I just learned about the "Cash Out" option on poker stars. This is what it is:
All-in Cash Out is a feature that gives eligible players who are all-in the option to collect the value of their hand without having to play the hand to its conclusion.
I was trying to figure out if it would make sense to just Cash out every time you are behind. Here's the hand I was playing.
Hero: QS QH
VILLIAN: AD 9H
BOARD: 10D 6D 3C 8S
I don't know why he called an all in here but, using equity I am 84% to win and so he is 16% to lose. He took the Cash out. Turn was a Ace. Bad for him but what about in the long run?
I worked out the math two ways and I get two different answers. Same situation with a $10 pot. Easy to calculate.
84% equity x 100 =$840 I should win, on average, $840 for every 100 times I'm an 84% favourite.
But if I calculate this way it's different. I win 84 hands at $10 a hand that's $840. But then I LOSE 16 hands at $10 a hand.
840
-160
780.
Why are the two answers different? If I play 100 hands of poker and I win, on average $8.40 I should have $840. Not $780...
What am I doing wrong with my EV calculation here?
