I meant to keep it simple to start with, so back to my simplistic assumptions. You have 8 outs to a straight and we assume that you always win when you hit. There are 46 unknown cards in the deck. So 38 out of 46 times, you will loose your 0.38 call. 8 times out of 46, your profit will be the amount in the pot before your call (0.31+0.38) AND the rest of villain's effective stack (1.72) for a total profit of 2.41.
So 38 out of 46 times (82.6%) you loose 0.38 and 8 out of 46 times (17.4%) you win 2.41, so:
EV = 0.174*2.41 - 0.826*0.38 = 0.105
So with these simplistic assumptions your call would be profitable. However, as MMM said:
- when you make your straight with Ac or 9c, sometimes villain will have a flush and you will loose
- when you make your straight with Ac or 9c and villain does not make a flush, he may stall and not stack off
- when you make your straight with an A, villain may also stall and not stack off
On the upside though:
- if any non A or 9 club comes on the river, villain may stall or slow down and you might have a bluff opportunity. Wouldn't recommend vs an 88/8 though, but this goes to show that you can count some bluff cards as outs in some circumstances
- if a K comes and villain slows down and you check behind or call a small bet, you can win
You could try and quantify all that, but I am confident your EV will end up negative in the end because
1) we were too optimistic when we assumed that we would always win the rest of villain's money (in other words, we overestimated our implied odds, which is a common trait of bad players who call too lightly with draws)
2) we loose to a flush sometimes when we make our straight
So yes, it's a fold ott.
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