Calculate odds to call for a chop in a split pot game
I've started playing Texas Holdem double board bomb pots. Typically the way the game plays is that it ends heads up on the river. Both opponents have the near nuts on one side of the board, and on the other they have a hand that beats some bluffs. Then it becomes a game of chicken. One opponent blasts, the other has to decide if they should call for a chop or not.
Pot - $2000
My opponent goes all in for $2000.
Total pot - $4000
I have 80% equity on the top board.
I have 5% equity on the bottom.
Can I call the bet?
If I am going to call a bet to chop, is it better just to bet myself?
3 Replies
80% of the time you'll win 2000 on the top board (1600) and 20% of the time lose $1k (-200) for an EV of +1400 on the top board.
5% of the time you'll win $2K on the bottom board (100) and 95% of the time you'll lose $1K (-950) for an EV of -850 on the bottom board.
Thus your overall EV of calling is $550. A clear call.
If you call there are 3 possible monetary outcomes:
1 You get scooped (- $2k)
2 you chop (+$1k)
3 you scoop (+$4k)
Your odds of getting scooped are 95%*20%=19%.
Your odds of scooping are 80%*5%=4%.
Odds of chopping is the remaining 77%.
+1k*77= +77k.
+4k*4 = +16k.
-2k*19= -38k.
77+16-38= 55k.
55k/100= $550.
That’s your EV for calling.
This happens in a lot of split pot games. PLO8 is an obvious example because only a certain starting hand class makes the nut low so you see the nut low or second nut low fairly often. A lot of the profit in these games comes from calling rivers to chop and splitting what was already in the pot from when it was multiway.
In bomb pot games check-raise goes up in value because you're often going to be splitting top board/bottom board and if you can trap a third player in the hand when you've got the nuts on one board you can profit from the chopped pots.
