Article Game Theory and Bluffing
Game Theory and Bluffing
I’m going to start off with a disclaimer. I will be taking a rather liberal approach to my definitions for the sake of simplicity and making a point. The true aim of this article is to help you with your poker game, not to teach a class on this rather arcane branch of mathematics.
Game theory is a branch of mathematics that was first developed by John Neumann in the 1940s. The basic definition of game theory I’ll use today is the pursuit of an optimal strategy that maximizes one’s wins or minimizes one’s losses against an opponent in a given scenario.
Game theory has been applied to economics, politics, war, and poker. Poker has long been studied by game theorists because it is a game that forces its players to deal with incomplete information (the opponent’s hole cards).
The good news for poker is that it is impossible to use game theory to develop a perfect strategy. The missing information has too great an affect on the outcome of the game. However that doesn’t mean that we can’t use game theory to our benefit at the poker table.
The best place to use game theory is in the randomization of your plays. Let’s use bluffing as an example.
Let’s say you are drawing to an opened-ended straight draw. With a straight draw, there are 8 cards that can make you hand. If you tried to bluff every single time you missed the straight, your opponent would catch on and start calling more. If you never bluffed when you missed, your opponent would always fold when you bet. You are trying to find a bluffing frequency somewhere in the middle of these two extremes.
The goal of game theory in this case is to find the optimal bluffing frequency to keep your opponents guessing. The optimal bluffing frequency is to match that frequency to the pot odds you are offering your opponent.
So, you’re hoping for one of those eight cards to hit. If you do hit the card or you decide to bluff, you have decided that you will bet $50 into a $150 pot. The pot odds you are offering to your opponent with this bet are 4-1. He must call $50 to have a chance at a $200 pot.
This means that the proper bluffing frequency would 1-4. One out of every four bets you make will be a bluff and the rest will be value bets when you actually do hit your hand. If you properly randomize your decision of bluffing, there is absolutely nothing your opponent can do about it. Even if you tell your opponent you are going to bluff 1 out of 4 times in this situation, there is no way he can exploit your bluffing frequency for money.
An easy method for properly randomizing this bluff is to pick two additional cards out of the deck that will be your trigger for a bluff. Say you decide that the black tens will be your bluff cards. So there are now 8 cards that can come with which you will be betting a real hand and 2 cards that will cause you to bluff. 8-2 reduces to 4-1 and you have now optimized your bluffing frequency.
There is one weakness to this strategy. The weakness is that it is a fixed strategy and does not adapt to your opponents. This strategy is defensive – it does not attempt to exploit your opponents, it only prevents you from being exploited. It is best used against good players or opponents with whom you aren’t yet familiar.
Let’s say you are playing against an opponent who always folds if you bet. Now your optimal strategy from above wouldn’t hurt you, but it sure wouldn’t be helping much either. Obviously if you were up against an opponent who always folded, you would bluff 100% of the time.
On the other hand if you were up against an opponent who called every single time you bet, the optimal strategy would be to lower your bluffing frequency to 0%. There would be no point in even the occasional bluff if the opponent was calling every single time.
When you tailor your strategy to take advantage of these types of weaknesses in your opponent, you are using an exploitative strategy to increase your gains. The optimal bluffing frequency from earlier is best against a good opponent or when you are unsure of how to play against your opponent. In this case your goal is to minimize your mistakes. If the opponent happens to deviate in any way from an optimal strategy against you, his losses will automatically become your gains.
Another good time to use game theory is to randomize the way you play certain hands. The point of randomizing your play is to keep yourself form becoming to predictable.
Let’s say you are holding AhQh and the board comes 2h7h7s. You have a pretty strong draw with two overcards so you push all-in and hope for a fold but aren’t too afraid of a call since you will probably have outs.
Let’s say instead you are holding As7c on this board. If your opponent comes out betting, the best play is usually to raise. You have a strong hand but don’t want to give your opponent a chance to catch up to you.
Now in the third example, let’s say you have pocket twos on the same board. Your opponent once again comes out betting and this time you elect to slowplay because there is not much chance of him catching up.
Each one of these plays isn’t bad by itself but if you play these hands exactly the same way every time, your opponents will catch on. This is especially true of opponents you play against regularly but even opponents who don’t know you will recognize these common lines.
The best way to keep you from becoming predictable is to occasionally mix the plays up. Occasionally just call with the flush draw so your opponent will be worried about slowplayed hands. Sometimes slowplay the trip sevens even at the risk of giving a free card. And every once in a while raise that full house on the flop.
I don’t recommend mixing it up super often, but just enough to keep it in the back of your opponents’ minds that you could have any of a variety of hands. As you get to know your opponents better, you can adjust the frequency of mixing up these plays. If an opponent is particularly timid, you can raise with draws more often and increase the slowplays. If the opponent is more of a calling station then you will obviously want to raise more with your strong hands and avoid pushing with draws. Most of your opponents will be somewhere between these two extremes so it’s up to you to determine the right frequency of these plays.
In practical application at the poker table, it’s impossible to turn game theory into an exact science. If it was possible, poker would not be a very interesting game. Even so, it is important to keep the concept of game theory in your mind. It is a more scientific way of thinking about the game and it can help you better analyze situations and make the proper adjustments.
Check Out More Poker All-In Articles
Send E-Mail to: alblmfld@hotmail.comThis page created using the webpage creation facilities of Webspawner.
Copyright © 2008 Alan Bloomfield. All Rights Reserved