A Medium-Strength Hand - Part I

One of the toughest situations in big bet poker is facing a large bet with a medium-strength hand. It's easy to play the bad hands and the good hands. It's the other hands that tend to separate the pros from the recreational players.

I'll give an example, using an actual hand a student of mine played in a $5-$10 online no-limit hold'em game. A middle position player opened for $35. It folded to my student in late position. He had $500 in front of him (he should've had more, but that's a subject for another column), and he had two black tens in the hole. He very reasonably decided to call.

Everyone else folded and the flop came Q-9-4, all different suits. The villain led out for $70 into the $85 pot. Should my student fold, call, or raise? And oh yeah, he had no information about the opponent.

In a lot of cases, especially when playing brick-and-mortar poker, questions like this one are questions of style and of table image. Let's say, for example, you're the only woman at a table full of super-macho men who try to bluff you out of every pot. Then you probably want to call, and let the guy bluff off all his money to you. Or let's say you're a young punk who everyone thinks is a maniac, and assumes you're bluffing every time you put money in. Then you probably want to raise and let your opponent call you down with ace high.

It goes without saying that you might always make a certain play for reasons of style and/or table image. But this column is mostly concerned with what you do absent other information - with which play is the best fundamental poker play. Oftentimes, especially when playing online, you won't have much to go on other than your opponent's actions. You'll only have the fundamentals.

Returning to our original question then, what should our hero do with his two tens? If he calls, he might induce another bluff on the next street, he might minimize his losses if he's against a big hand, he might allow his opponent to catch a card on the turn that beats him, or he might catch a two-outer on the turn himself. If he raises, he is unlikely to be beaten by a lucky turn card, but he is also likely to scare off hands such as 7-7 or A-5 suited - hands with few outs, but with which his opponent might consider firing a bluff on the turn or river. If he folds, he cuts his losses on this so-so flop and moves on to the next hand.

So what's the best play? In my view, the only way to answer this is to make some assumptions about how typical opponents play, put some numbers to those assumptions, and make some calculations.

Let's do the easiest calculation first. EV(Fold) = 0.

I told you that one would be easy. Now let's take on the other two.

To calculate EV(Call), I'm going to make some guesses about our opponent's range of hands, and how he might play that range on the turn. We know that he opened from middle position, so let's assign a reasonable range for a mid-position opener: 4-4+, A-10+, K-Q, K-Js, Q-Js, J-10s, 10-9s. I basically gave him almost any pair, the biggish aces, king-queen, and a few suited connectors. Now how does the flop action reduce his range? In my opinion, it doesn't reduce it much. Most players frequently make continuation bets with their entire range in a situation like this. (Incidentally, this is not a great way to play no-limit hold'em, but that's again a discussion for another column.) But to give our opponent some credit, I'll remove A-10, 5-5, and 6-6 from his range based on the fact that he bet the flop. It doesn't really matter much which specific hands I remove from his opening range, so long as the analysis reflects the idea that he doesn't bet the flop every single time he raises preflop.

OK, now that we've got that, it's time to take an educated guess at what might happen on the turn if we call. A reasonable play for our opponent would be to check some of his monsters, most of his busts, and a few of his medium-strength hands, but to fire again with some bluffs, some semibluffs, some of his monsters, and some strong hands that aren't quite monsters (like AA). Let's say he checks with top set and middle set, but fires again with bottom set. Let's say he bets planning to call a raise with A-A, checks planning to call a bet with A-Q and K-K, and bets planning to fold to a raise with K-Q and Q-Js. Let's say he semibluffs with A-K, K-Js, J-10s, 10-9s. And just for fun, let's say he makes a (relatively) pure bluff with A-J and 7-7. If an ace or king hits on the turn, assume he bets almost his entire range. Obviously these assumptions don't perfectly describe any one player, but in my opinion they are a good enough approximation of how typical opponents play to do a useful analysis.

What about our hero? Well, he's calling on the flop largely to induce a bluff on the turn, so assuming a safeish turn card, he's going to call the turn too. Let's ignore the river for a second, and come up with an estimate for EV(Call).

There are 47 possible turn cards. Four of them are aces, and the pocket tens have almost no equity when those aces hit. My student is pretty much folding to any bet when an ace comes. Four of the possible turn cards are kings. Those are tougher, but the king is also a really bad card for the hero. For simplicity's sake, let's assume he just mucks the turn when a king hits as well.
On any of the 39 other turn cards, he's calling again.

Clearly the tens are much better off with a deuce on the turn than a jack, even though the plan is to call in both cases. But I'm just going to use a deuce as the turn card when making the equity calculation. This slight boost in calculated equity shouldn't hurt the analysis too much, since I'm giving my student no chance to win the hand when an ace or king hits, when in fact he will win the pot every once in a while even on those terrible turn cards. Also, this calculation gives him no additional equity when a 10 hits on the turn. I actually think I'm underestimating his EV rather than overestimating it.

Given those assumptions, the tens have 57 percent equity against the range our opponent bets the turn with. Damn, that's a lot. One final assumption, when our opponent bets the turn, he bets $150.

So here's my guess to this point …
EV(Call) = (8/47)*(0-$70) + (39/47)(.57*$525-$225) = -$11.91 + $61.61 = $49.70

We haven't done the river analysis yet, but the action at that point will go check-check often enough that I don't expect a wild fluctuation in this number. It looks clear to me that calling on the flop is significantly better than folding. But is anyone surprised by this result? Few players would fold 10-10 to a standard continuation bet on a flop of Q-9-4 rainbow, and they're right to play on there. The real question remains, however - is it better to call here, or to raise? Tune in next column, as I attempt to tackle the question further.

Matt Matros is the author of The Making of a Poker Player, which is available online at www.cardplayer.com.