Protecting against flushes

[bizaff]

Ok, here we go.

Hero should win about 63% of the time from the flop.

EV of pushing on the flop = 75 * .627 - 25 * .373 = 37.7

Assuming you check on the flop and take a look at the turn, the following outcomes are possible:

Card (# possible / % chance \ Hero win % @ Villain win % | EV of hero pushing now)

2 of clubs (1 / 0.022 \ 0.068 @ 0.932 | -18.18)
Other club (8 / 0.178 \ 0.000 @ 1.000 | -25)
Other Q/J (6 / 0.133 \ 0.727 @ 0.273 | 47.73)
A spades (1 / 0.022 \ 0.818 @ 0.182 | 56.82)
Any K (3 / 0.067 \ 0.750 @ 0.250 | 50)
Any other (26 / 0.578 \ 0.795 @ 0.205 | 54.55)

We know 2 things: we're not going to push if we're behind without odds to draw (we'll assume villain will push and not let us draw free if he hits his flush) and villain will not draw without pot odds. This means any negative EV is reduced to zero, and any EV over 50, villain won't pay off and will fold, in which case we win the 50 in the pot for an EV of 50. After limiting EVs (0 < EV < 50) and multiplying each EV by the chance to get that particular outcome FROM THE FLOP, we sum them together to get 39.70. (47.73 * 0.133 + 50 * (0.022 + 0.067 + 0.578))

It's fairly close, but if the villain will play as specified, check the flop and push a safe turn.