Correcting Poker Odds on Draws

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Knowing when there is enough money in the pot to make a draw worthwhile is one of the most important skills in limit poker . Of course, you have to fi gure the number of cards that help you and do a little quick math, but cheaters’ jobs are made easier when they know that one or more of the cards they need are out of play because their partner folded them before the flop.

As an example, consider the hand shown here:

                                                            

Cheater 2                                                                                             Cheater 3

Cheater 1

89 is a decent enough hand, but not when two of the Tens and one of the Fives you need for a straight are out of play.

In this case, there are three colluding players at the same table, but two of them folded before the flop after the remaining cheater called with 8 9. The flop of 6 7 A is pretty good, giving the cheater an open-ended straight draw, but when a non-teammate raises after another player bets, the cheater must fi gure they are either up against a set, two pair, or an Ace with a good kicker. Four players each put $20 into the pot before the flop, for a total of $80. The first player bet $10 and the second player put in $20, for a total of $110. The cheater at this point can draw to his possible straight or fold. Under normal circumstances, the player would be drawing at eight cards: all of the Fives and all of the Tens. In this case, however, one of the other colluding players folded T5 before the flop, and the other threw away K5. That means three of the cards the remaining cheater needs for his straight, which he fi gures he needs to win, are out of play.

If the cheater thought he was drawing to eight out of 47 unseen cards, the odds of completing his straight on the next card would be 39 to 8 against, or just under 5 to 1. He will have to call $20 to win the $140 in the pot, which is 7 to 1 odds on his money. If he misses, he gets another shot on the river. Assuming there is $200 in the pot after the turn and the board has not paired, the cheater will be getting 10 to 1 odds on what is essentially a 5 to 1 draw. Calling on the flop is correct, and calling on the turn would also be correct so long as the board didn’t pair.

If the cheater knows he is only drawing to five out of 47 unseen cards, though, the math changes. It will cost him $20 to call after the flop, which means the $140 in the pot gives him 7 to 1 odds on the money. Because the odds against him completing his straight are 42 to 5, or 8.4 to 1, against, he knows he should fold.

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