Thoughts on Game Theory: Part Nine Blockers

Let’s continue the discussion of what game theory suggests you should do on the river. I have been using a pot-sized bet in these examples not only because it is a common bet size, but because many games like Omaha are played pot-limit, and in these games it is the maximum bet you can make.

Game theorists have calculated that when making a pot-sized bet on the river, you should have twice as many value bets as bluffs. Thus for 100 pot-sized bets, 67 percent should be value bets and 33 percent should be bluffs. If you reach the river in position with 100 hands and want to value bet 40 of them, then we have to decide what to do with the other 60, knowing that only 20 should be bluffs.

There will be obvious cases against opponents who don’t call enough. They must defend at least 50 percent of the time to prevent you from making an immediate profit. (This is their Minimum Defensive Frequency.)

If they don’t, then you can bluff any two cards. If they call much too often, bluff less and value bet a little lighter. This should be intuitively obvious. The harder question is what to do versus a good opponent or even an unknown one.

Returning to our sample of 60 hands that aren’t worth a value bet, how do we select the 20 or so hands we will use as bluffs?

Here is an example:

You raised first-in on the button and only the big blind has called. The flop comes J 8 4. You make a continuation bet on the flop and are called. The turn brings the 3, and you fire a second bullet, which gets called. The river is the 2.

Here are six hands you might have played this way that have missed. Which should you bet as a bluff?

Hand No. 1 – 6 6
Hand No. 2 – A Q
Hand No. 3 – K 7
Hand No. 4 – Q 10
Hand No. 5 – 10 9
Hand No. 6 – 7 6

Your opponent has never shown any aggression, and this pattern of check-calling suggests he has either a draw of some sort or a very weak calling hand like a medium pair. He might even have a jack with a weak kicker. Let’s examine what we should do and why.

We have shown strength and he has shown weakness, so our bluff has a reasonable chance of working (because we are telling a believable story). We also don’t want to bet hands that can win at showdown. He will generally fold all missed draws. He may fold some pairs, but if he has a pair, he might be willing to call again as a bluff catcher. You should bluff when he could logically have had a hand that missed its draw.

You don’t want to have cards that block hands that have missed. Therefore, we want to bet hands that make it more likely he has a draw, and less likely he has a pair. These are hands that don’t have cards that would be part of his most likely draws.

Hands 1 and 2 have reasonable showdown value. Hand 2 also contains two cards that could be part of a lot of his flush draws. You should definitely show them down, and expect to win some of the time. Hand 3 is weaker, but still might beat some draws at showdown. It has one blocker, the K. I’d probably tend to check it down most of the time. If it was K 7 (no blockers), I probably bluff, especially if I thought I had a tight image.

Hand 4 is another close call. Your hand is definitely weak enough to consider bluffing. You don’t have spade blockers, but your hand blocks a lot of straight draws and back door flush draws. Hand 5 blocks some straight cards, but does not block either of the possible flush draws. It does block some of the value hands he might have (J-10 or 9-8, for example.) An excellent candidate for a bluff.

Hand 6, has no showdown value, nothing that blocks his draws. Again, this is a very standard bluff. You might have checked the turn, but the fact that you picked up a gut-shot and think he might have a draw led you to fire again.

The idea is to bluff when you don’t hold cards that block some of his missed draws. Your expert opponent knows he has to call at least 50 percent of the time. When he selects his bluff catchers, he will select his best hands that don’t contain cards you might be bluffing with.

To summarize our pot-sized river play over 100 hands. Bet 40 for value. These are hands that beat his calling range. Bet 20 as bluffs. These bluffs should be hands that can’t win a showdown and don’t contain cards that might be part of his missed draws. The remaining 40 are just checked back. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With two WSOP bracelets and few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City -The Library near Houston and Doc Holliday’s on 9th St. are his favorites.