Bluffing is a central component of poker, and one of the most valuable weapons in the arsenal of a winning player. Most players do not fully understand the basic aspects of bluffing, nor the advanced principles underlying the decision to bluff by a strong player. A winning player must bluff an optimal amount, but in a manner which does not tip off his opponents to his bluffing patterns. In this article, we will discuss the concepts behind optimal bluffing.
First, let's start with the idea of Nash equilibriums. This comes from the mathematician featured in "A Beautiful Mind."
The idea here is that if you don't bluff enough, the proper counter-strategy for opponents will be to always fold to your bets unless they figure to beat your average holding. If you bluff too much, the proper counter-strategy for opponents will be to always call (or even raise) whenever they figure to beat your average holding. If you bluff at just the right ratio, there is no correct response.
The Nash equilibrium point (aka "the optimal bluffing ratio" and "equilibrium bluffing ratio") is when you bluff just enough that neither of these two simple options of always folding or always calling will work.
You will win the same amount from someone who always folds as you will from someone who always calls. The proper ratio at which to do this is a function of the potsize. If the pot is 7 small bets, and then you want to bluff this situation Betsize/(Potsize + 1), where Potsize is measured in units of Betsize.
Example: We're at the river. The pot is 2 bets and you bet 1. Three out of four times, you will bet for value with a hand that figures to win. One time out of four times, you will bluff. What's the result after four average trials?
Answer: If the opponent always folds to you, you will win the 2 bets in the pot all 4 times you try this (2x4 = 8). If your opponent always calls, you will win the pot plus the opponent's call three times, but lose your bluff bet once (3x3 - 1 = 8).
Note that for some numbers this comes out close, but not exact. Averaging over an infinite number of trials will smooth that out. (It's the number of trials that sometimes throws things off, but whether an opponent always folds or calls results in essentially the same net win in the average case.)
Further note that we assume you have no tells.
It wouldn't be good if your opponent sometimes calls and sometimes folds and is somehow right more than random chance. If you have no tells, and they are only right as much as random chance dictates, all the cases where a given opponent calls can be grouped into the always call category (with a net win of 8 for you when it happens) and all the cases where they fold can be grouped into the always fold category (with a net win of 8 for you when it happens).
In other words, it doesn't matter what people do as long as you are not telegraphing any information.
There is an implication here that human beings, being aware as they are, will seek out whether always calling or always folding is the more correct solution whenever you bluff at a ratio other than the equilibrium ratio.
In other words, don't underestimate your opponents. If calling you all the time *is* the better decision than folding, they will figure that out. The same holds true if folding all the time is the better decision versus the way you play. As a group, you can expect your opponents to tend toward the decision that aids them the most. Poker is a zero sum game for the most part, so this also means they will tend toward the decision that hurts you the most.
A player who bluffs optimally and has no tells puts his or her opponents in a pickle. First, there is no clear historical evidence on what the better decision is. Secondly, it doesn't even matter what they decide. It may be that an intuitive awareness develops in opponents that it's difficult to decide what to do against such a player.
If you want to be an A+ student of poker, then *learn* this. If you want to use "feel" for when someone might fold and etc., that's fine, but remember the ratio you're seeking and try to get as close to it as possible, as this will consternate opponents to the maximum degree.
Remember, if you're a student of poker, only the B+ and better students are going to avoid losing money. B+ is barely a step above break even in my mind--a person who wins small amounts over time, but can at least say they are up.
