Thanks to everyone who participated in the second and final part of the Hand of the Week. You can find discussion of the flop play here. I was really impressed with the quality of the comments. It didn’t seem like anyone was confused about a check was worth considering, and in fact you all made some good points that I failed to consider in game.
I’ll start by saying that although there are some interesting concepts at play here, this specific spot is not really an important one to get right. For one thing, it’s not exactly an everyday occurrence. Perhaps more importantly, everyone seems to be in agreement that Villain is unlikely to put another dollar in the pot no matter what Hero does, so we can expect the Expected Values of all available options to be quite similar.
Value Betting
There’s some game theory here related to whether Villain has any incentive to call the river with a bluff-catcher, whether Hero should be able to value bet an unimproved bluff catcher, whether Villain should ever check quads, etc. But there’s an important exploitive concept at play as well, which James Antill raises quite succiently: “Villain can’t make a calling mistake if we don’t bet.”
In theory there shouldn’t be much value in betting. Villain took a very polarizing line, and any showdown value he had would have been better played as a bluff-catcher than as such a big bluff. So really, he should either have a boat or better, or a hand that couldn’t even consider calling.
Of course, there also shouldn’t be much risk in betting. I’m embarrassed to say the very important question of whether I blocked 64s did not occur to me at the table. I don’t know for certain that the river was the 4d – I made up the suit for this post, wrongly thinking it unimportant. Of course, I did consider that Villain had no real reason to check a big boat or quads on the river. After all, we’re seriously considering not betting a hand that would almost certainly call a shove! Checking could induce a bluff, but what hand that benefits from bluffing could Hero take to the river?
Patrick raises the very good point that, “As played, it’s kind of a weird SPR by the river that makes getting stacks in hard to do without either an over bet or a raise, which…I’m not sure, but I would say it leans away from V having a stack able value hand like 33.” However, even seemingly good opponents make mistakes, and we want to give them the opportunity to do so. Both checking quads and calling the river without a 6 are probably mistakes, but the latter is a much easier mistake to make.
I don’t agree with James Antill that, “If villain takes this line with worse and is going to hero call it then he’s as likely to do it with 1.5x as 0.25x pot.” Our best hope is to offer Villain such good pot odds that he can’t resist calling (or spazzes out and shoves) with a hand that he wasn’t originally thinking of as a bluff-catcher. He certainly ought to be price-sensitive, given how easily Hero can have a 6 and how difficult it is to find a bluffing candidate.
Bluff Shoving
I also didn’t consider the option of shoving to get Villain off of a chop. I don’t think it’s the best way to play the hand, but it is worth considering, to kudos to those of you who thought of it.
Sean is right that if Villain is equally likely to check any given combo of 6x or 44, and he always folds the 6x, then shoving would be best. However, I think it’s far from certain that Villain will fold a 6 to a shove, even if that would be the correct play.
Checking
The one argument in favor checking that hasn’t yet been made is that we get to see Villain’s likely bluff. It’s very rare that I factor the value of seeing the Villain’s cards into my decision, and I can’t claim that I did so in real time either, but it did prove a bit interesting. And in this case, where there’s so little value in betting anyway, the small value of seeing Villain’s cards might actually outweigh it.
Results
I checked back, and Villain showed As 9s. This certainly raises the question of whether he might have called a $400 bet, but is interesting for other reasons as well. For instance, I don’t think it’s the best candidate for either donking or three-betting the flop. In fact, it probably has enough showdown value to check and call a bet.