Tricky flops: paired boards, draws, small pairs

Lesson 10 of 23 · Perfect strategy I: lowest edge · 7 min read

Where the flop rules need care, and where they're slightly wrong.

The flop rules from lesson 9 are short on purpose. Here are the cases that trip people up.

Pocket deuces. You checked them preflop, and they stay a check on a flop like K♦︎9♣︎5♥︎: −0.861 for checking against −0.964 for 2x. Any dealer pair beats them.

"Two pair" made from the board's pair. 2♣︎2♦︎ on 9♠︎9♥︎5♣︎ is technically two pair, nines and deuces. But the nines belong to everyone, and your deuces are the lowest pair there is. Perfect play checks (−0.131 vs −0.284 for 2x). The basic rule says "two pair, bet 2x" here, which is one of its rare mistakes.

Straight draws. An open-ended draw like 9♣︎8♦︎ on 10♠︎7♥︎2♣︎ is a check (−0.140 vs −0.235). A straight comes only about 1 time in 3 by the river, and you can wait and bet 1x when it does. With a higher draw like 10♣︎8♦︎ on J♠︎9♣︎4♥︎, the two options are dead even (−0.1526 vs −0.1532). Either is fine.

Flush draw plus straight draw. 7♥︎6♥︎ on 8♥︎5♣︎2♥︎ has a flush draw (no high heart in hand) and an open-ended straight draw. Perfect play bets 2x (+1.123 vs +1.044), but the basic rule checks because your best heart is only a seven. It's a small slip.

Overcards. K♣︎3♦︎ on 8♠︎5♥︎2♣︎: king high with no pair. Check (−1.108 vs −1.373), and decide on the river.

Trips on a paired board. J♦︎5♣︎ on 5♥︎5♠︎K♣︎ is three fives, using your card. Bet 2x (+3.845 vs +2.956).

Put together, all of these slips cost very little. Using the three flop rules instead of perfect flop play costs 0.086% of the Ante: about 26¢ an hour at $10. In this chapter the EV sheet always shows you the exact answer.

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