Situation while "running it twice" during home cash game

[PokerintheI]

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In this case it works out as:

River 1: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is: $261.3

River 2: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is $261.3

Total EV for Player A in scenario 2: $522.6

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Minor quibble- it won't be 80.4% the second time, it will be less. You've already run 3-5 cards out that didn't hurt your hand.

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I wasn't certain on this math, but here was my reasoning:

For the second river there are 2 possibilities:

There is a 19.6% chance you have 8 outs out of 45 because you hit your flush on the first river. This gives you a 17.77% chance to hit another flush card.

There is a 80.4% chance you have 9 outs out of 45 because you didn't hit the flush on the first river. This gives you a 20% chance to hit a flush.

17.77% x .196 + 20% x .804 =
3.469% + 16.08% =
weighted average chance of flush on second river = 19.55% = 19.6%

I felt like I might be missing something, but I'm not a math guru by any means.

[chillrob]

You are correct that the "meta EV" of keeping people in the game or hand could be good. I had never heard of people discussing running it twice before the money even went in.