Game theory is a complex topic combining mathematics and social psychology. Simply speaking, it is the analysis of decision-making in a game or conflict involving two or more participants. Game theory is implicated in many different contexts, such as the stock and bond markets, the economy in general, poker, gin, backgammon, and of course, professional sports. We'll elucidate some of the central concepts of game theory by first discussing one aspect of a popular parlor and gambling game—bluffing in poker.

As almost anyone who plays poker knows, the proper use of the bluff is an important weapon in the poker player's arsenal. In the interest of simplicity, we'll restrict the discussion to the strategy of bluffing against one opponent on the last bet in a typical poker game like Texas Hold'em or Seven-Card Stud. Suppose that after all the cards have been dealt, it's your turn to bet, and you are 100% sure that you can't win in a showdown (you are positive that your opponent has a better hand than you do). This means that the only way you can win is by betting and having your opponent fold his hand (a bluff). What should you do? Well, that's where game theory comes into play.

If your opponent never folds a hand in the face of a possible bluff, then clearly it is correct for you to never bluff. You would be throwing your money away. You simply check and fold, if your opponent bets, or you check and show down the hand if your opponent checks also. Of course, either way you lose, but at least it doesn't cost you an additional bet.

What about if your opponent always folds unless he has a strong hand—in other words, he never tries to pick off a bluff? In this case it would be correct for you to always try a bluff when your hand is too weak to win in a showdown. Even if your opponent sometimes calls your bet with a strong hand, he'll have enough weak hands, which he'll throw away, to make a bluff profitable for you in the long run (assuming there is enough money in the pot, which there usually will be).

Most opponents, however, fall somewhere in between these two extremes. That is, they sometimes fold their hand in the face of a potential bluff and they sometimes call with a weak hand, knowing that they can only beat a bluff. In this case, what do you do? It turns out that, if your opponent will call a potential bluff too often, as compared to what the game theory equilibrium point (we'll get to that in a minute) dictates—even a smidgen too often—it is correct for you to never bluff; if he folds his hand too often—again, even just a smidgen too often—in the face of a potential bluff, then it is correct for you to always bluff. Of course, if your opponent is observant and smart, eventually he will realize that you are always or never bluffing, and adjust his calling frequency accordingly. In fact, if your opponent figures out that you are bluffing too little or too much, it becomes correct for him to start calling or folding all the time. In that case, of course, you would then have to re-adjust your strategy. As you can see, this give and take, or constant re-adjusting of strategies, can go on and on ad infinitum.

What if you don't know your opponent's strategy with respect to calling potential bluffs, and you can't estimate it, or you suspect that your opponent is an expert player? Or what if your opponent is an expert player and he is trying to figure out how often to call and how often to fold against you? As it turns out, the mathematical solution to both of these problems, how often to bluff or call a potential bluff, is determined by the amount of money already in the pot, how often you bet (or check) your legitimate hands, how often those hands win, and the size of the last bet.