Run it once or twice

[Red_Diamond]

I never looked heavily into running it twice. I know it is for those who don't like variance and big swings, but I had also assumed it gave an extra break for the underdog. I used to think, if I'm all in on the flop with AA, and my opponent is all in with KK, it's best to refuse any extra runs. I wouldn't want my opponent to get any extra chances to catch his 2-outer. If he doesn't catch it the first run, well he has even greater chances on the second due to kings being higher enriched in the deck.

That being said, because we are playing for HALF-pots, I understand that it reduces variance, and starts to make sense. I'm not going to argue with anyone, if the majority says EV doesn't change... then I'll go with that.

But I would like to see some explanation on that Degenerate case.

[ApeAttack]

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I'm going to have to go against the grain here and disagree...running it twice (slightly) slightly changes the EV for both players.
ofcourse it makes sense that if there is replacement then it would be EV neutral but without....not so much.

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Prove that is does not change the EV for both players. You can't, because it doesn't.

[GiantBuddha]

First off, I apologize for starting a thread that's almost the same as this one. I'm new and my search for the subject didn't turn up anything. That said...

I'm under the impression there is a logical proof for this, and have actually been working on one myself, with little success thus far. Does anyone know where I could find such a proof?

Most of the logical answers don't offer so much assurance, as they sound reasonable, but don't take everything into consideration (regarding not replacing cards, etc.) and aren't precisely proofs. Obviously if you run it once, and you have a 4/44 chance, you'll win 1 out of 11 times. And if you run it all 44 times, you'll win precisely 4 of those times. However, this doesn't address what happens if you run it 3 times. Or five times. I've taken it upon myself to figure out the case of 4 outs remaining in 44 unseen cards with one card to come, and it does in fact work out to the same expectation as running it only once. But this is not a proof, either. Just an example that works.

[Aashaas]

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There is no difference in EV over the long run... but there are other reasons why you may want to run it only once.

Barry Greenstein said that he never runs it more than once for psychological reasons:

(1) people will be more scared to move in on him. If he runs it more than once, players may feel that they have some 'insurance' and will get (on average) a portion of their money back. These players might push all in with a draw more often if they feel they will win a portion back by running it multiple times. [...]



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Isn't that just what you want? They are pushing while being an underdog to your card. I usually don't want to demotivate people to make those plays.

[holdme]

It's been proven several times before that it does not change EV. I don't want to find one of these threads. You can. Search is your friend. Someone should sticky this or one like this so I can stop seeing the topic whenever I browse here.