one of the six had been dealt, then Fred’s Set would have been best on the Flop. The table nearby shows the probability for each of the patterns of threat cards being dealt to Fred’s nine opponents. The probabilities of the first seven patterns sum to .87815, so 87.8% of the time, those six cards either won’t be dealt or will be scattered among Fred’s opponents such that a Set isn’t possible.

The danger occurs when two threat cards are in one or more opponents’ hands. About 12% of the time two or more threat cards would be dealt suchthat one or two Sets would be possible. So, I had to look at the fine structure of each pattern.

There are nine patterns where two or more of the six cards would be in enemy hands. For example, if all six were dealt out, then they could be in the pattern 2-2-2, and Fred’s Set would have a 40% chance to prevail. Tabulating the chances for all the patterns obtains the little table shown below.

The chances were less than 5% that anyone else would have a pocket Pair that became a Set on the Flop. Fred was the victim of some bad luck because 95% of the time his Set would not face another Set on the Flop.

The next day, I informed Fred of the results and tried to console him. He understood that he had been unlucky, but he said his whole session had been unlucky, on the Flop, the Turn, and the River. Fred’s chance of being dealt a pocket Pair was 1 in 17. The chance of his flopping a Set was about 1 in 9, (just a Set, not a Set or better). The chance of anyone else flopping a Set was about 1 in 20, for a combined chance of roughly 1 in 3200. If, before the hand was dealt he were to offer anyone200 to 1 odds that (a) he wouldn’t have a pocket Pair, and (b) even if he did have a pocket Pair, he wouldn’t flop a Set, and (c) even if he did flop a Set, no one else would flop a Set, then he’d have a huge edge. You can bet on that.

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