Poker News

Richard G. Burke

Straights are the most misunderstood Hold’Em hands. Some “experts” opine, “Don’t play three-gap connectors, because when you make a Straight it could lose to a higher one,” and, “Never play the “idiot end’ of a Straight.”

That’s bunk. If you have the 2nd-nut or 3rd-nut Straight using both your cards, then bet it up because it’s quite likely you’ll have the best hand!

For the results that follow we spare showing you all the intermediate computations. We do want to point out that these results are not from simulations: they are from exact, mathematical proofs for a ten-handed Hold’Em game.

Suppose you have the 2nd-nut Straight, e.g., K-9; with Q-J-T-3-2 rainbow on the table. There are ten cards that could endanger your hand: four Aces; three Kings; and three Nines. Those danger-cards could be scattered among your nine opponents, or they could be concentrated in the hands of one, two, three, four or five opponents. The chances that four or five each hold two danger-cards are negligible.

The probability that your 2nd-nut Straight will win, lose, or tie depends on exactly which two danger-cards are held by your opponents. Each of the cases was examined and the table below shows the combined probability that your 2nd-nut Straight will win, lose, or tie.

You will win with your 2nd-nut Straight 81.9% of the time; lose to the nut Straight 10.6% of the time; divide the pot with one opponent or more 7.5% of the time. That’s not too shabby. In fact, it’s surprisingly good.

Suppose you have the 3rd-nut Straight, e.g., 9-8; with Q-J-T-3-2 rainbow on the table. If anyone has Ace- King or King-Nine, then you will lose. If anyone else has Nine-Eight, then you will tie. There are fourteen cards that could endanger your hand: four Aces; four Kings; three Nines; and three Eights. The probabilities are tiny that four or more opponents each hold two danger-cards, even in a ten-handed game. The probabilities that zero to three opponents each hold danger-card pairs are shown in the third row below.

The probability that you will win, lose, or tie depends on exactly which danger-card pairs the opponents hold. We examined all the cases: the results are that when you hold the 3rd-nut Straight, you’ll win about 71.1% of the time; you’ll tie 5.6% of the time, about one time in eighteen.

If there are four cards to a Straight, three or more suited cards, and/or there’s a pair on the table, then you could lose to a higher Straight, a flush, a full house or better. You’re a good enough player to slow down in the face of those threats, or muck when you’re sure you’re beaten.

If the nut Straight would be best after all the cards are out with exactly three connectors on the table, then the 2nd-nut Straight will win about 82% of the time and the 3rd-nut Straight will win 71% of the time. The myths about Straights are now debunked: you can bet on that.

Mr. Burke is the author of Flop: The Art of Winning at Low-Limit Hold ‘Em, 2nd ed., available from amazon.com, gamblersbook.com, and www.kokopellipress.com.

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