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Math
Corner
Value Betting
Wednesday, October 06, 2004 Value betting is a vitally important part of a strong Limit Hold 'Em strategy. Many otherwise good players have a massive leak in their games in that they don't bet the river nearly enough. Let's look at an example. You have QQ and raise preflop. You get called by only the button, a loose, passive player. 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 the opponent does not give off any tells. What's your play? To further specify the question, I'll pick a reasonable range of hands for our opponent. I think it's fair to say our opponent's range is AK, KQ, KJ, KT, K9, Kxs (without having flopped two pair), JJ, TT, 99, 77, 66, 55, 44, 22, AQ, AJ, AT, A8, Q8, J8, T8, 98, 87, 86, 85, A3, Q3s, 53, 43, 63s, and any two hearts. I'll say the flop was Kd8h3h, I'll say the turn and river were the 5c and Th, and I'll say we have QcQs. Finally, I'll say 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 any hand 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 our opponent can have. 134 beat us (45 flushes, 44 two pair and sets, 45 one pair). 164, we beat (22 busts, 142 one pairs). So a lot of our loose opponent's hands—specifically 45% 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, with which he will raise. 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, for a net loss of .12 bets per hand. As you can see, value betting loses money on the river action (i.e., the bet we make on the river will not be refunded to us from other money put into the pot on the river). But what is the alternative? If we check, our opponent will bet two pair or better, but will check behind with one pair, and bluff his ace highs. Assuming we have to pay off, this means we lose one bet on the river 89 times and win one bet 23 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 here. 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). This is because the pot is big enough so 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. The proof of this is in the calculations we've already done, and is also left as an exercise to the reader.) I encourage you to seriously consider the value of betting the river with your made hands in Limit Hold 'Em, even the weaker ones. I suspect you'll find it to be the correct play a surprisingly large percentage of the time. September 2004 | October 2004 | January 2005 | |
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© 2004-2005 by Matt Matros | All Rights Reserved |
