For people who think running it twice changes EV

[The 13th 4postle]

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

[DrVanNostrin]

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.

[The 13th 4postle]

[ 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.

[DrVanNostrin]

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

[The 13th 4postle]

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

[/ QUOTE ]

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.

[DrVanNostrin]

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.

[pzhon]

To summarize, running it twice doesn't change EV. However, this explanation was terrible, incorrect, and not convincing to anyone who was not ready to be convinced.

Unfortunately, I don't think there is any really simple, convincing explanation (which is not a given, despite the controversy). One attempt is to say that burn cards don't affect equity, so the equity of the second time is the same as the equity of the first time. Running it twice takes the average of using burn cards or not. This may not be convincing for people who have no intuition about equity, or who think burn cards may hurt one player, but I think it is more commonly accepted that burn cards are harmless than that running it twice does not favor either player.

By the way, there are more than psychological effects. Running it twice may decrease the amount of money on the table, on average, since players will not rebuy after a split pot. Running it twice may keep the game going when a player is not willing to rebuy.

[The 13th 4postle]

[ QUOTE ]
To summarize, running it twice doesn't change EV. However, this explanation was terrible, incorrect, and not convincing to anyone who was not ready to be convinced.


[/ QUOTE ]

In defense of my post, I made a very simple EV equation to convince those non-believers and came out with the right answer. Yeah it could be a lot more complicated and come right at the same answer. If the process is wrong it would not get the right answer plain and simple.

[ShaneP]

[ QUOTE ]
[ QUOTE ]
To summarize, running it twice doesn't change EV. However, this explanation was terrible, incorrect, and not convincing to anyone who was not ready to be convinced.


[/ QUOTE ]

In defense of my post, I made a very simple EV equation to convince those non-believers and came out with the right answer. Yeah it could be a lot more complicated and come right at the same answer. If the process is wrong it would not get the right answer plain and simple.

[/ QUOTE ]

Well, when you're trying to convince someone of something, and you have an obvious error in your argument, it's sort of hard to convince them. It might give the same answer, but it can be coincidental--and if you don't do things correctly, it could have been wrong, and there's no way of really knowing, and that's the problem...if the people you're trying to convince don't believe the answer to begin with, and see problems in your argument, you've gone nowhere.

[Charles256]

[ QUOTE ]
[ QUOTE ]
To summarize, running it twice doesn't change EV. However, this explanation was terrible, incorrect, and not convincing to anyone who was not ready to be convinced.


[/ QUOTE ]

In defense of my post, I made a very simple EV equation to convince those non-believers and came out with the right answer. Yeah it could be a lot more complicated and come right at the same answer. If the process is wrong it would not get the right answer plain and simple.

[/ QUOTE ]

Just so we're clean the process can be wrong and you still get the right answer. Several years of advanced mathematics will teach you that. So, it's not that "plain and simple". I'm not arguing with your conclusion though. Just trying to reduce the amount of people that are mis informed by your statement. A child going well the sky is blue today so 1+1 must be 2. Does that mean the child is right? Technically , yes. But boy is he screwed when the sky is dark blue the next day. :-D