Much Fruit of Sense

"Words are like leaves and where they most abound,

Much fruit of sense beneath is rarely found."

- "An Essay on Criticism," Alexander Pope



I guess it's a good job that Alexander Pope didn't get to experience the joys of the Internet. Certainly, the amount of leaves is without parallel, and any passing fruit bats may find they fly on hungry. Poker knowledge on the Net is just the same. How does a novice pick out the choice, juicy profit-earning "fruit" without being overwhelmed by shiny but ultimately valueless "leaves?" One of the ideas that is often bandied around online is the idea of "folding equity" and in this column we will examine what it means and marry it to real-money play from online. Will it be fruit or leaves?



The concept of "equity" in gambling terms probably deserves a brief introduction. As it probably sounds, equity is a mathematical term, but it is likely that this idea crossed into poker from its near cousin backgammon, where it had been a popular and well-understood thinking tool for some time. Basically, equity meant the value of a position, in terms of points or dollars, if the game was played to completion from that point on. With the advances in computer simulations, this was calculable to a reasonable degree of certainty, and it became a very popular way of understanding situations in the game. The fact that wrestling with such weighty concepts is bread-and-butter to the serious backgammon pro also probably explains why, at the higher levels, backgammon players are "theoretically" better gamblers than poker players, and make the transition from the ivory checker to the pasteboard quite comfortably.



In poker, the concept has a very similar, if less easily calculated, function. If I bet, call, or raise at this point, so that there is no more betting, how much is this situation worth to me? A positive dollar value or equity is good, and just like your bank balance, a negative equity value is bad. There are problems in calculating this in comparison to backgammon. In backgammon, your opponent's position is perfectly transparent; the problem is probability. I know where he is now, but what is likely to happen when the dice get rolling? In poker, telepathy excluded, you do not know your opponents' positions, either. Instead, you have to put them on a range of holdings, then mix in the probability element of cards to come.



This brings us nicely around to the concept of folding equity. Because poker is a game that often rewards selective aggression, you may be able to increase your equity by betting or raising and winning the pot uncontested because your foe passes his hand. This is your folding equity. An example from online no-limit hold'em play will help clarify.



Playing with $5-$10 blinds in a sixhanded game, our hero raises to $30 from the button with K-Q suited. Only a slightly loose, weak foe calls from the small blind. Both have about $1,000 in front of them. The flop comes K-J-9 with one of our hero's suit, giving him top pair/good kicker, a gutshot-straight draw, and a backdoor-flush draw. The foe checks, our hero bets an amount just less than the pot, and the foe makes a slightly larger than minimum check-raise. Our hero moves all in. This looks like a classic use of folding equity. Our hero probably is not ahead of the foe's range of hands, but his aggression might make him fold. So, overall, it becomes a positive equity play, doesn't it?



Let's freeze the action here and see what kind of situation our hero has got himself into. First, here's one assumption: Although the foe is a poor player, he isn't going to be calling such a big bet with top pair/bad kicker. In fact, upon reflection, it is reasonable to assume that there is no real hand the foe will call with here that's ahead of our hero. So, if he calls, our hero has to outdraw his probable holdings of two pair or A-K, a set, or a straight. When you review the math of this, it becomes clear that our hero needs his foe to pass at least 65 percent of the time. How many hands is such a foe likely to make a small check-raise with and then pass? They almost certainly don't add up to 65 percent.



For the results-oriented, the foe actually had K-9 offsuit and called instantly, and it stood up.



Here is the real problem of the whole concept. Although it's a useful addition to the arsenal of ways to think about hands away from the table, with inexperienced players, this "little learning" leads players to grossly overplay their hands, believing that they have significant folding equity and not taking into account the fact that if they are called, they have very little chance to be ahead. And as we have found, if this is the case, you are going to need your opponents to do a lot of folding.



It's time to look for more fruit.