Game Theory and NLHE

[Lloyd]

I came up with the number 8 by using the same method that Sklansky used in "Theory of Poker" when discussing Game Theory and Bluffing. Essentially, he said that you should bluff in the same frequency as the odds your opponent is getting. So if you're on a flush draw in a game where your oppontent doesn't see your last card, there are 9 cards that will make your flush. If you opponent is getting 5 to 1 odds if you bet, your ratio of made cards to bluff cards should be 5 to 1. So in this example, you will make your flush with any of 9 cards, and you would select two random cards with which you would bluff (it's actually a little less than two but I rounded up). If you never bluffed, then your opponenet would simply fold if you bet and bet if you checked. By introducing a bluff you have optimized your profits on this hand as sometimes they will call you when you've made the hand and sometimes they will fold when you are bluffing. This more than makes up for the times when you are called on a bluff.

The same logic can be applied to starting hands. If your opponents know that you will only open UTG with pocket 8s and higher, or AQ and higher, they should simply fold if they can't beat those hands. By introducing a bluff to your starting hand requirements, they won't know exactly what to do. If for instance you'll open UTG with 76s, get called, hit the flop and go to a showdown, you would have them off-balanced on what to do with your opening raises. Now they might be more likely to call you with inferior hands. The question, in this instance, is what is the ratio of true starting hands to bluffs that would lead to optimal results.

My limited understanding of game theory is that it is only appropriate when you're playing against people of equal calibre. If you're playing online against people who don't have a clue, you don't need to introduce bluffs to your starting hand requirements because they'll call you with inferior hands anyway. But if you're in a large buy-in tournament at the Bellagio with a bunch of great players, you might need to alter your strategy to keep people off balance. This is where game theory would be useful.