Should You ‘Run Them Twice’?

You buy into a $1-$2 no-limit hold’em cash game for $100. Three hours later, you have worked your stack up to $450. You are feeling good about yourself, and are starting to have fleeting thoughts of leaving with your nice profit. You decide to play one more round and see what happens.

In the big blind, you pick up the 8 7. Everyone folds to the small blind, who raises $5 more. You check his stack, and he has around $600. You call with position. The flop is 9 6 2. The small blind makes a continuation-bet of $10. With tremendous implied odds for your open-end straight draw, you call.

Delightfully, the turn is the 5. You have the absolute nuts. The pot is $34 and you start thinking about how you can get the maximum out of your opponent. Again, he bets — this time, $30. Hoping that he has something, you decide to slightly overbet the pot and raise $100 more, putting in $130. He starts thinking. Well, at least he didn’t fold right away.

All of a sudden, he looks up and says, “I’m all in.” A fleeting thought crosses your mind that he can have the 8 7 and be freerolling you. Then you realize that there are many other hands he can have on this very nonthreatening board, including a set, two pair, pocket aces, or maybe even a bluff. You certainly can’t fold the nuts here, so you call.

The pot now has $900 in it (your $450, and his). You flip over your straight, and he turns over the A K. He was making a big move with two (worthless) overcards and a flush draw. If he makes his flush, you are broke.

“Would you like to run it twice?” he asks. You are not sure. You are a big favorite, so why give him two chances? On the other hand, half a pot is better than none if the next card to hit the board is going to be a spade. What should you do?

Before we decide, let’s look at the mechanics and math of running it twice.

The mechanics: If you agree to run it twice, the dealer will divide the pot into halves. He will then burn and turn, and award half the pot to the winner. Without replacing the dealt cards or shuffling again, he will burn and turn again. The winner of that round wins the second half of the pot.

Had this happened on the flop, the dealer would have put out a turn card and a river card, then put out another turn card and river card, burning each time.

The math: Let’s look at the math of your straight against his flush draw. You are looking at eight cards faceup, so there are 44 left in the deck. Nine are good for him and 35 are good for you. At this moment, you are entitled to 35/44 of the pot, or $715.91. If you played this out millions of times, that is just about what you would average. In fact, you could equitably offer to split the pot right now, with you taking your $715.91 and your opponent getting the balance. But you came to play poker; you will see this through to the end.

What impact does running it twice have on your expectation? More math:
You could win both: 35/44 × 34/43 = 1,190/1,892 = .629. (Notice that after having won the first one, there are only 34 good cards left for you, and 43 in the deck.)

You could win the first one and lose the second one: 35/44 × 9/43 = 315/1,892 = .1665. (The 9/43 is the chance that he has to win the second pot.)

You could lose the first one and win the second one: 9/44 × 35/43 = 315/1,892 = .1665.

Thus, the chance that you will win one of two is the sum of those: 630/1,892, which is .333.

Finally, you could lose both: 9/44 × 8/43 = 72/1,892 = .038.

62.9 percent of the time, you will get back $900: .629 x $900 = $566.10.

33.3 percent of the time, you will get back $450: .333 x $450 = $149.85.

3.8 percent of the time, you will get back $0.

Thus, your total expectation for running it twice is $566.10 + $149.85, which is $715.95, virtually the same number you got by running it once. It makes no difference mathematically whether you run a hand once or twice (or, for that matter, three or four times, but you will have to do the math yourself).

Why run it twice? The biggest difference is the chance that you will lose it all. If you run it once, you will lose the whole pot nine times out of 44, which is 20.5 percent of the time. If you run it twice, you will lose the entire pot less than 4 percent of the time. You sacrifice some of your possible earnings when you win for a greater assurance that you will at least get your money back.

If your cardroom permits it, running hands twice smooths out swings for both the player who’s ahead and the player who’s behind. Remember, mathematically, you lose nothing.

Are there times that you should not agree (or offer) to run hands two or three times? In general, the more comfortable you are with the swings, the more you may want to simply gamble on one trial.

Sometimes your game will have a very aggressive player who is constantly making big semibluff moves. If he wins because you fold, he is very happy. When you call him, he always clamors to run it several times, so that he won’t lose large amounts. He wants to keep swings as low as possible, so that he can continue stealing.

If you can afford (financially and psychologically) to gamble, decline his offer. By seeing that he will face a bigger gamble if he makes an unsuccessful move on you, he may be less likely to try it.

Apart from that, you can reduce your risk with no loss of expectation just by agreeing to run it twice.

Many thanks to Ed Hill for his suggestions and help with this column, the example, and the math.

Barry Tanenbaum is the author of Advanced Limit Hold’em Strategy, and collaborator on Limit Hold’em: Winning Short-Handed Strategies, both available at www.CardPlayer.com. Barry offers private lessons tailored to the individual student. Please see his website, www.barrytanenbaum.com, or write to him at [email protected].