[Pokey]

To those who are advocating a smaller bet:

What smaller hands call a half-pot bet that fold to a pot-sized all-in bet? I think the added $40 from a called push more than makes up for the few extra folds this play earns. I'd prefer to get the money in while he's still got hope for a lucky river card, rather than waiting to let him see that he's iced before I try to get the cash.

Plus, I'm hoping that my aggressive win-before-the-flop betting style has planted just enough suspicion in his head to warrant a call by a hand that I'm clobbering.

I hear what you're all saying, but I'm vividly reminded of NLHTAP's numerous discussions of small value bets versus large value bets, and the EV calculations. Unless this overbet reduces the probability that villain calls by a TON, it's the better choice. This is especially true since almost 20% of the deck counterfeits my hand if I'm ahead, meaning that scooping the pot right now is not the worst thing that could happen.

Example: assume villain has QQ. If villain calls, I win 77.3% of the time at showdown, and tie 9.1% of the time. Say that villain calls 50% of the time when I make a small value bet of $30. My EV from this play:

EV = 0.5*(+$66) + 0.5*(0.7727*(+$96) + 0.0455*(-$30) + 0.1818*(+$33)) = +$73.91

Now, say that villain calls a $74 push with probability C:

EV = (1-C)*(66) + C*(0.7727*(140) + 0.0455*(-74) + 0.1818*(+$33))

This gives the same EV as the smaller value bet when C = 17.7%! So long as villain doesn't reduce his calling probability from 50% down to below 18%, we're better off pushing.

Why do we get such a surprising result? Because our hand is still reasonably fragile, and there's a BUNCH of dead money in the middle. At this point in the hand, having villain fold isn't a bad thing, even against a hand as badly beaten as QQ. If he's calling, I need to make sure it's a BIG mistake for him, and with as much dead money as there already is in the middle, that requires a good-sized bet. Note that with as much dead money as is already in the pot, I'm not even making much of a mistake in pushing against a made straight: my full house outs make this a roughly break-even play.

The large pot and the numerous cards that kill my hand make pushing here a good thing, even if villain folds almost always. The more I think about this problem, the more I think a smaller bet, even if it gets called extremely frequently, would be a mistake.

EDIT: math is hard.