For people who think running it twice changes EV
 

Here are some EV equations for running it twice, anyone who thinks otherwise is mistaken and you can link to this thread for future reference.

Hypothesis – EV of running it twice after the flop is the same as running it once after the flop.

For this situation we are going to have a 70% favorite vs. a 30% dog for a $100 pot

EV(Running Once for Favorite) = (.7 * $100) – (.3 * $100) = $70
EV(Running Once for Dog) = (.3 * $100) – (.7 * $100) = $30

Now to win the entire pot they have to win both runs

Since this is like flipping a coin twice we can use this as an example

Pr(flipping heads or tails twice) = (.5) * (.5) = (.25) or 25%

Pr(winning twice for favorite) = (.7) * (.7) = (.49) or 49%
Pr(winning twice for dog) = (.3) * (.3) = (.09) or 9%
Pr(splitting) = 1 – ((.49) + (.09)) = (.42) or 42%

EV(Running Twice for Favorite) = (.49 * $100) + (.42 * $50) = $70
EV(Running Twice for Dog) = (.09 * $100) + (.42 * $50) = $30

Conclusion – Running it twice is the same EV as running it once, if it has any effect whatsoever it is only psychological

Re: For people who think running it twice changes EV
 

It's a little more complicated than this. You're assuming that the events are independant. Since cards are not being replaced the events are not independant. For example, if you win the first time there are fewer favorable cards left in the deck, so you're less likely to win the second time. What you've done doesn't show that running it twice doesn't alter the EV. From what I understand it's actually quite difficult to prove that running it twice does not alter the EV.

But yeah, running it twice doesn't change the EV, only the SD.

Re: For people who think running it twice changes EV
 

[ QUOTE ]
It's a little more complicated than this. You're assuming that the events are independant. Since cards are not being replaced the events are not independant. For example, if you win the first time there are fewer favorable cards left in the deck, so you're less likely to win the second time. What you've done doesn't show that running it twice doesn't alter the EV. From what I understand it's actually quite difficult to prove that running it twice does not alter the EV.

But yeah, running it twice doesn't change the EV, only the SD.

[/ QUOTE ]

Well I guess I found the shortcut because this will work with any situation.

Re: For people who think running it twice changes EV
 

While the mean you calculated was correct, the distribution you used for your calculation was wrong.

Re: For people who think running it twice changes EV
 

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While the mean you calculated was correct, the distribution you used for your calculation was wrong.

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Dude you're not making much sense...There is no distribution above and unless I'm mistaken the mean means average which I did not calculate.

Re: For people who think running it twice changes EV
 

You're assuming the distribution of the 70% equity guy is:

$0 with p_0 = 0.3*0.3
$50 with p_50 = 0.3*0.7 + 0.7*0.3
$100 with p_100 = 0.7*0.7

That is not the case. p_0 and p_100 are less than what you claim; p_50 is greater than what you claim.

Re: For people who think running it twice changes EV
 

I don't think anyone believes it changes EV. Its obvious it doesn't.

Re: For people who think running it twice changes EV
 

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I don't think anyone believes it changes EV. Its obvious it doesn't.

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Maybe not in the poker theory forum but in the other ones, definitely people argue about it all the time and I'm tired of it.

Re: For people who think running it twice changes EV
 

[ QUOTE ]
[ QUOTE ]
I don't think anyone believes it changes EV. Its obvious it doesn't.

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Maybe not in the poker theory forum but in the other ones, definitely people argue about it all the time and I'm tired of it.

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The type of people who are convinced running it twice alters the EV usually won't buy a bunch of mathematical mumbo jumbo anyway. You know you're right, it's not worth arguing over.

Re: For people who think running it twice changes EV
 

Running it twice is done to cut down on variance, right?