 
Mastering the Mathematics of Bluffing in Poker
A lot of people play poker based on the idea of feel. That is, they rely on their experience or ideas, whether valid or not, to guide their play when it comes to close situations. The problem with this approach is that it's often inaccurate when a player is trying to determine the correct play, and doesn't give the player any logical way to analyze his or her play to get better. This kind of thinking is like a bingo player who refuses to think outside the box and optimize his or her playing environment. A player who relies on their feel for poker in bluffing situations would see much better results if instead he or she focused on learning the intricacies of the mathematics involved when bluffing. The following is a primer that can help you gain a better understanding the math that drives bluffing scenarios. When this information is applied to your game, you will perform at a high level in bluffing situations.
The Alpha Value and its Significance
There is a ratio that comes up very often when studying mathematical ideas in poker, and it's called the alpha value. You get this ratio by dividing the amount you're betting by how much will be in the pot after you bet. This value is important in bluffing because it tells you how often you must take the pot down on a pure bluff for your bluff attempt to be profitable in the long run. In progressive forms of bingo, this is analogous to dividing the jackpot overlay by the number of cards in play and comparing the result to how many cards you're playing.
Suppose you face one opponent on the turn in a no-limit hold'em cash game and you are first to act. For this example, let's assume the pot is 60 big blinds, and you are considering various bet sizes for a bluff. Each bet size will have a corresponding alpha value that tells you how often your opponent will have to fold for your bluff to be profitable no matter what the cards are.
If you were considering betting 30 big blinds into the pot of 60 big blinds, then your alpha value is 30 divided by 90, which gives you 0.33 or 33%. This means that for your bluff to be profitable, your opponent will have to be folding more than one-third of the time. Along similar lines, if you were going to bet 40 big blinds into the pot of 60 big blinds, then the alpha value would be 40 divided by 100, which is 0.40 or just 40%.
Understanding Why Multi-Way Bluffing is Usually Bad
To show why multi-way bluffing is so bad, let's consider a similar example to the one we just looked at. You're on the turn with a pot of 60 big blinds, and this time you're facing two opponents, but you're still the first player to act. If you consider a bet of 40 big blinds, you know that the alpha value is 40%. However, this doesn't mean that each player has to fold 40% of the time individually for your bluff to be profitable. It means that everyone in the hand besides you have to all fold 40% of the time. If both players fold 60% of the time each, then they both fold only 0.60 * 0.60 = 0.36 or 36% of the time, and your bluff will not be profitable.
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