Limit Hold'em Lessons Part II – Value betting is a great strategy against loose/passive opponents

In my last column, I posed the following two limit hold'em problems. In both, assume your opponent is a loose/passive, bad player.

1. You have Q-Q and raise preflop. You get called by only the button. The flop is king high with a two-flush, and your opponent calls your bet. The turn is a blank, and your opponent calls you again. The river brings the flush card, and your opponent does not give off any tells. What's your play?

2. You raise from the button with A-J and the big blind calls. The flop comes J-J-7 and the big blind check-calls. The turn is an 8, and again the big blind check-calls. The river is a 9, making the board J-J-7-8-9. Again, the big blind checks. What's your play?

If you read my last column, I hope you gave these questions some thought. If you're seeing them for the first time, take a few minutes to think about what you'd do in each hand before you read on.

Got your answers?

OK, in question No. 1, I think it's fair to say our opponent would've called us down this far with any pair or any flush draw. We'll give him some credit for preflop selectivity, but not much. We'll rule out hands like 7-2 offsuit and J-3 offsuit, but we'll say he would've called with any two suited cards. Let's specify the flop as being the K 8 3. That makes his range up to this point A-K, K-Q, K-J, K-10, K-9, K-X suited (without having flopped two pair), J-J, 10-10, 9-9, 7-7, 6-6, 5-5, 4-4, 2-2, A-Q, A-J, A-10, A-8, Q-8, J-8, 10-8, 9-8, 8-7, 8-6, 8-5, A-3, Q-3 suited, 5-3, 4-3, 6-3 suited, and any two hearts. I'll say, just so that we can do some exact calculations, that the turn and river were the 5 and 10 (to keep things easier, assume that if this guy turned a set of fives, he lost his mind and chose not to raise), and I'll say that we have the Q Q. Finally, I'll say that our opponent will raise our bet only with a flush, call if he has at least a pair, and fold his ace highs. If we check, our opponent will value bet two pair or better, and bluff with his ace highs.

Based on the reasonable assumptions I've made above, we've now completely defined this problem so that there is an exact, correct solution. Let's see what it is.

There are 298 total hand combinations that our opponent can have; 134 beat us (45 flushes, 44 two pair and sets, and 45 one pair); 164, we beat (22 busts, 142 one pair).

So, a lot of our loose opponent's hands – specifically, 45 percent of our opponent's hands – beat us. Of the hands that don't beat us, we've said our loose opponent will call with everything except the ace highs. That is, there are 22 hands he will simply fold to our bet. There are 142 hands with which he will call and lose. Of the hands that beat us, we said he will call with everything except the flushes, and he'll raise with the flushes. So, he'll call with 89 hands that beat us and raise with 45.

By value betting, therefore, we win one bet 142 times, lose one bet 89 times, and lose two bets 45 times (because we're not betting for value and then folding to a raise – a topic for another column), for a net loss of .12 bets per hand. As you can see, value betting loses money on the river action; by that I mean, if we ignore the rest of the pot and look at only the money wagered on the river, our bet will be a loser.

But what is the alternative? If we check, our opponent will bet two pair or better, check behind with one pair, and bluff his ace highs. Assuming that we have to pay off, this means we lose one bet on the river 89 times and win one bet 22 times. This results in a net loss of .22 bets per hand.

You can see that value betting is clearly superior to checking and calling. It turns out that checking and folding does a solid .2 bets worse than even checking and calling in this situation. Proof of this is left as an exercise to the reader. (Sorry to borrow a sentence from the math textbooks.) This is because the pot is big enough that those 22 times you check and get bluffed out of the pot end up being a disaster. Value betting is your best play, bar none. (Note: If you had been second to act and your opponent had checked dark, checking behind would've been the correct play.)

Surprised? Many people are. After all, the flush came in, our opponent has called the whole way, and we don't even have top pair. It still makes sense to bet against a calling station.

Let's look at question No. 2. There is a four-straight on board, and we don't have one. Unlike the last problem, we're second to act, and could just check and see a showdown if we wanted to. So, do we want to?

It turns out that it depends on just how loose/passive our opponent is. Will he call with his underpairs even with this scary board? Will he check-call with a straight, rather than raise in the face of a possible full house? If the answer is yes to these questions, we want to bet for value. Actually, the second question is much more important than the first. It's fairly easy for our opponent to have fluked into a straight with this board – but if he doesn't check-raise with it, we still make money by betting.

Let's say his range going into the river was something like 2-2 to 6-6, 7-8 to 7-A (including 7-J – he might have slow-played), 8-9, 9-10, 8-10, 8-8, 9-9, 10-10, any suited jack (slow-played), J-7 to J-A (slow-played), A-8, A-9, A-10, A-Q, A-K, K-8, K-9, K-10, K-Q. Even if he folds his underpairs, there are 130 combinations of hands with which he'll call our bet. Assuming our opponent will check-raise with only a full house, he doesn't get enough value from his good hands to make up for all of his loose calls, and he loses money on the river action. To make money, he also would have to check-raise his straights. So, against a truly passive opponent, one who fears raising his straights with paired boards, it is correct to bet for value here.

As the examples should've illustrated, value betting is a great strategy against loose/passive opponents – players who are unlikely to bluff or bet mediocre holdings, but are very likely to call with almost any two cards. We, as players, should be seeking out these opponents all the time. You'll hear a lot of the "experts" complaining about how they hate limit hold'em because they can't bluff bad players. This comes as no shock to those of us who make our living off bad players. The "experts" are right. You don't bluff bad players – you value bet them to death.

Matt Matros finished third in the 2004 World Poker Tour Championship, and made the final table of this year's $3,000 limit hold'em event at the World Series of Poker. His book, The Making of a Poker Player, is on the shelves now.