Thanks to everyone who sounded off on the special HUD edition of “What’s Your Play?”. As always your comments were thought-provoking, and I was actually led to conclude that the answer isn’t as open-and-shut as I thought.
I’ll start by giving you the results, and then I’ll let you know how and why I made the decision that I did and what my thinking is on the most relevant HUD statistics.
Hero (SB) ($1000)
Preflop: Hero is SB with 7, K
3 folds, Hero bets $40, BB calls $30
Flop: ($80) 6, 8, 6 (2 players)
Hero bets $55, BB calls $55
Turn: ($190) K (2 players)
Hero checks, BB bets $150, Hero calls $150
River: ($490) 3 (2 players)
Hero checks, BB bets $772 (All-In), Hero calls $755 (All-In)
Total pot: $2000 | Rake: $3
Hero had 7, K (two pair, Kings and sixes).
BB had A, 10 (one pair, sixes).
Outcome: Hero won $1997
When I checked the river, it was with the intention of calling a reasonably sized bet. If Villain bets something in the neighborhood of $300, he can conceivably be value betting as wide as A8, and my K7 is an easy call. As many of you pointed out, the overbet almost certainly polarizes him to air or hands that are better than mine. I suppose he could be shoving a worse K, in which case we’d chop, but that’s not going to be a major consideration.
I don’t know enough about this player to tell you just how wide he’s value betting the river or whether he’s capable of overbetting as a bluff- some people just don’t do it.
When someone is representing a narrow range, a key question for me is how wide his range is for getting to this point in the hand. Without knowing anything a player’s specific river tendencies, I’m comfortable assuming that the likelihood of his bluffing a particular street increases considerably when he can get to that point in the hand with a lot of air.
Good players are almost always capable of having relatively wide ranges for betting. In other words, I rarely take a bet as evidence that a guy has a hand. Likewise, most good players will recognize that they can call a raise in position blind vs. blind with a lot of hands, so regardless of what his pre-flop statistics look like, I’m going to assume his range isn’t all that narrow pre-flop. As Chris M. points out, his 3B% is potentially relevant for ruling out some of his thin value range such as KQ/KJ/KT. This is potentially a tough decision even we can rule out KT+, as many commenters did, and I also don’t know that a number would actually give us that information. I can tell you that my 3B% is generally pretty high in Villain’s shoes but that I often flat-call KT and KJ.
The decision point that is most likely to narrow Villain’s range is the flop. Moreso than betting or raising, calling is generally an indication that a player likes his hand at least a little bit.
I take it as a given that any good player with a wide flop calling range is going to be aggressive on the turn. Presumably if he calls the flop with a weak hand, it’s with the intention of bluffing the turn, so I rule out TAFq as a deciding factor.
RAFq is problematic for a few reasons. For one, the deeper we get into the hand, the less reliable our statistics become. Compounding the problem is the fact that this is a rather unique situation. Thus, I don’t expect to find much useful information in this statistic, nor did many of you.
When I posted this question, I intended for FCB to be the correct answer. However, several people made a compelling case for FAFq, enough so that if this were a test I’d give credit for either answer. I may have been biased because Villains FCB was actually extraordinarily low, such that it was even more of a determining factor for me than it otherwise would have been. Over nearly 400 hands, I’d seen him fold just 10% of the time to a continuation bet.
What this tells me is that he is fighting hand, probably too hard, for every pot in which he is involved. As soon as I saw that, I clicked “Call”. Not only does this very low number suggest that Villain can get to the river with a wide range, but it also tells me something about his approach to the game. He is clearly willing to put players to the test, and that seems to be exactly what was going on here.
I took it for granted that a low FCB would imply a lot of floating, but the people arguing for FAFq, primarily Shawn and Drew, raised a good point. It’s possible that he prefers attacking continuation bets by bluff-raising rather than by floating. Thus, it’s theoretically possible that even if he has a low FCB, he nevertheless does not get to the river this way with air because he would have raised rather than called his air on the flop. The FAFq statistic would help us figure out whether this was the case.
I think that would be more relevant if his FCB weren’t so absurdly low, which of course is information that you all did not have. Had his FCB been more like 40%, I would definitely want to look next to FAFq to figure out whether he was raising or calling his air on the flop.
As an aside, I find it odd that Villain chose to turn AT into a bluff on the turn. Perhaps he thought that my checking a good barreling card indicated that I could beat A-high. I’m sure he realized that he would have the best hand more often than not on the flop, and I’d expect a lot of people just to check it down.
Thanks again to everyone who participated.
PS If you’re interested in learning more about floating, I recommend Float On, a strategy article that I wrote on the subject.