You are playing pot limit poker. You and your lone opponent have each put $100 into the pot. It is the last round of betting and he has checked what you know is a pretty good hand. However you believe that there is a 60 percent chance your hand is better. Assuming all bets and raises must be pot size, should you bet $200?
To answer this question accurately, it is necessary that we know a little bit about how the other guy plays. For instance, if there is some chance that he will fold a better hand than yours if you bet, then you should probably do it. But say that is not the case. Say the only hands he might fold are worse than yours. For instance, say he will fold half of the 60 percent of the time you have him beaten. If so a value bet would be wrong since he will call 70 percent of the time, and 40 of those 70 percent he beats you. Thus, you have made a negative expectation bet.
But what about if you know he will never fold? Could it still be wrong to bet? If so it must be because you fear he will raise. That is a legitimate fear, but only if you worry he might raise without having you beat. That is he will occasionally raise as a bluff.
If you know this fellow is not capable of raising without a very big hand (bigger than yours), you should go ahead and bet, winning that extra $200 60 percent of the time, while losing $200 when he calls or raises with a better hand.
The question is whether a player who will just sometimes raise with a worse hand forces you to check behind him, even though you know he will never fold. Suppose, for instance, that he raises 12 of the 60 percent you have him beaten, as well as the 40 percent he has you beat. That means he will raise $600 a total of 52 percent of the time (and call the remaining 48 percent). The problem is that you must fold when he raises. He is a 40-to-12 favorite to have you beat and you are getting only 2-to-1 pot odds. Bottom line is that you win the $600 pot 48 percent of the time, while losing it 52 percent. Much better to win the $200 pot 60 percent. That is a $20 expected profit for you. In this case, if he raise “bluffs” as little as 7 _ percent of the 60 percent he is beaten, you should avoid betting. (You win $300 53 _ percent of the time and lose $300 47 _ percent of the time, which is also a $20 expectation.)
Suppose you think he will raise bluff often enough that you should call him. Say he does it 5/12 of the 60 percent he’s beaten or 25 percent altogether. Since it is 40-25 he has you beat (assuming he always raises when he does), you must call getting 2-to-1. Altogether you win $300 35 percent of the time, $900 25 percent of the time, and lose $900 40 percent of the time. That’s an EV of negative thirty bucks. It matters not that you can call his raise. Thus, you still lose money even though it is now right to call.
Only if his raise bluffs are almost as frequent as his real hands does his “trickiness” not cost you money if you bet. For example if he were to call only 25 percent and raise the remaining 75 percent, you would win $300 25 percent of the time ($75 EV), win $900 another 35 percent of the time ($315 EV), and lose $900 40 percent of the time (-$360 EV). That $30 EV is only $10 more than had you simply showed your cards down (with an eightfold increase in risk). (Of course, if you are adequately bankrolled, you will want to win that (theoretical) additional $10. But if reducing fluctuations is important to you, you may not even want to bet in this spot even though it is profitable to do so.)
Bottom line: Be wary about betting marginal situations in last position against tricky players who will sometime, but not usually, raise with worse hands. Bets that might seem profitable at first glance, against the wrong players, might be costing you money in the long run.
Dieser Artikel erschien auf PokerOlymp am 08.08.2007.