Photo courtesy of Jennifer W
Running it twice means you deal the rest of the hand twice and give half the pot to the winner of each hand.
Example of running it twice
Two players move all in on the turn in a cash game, creating a $1,000 pot. One has a set, the other a flush draw. They agree on running it twice.
The first river card is a blank. The set wins half the pot, or $500. The second river card fills up the other player's flush. He wins the rest of the pot, also $500.
If they hadn't run it twice, the set would have won $1,000.
EV does not change - variance does
Whatever you may have concluded from the above example, your EV doesn't change if you run it twice. If you're a 25% dog, you're a 25% dog - unfortunately.
On the other hand, the variance goes down. This is because you decrease the probability of the most extreme outcomes and introduce new outcomes in the middle of the scale.
Detailed example of running it twice
For example, you're all in on the turn against one opponent with a 25% chance to win. Below are the numbers for running it once, twice and three times.
We use the standard deviation instead of the variance just because it's easier to read, but the effect is the same. Read more about variance and standard deviation here.
Run it once:
Possible outcomes | Probability (%) | EV | Standard deviation |
0 | 75 | 0 | |
1,000 | 25 | 250 | |
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Run it twice:
Possible outcomes | Probability (%) | EV | Standard deviation |
0 | 56 | 0 | |
500 | 38 | 190 | |
1,000 | 6 | 60 | |
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Run it three times:
Possible outcomes | Probability (%) | EV | Standard deviation |
0 | 42 | 0 | |
333 | 42 | 140 | |
667 | 14 | 94 | |
1,000 | 2 | 16 | |
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You can see how the probability moves away from the extremes and into the middle. The EV remains the same while variance (or standard deviation) goes down.
Conclusion
If you're behind, you're behind. Running it twice can't help you. If anything, it makes it more certain that you will not win the whole pot.
But it does take down your swings, regardless if you're behind or in the lead. If you want a more stable curve, definitely run it twice or even more times.
If you run through all the remaining cards, you'll end up really close to your EV.
/Charlie River
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Comments on this Article
Charlie River (Nov 01, 2010)
Okay BB, I changed that writing a little bit to avoid misunderstandings.
Note, though, that taking a high variance route in this case just means not running it twice. I'm dissecting the phenomenon of running it twice, not advicing anyone to play in any particular fashion.
BB (Oct 29, 2010)
Say your a beginner and you're starting out while taking some losses. If you run those twice you'll be paying out slowly. Picking up some half pots. Keeping money on them.
I think EV is flawed because it's got no relation to poker. There made up numbers that don't involve or apply to poker. They just make up ratios to see common poker logic.
BB (Oct 29, 2010)
"If anything it makes it more certain you will lose."
As if taking a high variance route will cure that.
Charlie River (Oct 29, 2010)
Where am I saying that? Running it twice decreases variance. EV remains unchanged. If you're behind, you're behind.
BB (Oct 29, 2010)
You want them to increase variance and gamble to avoid the loss? There's a flip side to this and increasing variance on a losing side is not proper advice.
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