To simplify it, say we have the following scenario:

We're in the HJ with Kd9d, a few people limp in EP, we raise it quite big to 8x the bb. We get 4 callers.

We're 200 bb effective.

The flop comes Ad, 9c, Qd (pot 40 bb)

We put in a continuation bet of 60% pot, 24 bb. Everybody folds except BTN.

Turn Jc (pot 88 bb)

We bet again, 48 bb.

Now BTN goes all-in for another 120 bb.

Do we have to call? If we assume villain's range only conists of value hands that have us beat, we have roughly 31% vs that range.

Am I calculating the EV correctly in this way: we need to call off our remaining 120 bb in order to win a pot that is now the size of 304 bb (the initial size of the pot OTT, 88 bb + our bet 48 bb + villain's shove for 48 bb + 120 bb)?

Using the EV formula, EV = (W%*$W) – (L%*$L), my results tell me that the call would be very slightly +EV. Does this mean that we absolutely have to call here in order to play this situation profitably, assuming we get ourselves into this spot by betting OTT?

Well, yeah, in a cash game. You would have made this decision before you bet the turn. A check on the turn would allow BTN to make a mistake with bet sizing or free river. As played, neither player can make a mistake, unless BTN is a nit and you are trying to shovel him money.
I believe you forced him into an optimal play, basically.

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If he is mostly value, then it is
-EV since I cant even find the hands that offer you 31 percent. Also you are putting in 39.4 percent of the monies, with a call. But I assume you meant for the example to offer you break even odds. You need several bluff combos in villain range here.


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After villain's raise, the pot is 304bb and you need to call 120bb.
To break even, you need equity of 120/(304+120) = 120/424 = 28.3%

If you think/calculate you have as much as 31% equity*, it's a clear call, since your final call represents 28% of the final pot, but you expect to get back 31% of the pot on average.

* I think you're more likely to have nearer 29% equity, since villain probably has some straights, sets and two pairs, so not all your "outs" are live.

Dang, math fail on my part.


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