Am I Making a Good Bet? Part 6

I ended the last column by posing a question relating to a semi-bluff. One player has A Q and his opponent has K K. On fourth street, the board is 8 8 5 4. The A Q goes all-in with a pot-sized bet. What should the kings do?

They might be up against a strong hand, and have few or even no outs. If the bettor has a full house, a straight, any eight, or aces, the kings have only two outs. If he has quads, the kings have no outs. It takes a pretty brave player to make this call. But even if he does make it, the semi-bluffer will still win 25 percent of the time. There are 44 unknown cards, three aces and eight of the nine remaining spades will win for him. He wins with 11 of 44 cards or 25 percent of the time. (Note that the K makes his full house.)

When someone makes a pot-sized pure bluff, with no outs, their opponent must call at least half the time to prevent them making an immediate profit. If there were 500 in the pot, and you bet 500, now he has to call at least half the time to prevent you from making an immediate profit. If the ordinary bluff is called 60 percent of the time, the bluffer loses 500 times .6 and wins 500 times .4, so he’d lose 100 on the bluff.

In the case when the bet is a semi-bluff, the bettor has outs when called. Now suppose the kings call 60 percent of the time. The semi-bluff does much better than if it was a pure bluff. In this case, it will win 25 percent of the times when called. There are now three cases. You win 500 times .4 when he folds, and you win 1000 times .15 when he calls and you hit an out, while only losing 500 times .45 for a net plus of 125.

At the end of the last column, I asked you to calculate how often the kings must call to break even. The answer is the kings must call 80 percent of the time to break even. As this series of columns has suggested, I am always trying to make good bets. I would happily bet that out of the thousands of Card Player readers, fewer than 10 took the time to solve this problem.

The easy way to approximate a solution is to test a few cases. We saw above that calling 60 percent of the time wasn’t enough. Suppose we run the numbers to see how calling 75 percent of the time does. The semi-bluffer still shows around a profit of a little over 30. Based on this we can assume the kings would have to call almost every time for the bluffer to lose significant money.

It should be noted that this was a particularly strong semi-bluff. It has a lot of outs. Semi-bluffs are still often good bets even when the semi-bluffer’s hand is weaker. Suppose the semi-bluff was made with a gutshot straight draw, a hand with only four outs if called. The best hand still has to call almost 60 percent of the time to break even.
Unless your opponent is a ‘calling station,’ semi-bluffs with a scary board are very good bets to make. There is a hidden benefit to making a lot of semi-bluffs. You will occasionally be caught bluffing. And even though you win some of the times you are caught, you’ll lose most of them. Your opponents will remember you are someone who bluffs a lot, especially when there is a scary board, so they will call you more often. But some of the time you won’t be bluffing or semi-bluffing. In fact, they will be more likely to call you when you have them crushed. You shouldn’t lose money on your semi-bluffs, but even if you do lose a little, you’ll gain much more when they call your great hands.

I apologize for talking about math and asking you to do hard work, but that is what it takes to win. Perhaps you can find a friend or hire a coach who is good at math, and they can help you get comfortable with common situations and problems. You want to make good bets and avoid making bad ones. Math is frequently the only way you can tell them apart.

To end on a lighter note, a physicist, a mathematician and a poker player discuss which is better: a wife or a girlfriend. The physicist says, “A girlfriend. You still have freedom to experiment.” The mathematician says, “A wife. You avoid unknown variables.” The poker player says “Both. When I’m not with my wife, she thinks I’m with my girlfriend. My girlfriend thinks I’m with my wife. So I can play poker without anyone disturbing me!” ♠

Steve ‘Zee’ Zolotow aka Zebra is a very successful gamesplayer. He has been a full-time gambler for over 40 years. With two WSOP bracelets, over 50 cashes, and a few million in tournament cashes, he is easing into retirement. He currently devotes most of his Vegas gaming time to poker, and can be found in cash games at Bellagio and at tournaments during the WSOP. When escaping from poker, he spends the spring and the fall in New York City where he hangs out at his bars: Doc Holliday’s, The Library and DBA.