|
|
Math
Corner
Inducing a Bluff vs. Making Him Pay
Friday, September 24, 2004 Many poker players are mortified about giving their opponents free cards. So often, I'll hear a player who lost a hand say something like, "I played it wrong-if I had bet the turn he would've folded, and I would've won the pot." There are many truisms in poker. Here are two. 1) Winning the pot is not the most important thing--winning the most money is. 2) Just because you lost a hand, doesn't necessarily mean you played it badly. Let's say you're playing No Limit Hold 'Em, and you have a strong, but beatable hand on the turn. Your opponent is a loose, tricky player who is capable of holding just about anything. In this hand, based on the play of the prior streets, you think he might be on a draw. This opponent is smart enough to know he can't call a large bet with just a draw. His play, however, was also consistent with his having the nuts. So he either has a draw or the nuts. He has already checked. There is $200 in the pot, and you each have $150 in front of you. Now here's the problem. If you bet your stack, your opponent will only call if he has you beat. But if you check behind your opponent, you are confident he will bet his stack on the river no matter what comes. Your check, however, gives your opponent a free shot to draw out on you, if he is in fact on a draw. Let's assume you don't know what kind of draw he's on, and that if you check behind your opponent you are going to pay off his river bet no matter what. Let's further assume that if your opponent has the nuts right now, you are drawing dead. What is your best play? First, we'll calculate the equity from betting our stack on the turn. The fraction of the time our opponent is drawing (call it D), we win the pot, $200. The fraction of the time our opponent has the nuts (1-D), we lose our bet, $150. So our equity is 200D - 150(1-D) = 350D - 150 So it is profitable to bet the turn when 350D - 150 > 0, or D > 150/350 =~ 42.9% That is, we make money by betting the turn if there is a greater than 42.9% chance our opponent is on a draw. That doesn't mean betting the turn is our best strategy in that case, just that it's a profitable strategy. Next, we'll calculate the equity from checking behind on the turn to call on the river. Let's assume that if our opponent is drawing, he'll hit his draw one-fifth of the time (this would be roughly his chances of hitting a flush draw). When he's drawing, we lose $150 one-fifth of the time (when he hits) and we win $350 (the pot plus his river bet) four-fifths of the time (when he misses). We also lose $150 when he has the nuts. So our equity is 350(.8D) - 150(.2D) - 150(1-D) = 400D - 150 This strategy will be profitable when 400D - 150 > 0, or D > 37.5% So our opponent needs to be drawing only 37.5% of the time for checking behind to earn us money, as compared to 42.9% of the time for betting the turn to earn us money. Wait, it gets better. Let's compare the two equity calculations. Betting the turn: 350D - 150 Checking behind: 400D - 150 Notice that checking behind earns more money no matter what D is! However often our opponent has the nuts (unless he always has the nuts, in which case we lose the same $150 every time), betting the turn will be an inferior strategy to giving the free card. This is, of course, because we have an opponent who is committed to bluffing the river no matter what. Against such an opponent, it should actually be obvious that checking behind on the turn to induce the bluff is always better than betting. Calling his bluff is the only way we make money when we're ahead, and we lose the same amount when we're behind. Obviously if our opponent has the nuts too often, the best strategy is to check behind on the turn with the intention of folding on the river. But if our read is even remotely accurate, and there is more than a 37.5% chance that our opponent is on a draw, then inducing the bluff is best. Betting on the turn is never best. Inducing the bluff is an even better play if you have a good guess at what kind of draw your opponent is on, and you can safely muck the river to a scare card. In that ideal scenario, inducing the bluff wins the maximum when you're ahead, and loses the minimum when your opponent hits his draw. How many times have you played No Limit or Pot Limit Hold 'Em against a player who can't resist bluffing the river? A player who, if you check behind him on an earlier street, will shove all-in on the next street virtually every time? Let him do it. You'll be a richer poker player for it. September 2004 | October 2004 | January 2005 | |
Poll
|
Copyright
© 2004-2005 by Matt Matros | All Rights Reserved |
