Originally Posted by BelgoSuisse
ok, so let's do some math and assume your read is 100% correct, which i think is a bit unsure. Could have small overpairs and things like that in his range, imo. Anyway, let's trust you.
you play for stacks on flop. you have 65% equity vs. a set and that means your EV is $260
you wait turn to play for stacks. You check-fold when the board pairs, i.e. 7 times out of 45, which keeps $180 in your stack. 34 times a blank comes and you stack with 77% equity, which has an EV of $308, and 4 times out of 45 a scare card (4 or 6) comes and villain flats your $30 bet on turn, you check fold river when it pairs (24%), and he hero calls another $80 bet on river when he wiffs (76%).
you EV there is (7*180+34*308+4*(0.24*150+0.76*330))/45 = $286
if he fold river when he board does not pair after the scare card hits, that's only (7*180+34*308+4*(0.24*150+0.76*250))/45 = $280, which is still +EV compared to stacking on flop.
Would you actually rather wait till river to play for stacks? Probably even more +EV, tbh
Belgo, I'm not sure where that math came from, but I'm preeeety sure you can't have an EV that is larger than your opponent's stack. That may be a working relative measure of value, but it's not the expected value
For the shove decision I'm getting the following:
EV = 0.65 * ($213) - 0.35 * ($192)
EV = 138.45 - 67.20
EV = $71.25
For the delayed approach, there are 32 safe cards, 6 scare cards for him (3 each of 6 and 4), and 7 cards where you lose and fold.
EV = 0.71 * (0.80 * $213 - 0.20 * $192) - 0.16 * ($12) + 0.13 * (0.80 * $122 - 0.20 * $42)
EV = $93.72 - $1.92 + $11.60
EV = $103.40
So it is clear that at least with the assumptions Belgo made, the delayed approach is far more profitable than getting it all in on the flop. Although the upside is less ($93.72 is less than $138.45), there is almost no downside. That is because you get to bail on the hand at little cost if the board pairs.
I think the deepness of the relative stacks is very important in this decision. Here's looking at what would happen with relative stacks of only $50 (assuming a turn shove, not a bet of $30):
EV(shove) = 0.65 * $63 - 0.35 * $42
EV(shove) = $40.95 - $14.70
EV(shove) = $26.25
EV(delay) = 0.71 * (0.80 * $63 - 0.20 * $42) - 0.16 * ($12) + 0.13 * (0.80 * $63 - 0.20 * $42)
EV(delay) = $23.86 - $1.92 + $4.37
EV(delay) = $26.31
So when you reduce the amount of money you have behind, you can reduce the benefit of this approach down to a negligible amount.