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