CardSharp

Previously, I discussed how bets can at least loosely be classified into one of two classes, value bets or bluffs. I now want to discuss the theory behind bluffing.

First, let’s reiterate what it means to bluff:

A bluff is a bet where you believe you do not have the best hand, and believe all of your opponents with better hands will fold if you bet.

Now, that seems like a pretty simple definition. But there’s actually a lot of complexity hidden in there. For example, what does it mean to “believe” your opponent will fold? What does it mean to have the “best hand”?

What Is The Best Hand?

As previously discussed in the “play on the end” series, it’s pretty easy to define what constitutes the best poker hand on the last betting round. It’s the highest ranked made hand and subsequent play will not change that. However, on earlier betting rounds, it’s not quite so clear what constitutes the best hand. One possible definition is that it’s the best made hand. Another possible definition is that it’s the hand with the highest equity. In practice, either of these definitions is usually servicable as the best made hand is usually also the equity favorite in most games. This isn’t always the case, but is far more common than the exceptions. In practice, if think your hand is best by either definition you shouldn’t consider yourself to be bluffing.

Beliefs About Your Opponent’s Hand

In order to bluff, you first must have reason to believe that you opponent holds a stronger hand. This belief may come from several sources. Most simply, it may arise because you hand is very weak. If you are playing holdem, the board is 7s9sTs and you hold 4h5h your opponents’ hands are likely better if for no other reason than they can’t be much worse. A more complicated situation arises when you hold a made hand with some value, but your opponents’ play has lead to to credit him with a bigger hand.

Beliefs About Your Opponent’s Future Actions

Believing your opponent has a stronger hand obviously isn’t enough to justify a bluff. It’s very possible that your opponent has a made hand sufficiently strong that he won’t fold no matter what action you take. In other words, your opponent may be committed to the pot.

It’s worth noting that you should be most interested your opponents’ likely actions IF they hold a hand that beats you.  If they hold a hand even worse than your bluffing hand, it’s quite likely they’ll be folding.

Odds

Once you form beliefs about your opponent’s likely holding and likely future actions, you then have a fairly simple problem to decide if a bluff is correct. Suppose you believe about 50% of the time your opponent holds a hand that beats you. And you believe he will fold 40% of the time if you bet some amount X. Then if the pot is at least 4*X, you will break even by bluffing in this spot since you will win 4*X every time your bluff works (which will happen with probability 0.5 * 0.4), and lose X every time it fails. If the pot is bigger than 4*X, you will turn a profit bluffing in this spot. This is very similar to the pot odds calculations used for drawing, but differers in terms of how you plan to win the pot. Unlike pot odds for drawing, the chance of winning here is not so obvious – you have to make an estimate of how likely you think it is that your opponent will fold. But once you’ve made that estimate, it’s easy to determine what the correct action is via a little math.

Semi-bluffing

The similarity noted above between bluffing and drawing is very important.  Simply put drawing hands make good bluffing hands.  They’re rarely best in terms of being the strongest made hand or having the highest equity.  Even more importantly, when you bluff with a drawing hand you have two ways to win.  Your opponent may fold, and if he doesn’t you may make your draw.  This part-bluff-part-draw play is called a semi-bluff and they’re very important, especially in big-bet games.

I’ve only scratched the surface of the topic of bluffing here.  But I wanted to define some important terminology.  I’ll be re-visiting this subject a lot, starting with the “continuation bet” in no limit holdem.