[betterbettor]

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But he's probably only going to call you from way ahead, if he's got 2 cards higher than 7 and won't call without a pair (and who is putting 7.50 into a 5 pot without even a pair?)

That means that 66% of the time you make 2.50, while 33% of the time you lose 10, +/- for suckouts/when you hit a set and he hits a pair/etc.

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There's a few problems with your calculation. First, We win more than 2.50 when he folds. If we are considering play on the flop than the money already in the pot doesn't count as ours any longer, so if he folds we win the current pot, 5.75, and when we are behind we lose the 7.50 we bet on the flop.

So 67% of the time we win the pot, 5.75. The other 34% our 7.50 bet is called with about a 9% equity. So our EV is:

EV = (.67)(5.75) + (.34)(.91 * -7.5)
EV = 3.825 - 2.32
EV = +1.50

So we are +EV if we always shove and he only calls when we are beat, assuming he outflops us 34% of the time.

If we always shove, and he always calls, and we assume he has about 25% equity on average when behind (6 outs) and we have about 9% when we're behind (2 outs)

EV = (.67)(.75)(7.5) + (.34)(.91)(-7.5)
EV = 3.77 - 2.32
EV = 1.45

So he gains a small amount by always calling, but we are still +EV.

Of course all this is based on the somewhat tenuous assumption that he is only calling a 2.50 pre-flop raise with overcards to our sevens. I figured this was fair enough since if he also calls with 66-22 and 88-JJ they should more or less cancel each other out, and he probably wouldn't normally call with only one overcard (hands like J5o). I'm also assuming he's shoving preflop with AA-QQ, and we're ignoring cases where he flops a strong draw. With just a 9-out draw it's very slightly +EV for us, and in the worst case with a flush draw and two overs he has about 56% equity. Even including these cases I think we still have positive equity against a reasonable range that he can have after checking his posted blind and then calling a raise.

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Nice post, but I see a problem.

The EV cals in the bottom half of your post are ignoring the $5.75 already in the pot on the flop.

Intuitively, we want our opponent to call all the time (blindly). 67% of the time we are the favorite on the flop vs two overs, and we will deserve 75% of any more $ that goes into the middle when he misses.