What’s Your Play? Rivered Top Pair Results

Thanks for all the comments on What’s Your Play? Rivered Top Pair. This was an interesting one for me because although there were quite a few different opinions, no one suggested what I consider to be the best play. I do think many options are close, but that doesn’t mean your choice is irrelevant. On the contrary, circumstances such as this arise frequently enough that getting them right is important.

Value Targeting

Often, the correct hand to target when betting for value is the hand just slightly weaker than yours. An important exception is when those slightly weaker hands are strong enough that it doesn’t matter what you do, and I think that’s the case here. If Villain has a smaller Ax, he will most likely value bet if checked to or call any reasonably sized bet, meaning that one bet goes into the pot whether Hero bets or checks.

Moreover, If we assume Villain will play suited Ace-rag but not offsuit, then there are 10 combos of Ax that we can get value from on the river. Meanwhile, there are 16 combos of AQ and AK, so we really shouldn’t be too eager to put money into the pot against a range that will only consist of Ax. This is true even if we assume he will occasionally bet AK/AQ earlier in the hand and occasionally play weaker offsuit Aces.

Against an opponent who you know will play any Ace, winning the most against his Ax is much more important and it may make sense to make a big river bet of your own rather than check and risk him making a smaller bet. Here, though, I think we ought to be more concerned about squeezing value from non-Aces.

I’ll also add, with Todd, that “any hand that beats us is extremely likely to be betting on the river, and we plan on calling that bet if we check. The point being that since we are going to be putting in money on the river against all the hands that beat us by check calling we should be looking only at the range of hands of that we beat to see if betting or check-calling is best.”

Check-Calling

John V. argues that, “About any worse hand that villain will call hero’s river bet with (smaller aces) will likely bet anyway if hero checks. Checking and calling gets value plus catches some bluffs. Villain can have KQ/KT/QT and figure the A is a good bluff card for him.”

The only thing I disagree with is that Villain would want to bluff with KQ/KT/QT. Those are actually hands that still have a decent amount of showdown value. From Villain’s perspective, there’s not a lot of evidence that Hero has a pair. After three checks, there’s a good chance Villain will either consider the pot too small to be worth bluffing at and/or his hand good enough to showdown. That’s assuming he’d even get to the river with those hands.

AndyAdler does a fantastic job of narrowing Villain’s range from street to street, and I encourage you to read his entire comment to see how he reaches the conclusion that, “I don’t think Villain will bluff the river often. His range after check/checking IP is skewed towards his showdown hands and away from his strong hands and drawing hands. I estimated he opened with ~20%. That range is such that it doesn’t leave behind much air (and he would have probably bet air on the flop often).”

Although the Ace is a good bluff card, there simply isn’t much air left in Villain’s range to bluff. Moreover, it’s often the case that a Villain who doesn’t bluff early in the hand simply isn’t interested in doing so and won’t take a good opportunity later. That’s not how we’d expect a game theoretically optimal computer or an elite player to play, and against them I’d like to check and call the river, but inducing bluffs isn’t generally the best way to exploit passive players, and the limited evidence we have on this player, meaning his flop and turn checks, suggest that he’s inclined towards passivity.

Once we rule out bluff-catching, the question becomes how can we convince Villain to call a river bet with hands weaker than Ax?

“Normal” Value Betting

Many people proposed bets in the 240 – 400 neighborhood, roughly 50% to 85% of pot. I didn’t see a lot of justification for these sizes other than that they are “normal”, consistent with how one might value bet or bluff in other situations, and/or consistent with what Villain might expect. Those are reasonable criteria, but when we have such a good idea of what we’re trying to get Villain to do here, I think it makes more sense to focus on why your proposed bet size is the best way to maximize value against exactly hands weaker than top pair. Personally, I don’t think that it is, and I think that defaulting to these sizes simply because they are normal can be an expensive leak.

Overbetting

A few commenters proposed overbetting, on the theory that it would look suspicious. It might (though I didn’t really see a lot of justification for why it would), and if had a well-concealed monster hand, I might be in favor of this (though check-raise overbetting would probably be better).

The problem is that looking suspicious isn’t enough to get calls from the bottom of Villain’s range. Overbetting the pot polarizes your range to the extent that even strong hands like AK and AQ become bluff-catchers for Villain. Even if he’s inclined to get suspicious, he can use all that Ax in his range for his bluff-catching. There’s no reason to think he’s going to get so suspicious that he’d call with third pair or something.

Generally speaking, large bets get called less often that small bets, even if not proportionately so. Here we want to widen Villain’s calling range, which brings us to…

Underbetting

The best way to induce a call from really weak hands is to give irresistible odds. Small stakes players like to see showdown and they don’t do a lot of hand reading or disciplined folding. Even if it seems like an “obvious value bet”, many will call simply out of curiosity.

If Hero actually expects to be behind Villain’s Ax range, which I think is conceivable, then this has the added benefit of putting less money into the pot against that range.

Results

Hero bet 122, and Villain called with A4o.

As I mentioned above, the introduction of weaker Ax offsuit into Villain’s range changes this situation significantly, and after seeing this hand I would play differently against this player in the future. Given the information available at the time, I think that putting Villain on all Axs but only stronger Axo is best and that the line taken by Hero is the best way to playing against that range.

Dealing With a Raise

Easy fold, even if you underbet.

Your opponents don’t bluff as often as you’d think. Most people worry way too much about getting bluff-raised, when in fact it happens quite rarely, especially on the river, in small stakes games.

My philosophy is that non-elite players strongly prefer cheap bluffs to expensive bluffs. So I’m not going to expect a guy who passed up two opportunities to take a small stab at the pot in a very standard/easy spot to suddenly make a much larger bluff raise in a much more uncommon bluffing spot.