Nor is the bluff limited to poker. Threaten the boss with an ultimatum for a raise, tell the ladylove that it’s now or never, dare the bully to put up or shut up - in life, as in poker, you bluff at your peril or to your gain. Although the bluff would no doubt exist independently of poker and its predecessors (ancient Persian as has, English bragg, and French ambigu all embodied the bluff), it is nonetheless the most adventurous idea ever perpetuated by a card game. Owing largely to the bluff, poker has influenced our thinking on life, love, business, and even war. In fact, the mathematical theory of games was given a high-security classification by the armed services during World War II!

In a popular treatment of the highly technical theory, John McDonald called the bluff the spirit of poker. The statement is valid within the context of poker as a game. By bluffing, a spunky player can win the pot without having the best hand. This possibility of individual character, cunning, and even foolhardiness winning out, regardless of the run of the cards, distinguishes poker from such pure gambling games as craps and roulette.

If, on the other hand, poker were to be divested of the bluff - if all players had to size their bets in strict relation to the hierarchic value of their hands, which in turn is based on mathematical probability - poker would be reduced to mere chance. It would require less skill, less sense of strategy, less faculty of judgment. Other than knowing the correct odds against making a successful draw to a bobtail straight (and similar carding situations), the knowledgeable player would have only a negligible advantage over the tyro and the dullard. Except for patience, individual character traits would not be important. A computer would play a perfect game. In short, poker without the bluff would indeed have no spirit. It would quickly die out.

Spirit or not, however, the bluff, as such, is generally a losing proposition. The player who bluffs every hand will surely go broke. The image of the expert player as frequent bluffer is false, and the famed poker face is largely a myth. Steady winners do not bluff often. Yet, bluff they must, from time to time. Moreover, they must be caught bluffing for the purpose of strategy over a long series of plays. In other words, the poker player has to bluff occasionally to keep his opponents guessing. Such is the nature of the game.

How often should the complete strategist run a bluff in poker? One authority recommends that he bluff until he is caught twice in a particular session. Well, twice is a good enough rule of thumb, but what happens in a regular game after the opposition takes note of the “twice” habit? To be effective strategically, the bluff must be completely random, but yet not spontaneous, and not whenever a certain situation takes shape. Far too many players, for instance, have an urge to bluff on a busted flush, so that a one-card draw does not leave their bluff on random footing.

Can the expert player show an outright profit on the bluff? Perhaps. If he really is an expert. Paradoxically, he can make more successful bluffs against competent players than against poor ones. A poker adage: Never bluff a poor player, a heavy winner, or a heavy loser. There is a good deal of truth in the statement; but the expert, who expects to turn a profit on his bluffs in addition to strategic value, will not always follow any such advice. Some players are relatively easy to bluff when they are heavy winners or heavy losers, and a smattering of poor players are easy to bluff. It depends on the player, the situation at each particular bluffing instance, the limits of the game, and on the general disposition of the group.

Another paradox is that the expert can make more successful bluffs from a poor betting position than from a good one. For example, player A opens in jacks with two small pairs. Player B calls, holding four cards to a flush. Player C calls with a pair of aces. After the draw, player A checks to the possible flush. Having busted the flush, Player B also checks. Knowing that the flush (or straight) hasn’t connected, player C bets, hoping to bluff A out. Most likely player A will call, simply because C was in a “good” bluffing position. The bluff would have been more likely to succeed if B and C had changed seats: Player A checks, C bets into the possible flush, thereby indicating strength.

The squeeze play works even better. Let C open with a pair of jacks. Player A calls with a pair of kings. Player B calls with a four-flush. None of them improves on the draw. Bluffing, C bets the limit. He knows that A (if A is a competent player) has a pair higher than jacks. He also knows that B drew one card to a flush or straight, because otherwise he (B) would have raised on two pairs or a triplet-kicker hand. Chances are that B missed the flush. Thus, by betting under the gun, which would on first thought seem to be a very bad bluffing position, C puts A in the whipsaw, and his bluff is likely to succeed. Of course, B may connect on the flush, but, then, the bluff is a hazardous play under any circumstances.

The big payoff on the bluff comes indirectly, and more or less perversely, not from the mentalities of game theory and strategy, but from a deeper realm of the gambler’s psyche. The expert profits on the bluff in an inverse way, at the expense of the poor player and the psychologically chronic loser. How? Why? Because the poor player, and especially the chronic loser, suspects almost every bet of being a bluff. The mere possibility of a bluff gives him the excuse he needs to get into the action, to give his money away.

Of course, the poor player loses in a number of other ways, such as drawing to a short pair at unfavorable odds. The chronic loser, however, may be, in other respects, a complete poker player. He may know the correct odds and may even have enough self-control and patience to play accordingly. In fact, the correct mathematical odds may even support his rationalization of calling a suspected bluff.

I used to play poker with a professional mathematician. He knew how to figure odds, and he played by them. Yet he seldom won. His downfall was not that he bluffed too often or that he bucked the odds by drawing to inside straights, but simply that he called too many end bets. One night, we were playing a seven-handed game of draw poker. Dollar ante; $50 maximum bet. He opened for $5 with a pair of kings. Another player called. I called with an ace-high four-flush. Of course I knew that the odds were against my filling the flush; on the other hand, I knew that if I did fill it the mathematician would more than likely call my $50 end bet.

Luckily, I squeezed out an all-red hand of hearts. The mathematician caught another pair to go with his kings, so he bet $20 after the draw. The middle player folded. I called and raised $50. He called. I showed him my flush and raked in the pot. He shook his head contemptuously, saying, “The odds agains making that flush were 4 1/4 to 1!”

No doubt he though I had made a bad play by drawing to the flush in the first place. Perhaps I had; but I would never have made the draw against any other player at the table, because I knew that they might not call my end bet if I did connect on the flush.) I think he made a very bad play by calling my $50 raise. True, the mathematical odds had been 4 1/4 to 1. But I probably don’t bluff more than once in a hundred hands, which put the empirical odds at 99 to 1 that I wasn’t bluffing! What’s more, I wouldn’t make an outright bluff against that particular player once in a thousand hands of draw poker, which puts the odd at 999 to 1 that I wasn’t bluffing!

With other chronic losers it’s not the mathematics that provides the excuse to supsect a bluff; rather, it’s a point of honor with them to “keep you honest,” as the saying goes. They hold it as nothing short of dishonor to be bluffed out when they actually held the winning hand. In a way, they’re right. But good players - consistent players - have no such scruples about throwing in a winning hand; if they suffer from breach of code, they do so on the way to the bank to deposit the money they have won from the chivalrous. In short, the player who never throws in a winning hand is a sure loser. (But the complete strategist must make an unsound call from time to time, for the same reason that he must bluff from time to time.)

Another kind of steady loser seems to harbor some sort of persecution complex. He thinks people are trying to push him around all the time, that the other players are trying to bully him out of pots. I knew one such player, and he attributed his heavy poker losses to bad luck. “Oh, you catch your share of winning cards,” I said, feeling sorry for the guy and sincerely wanting to give him some helpful advice. “The trouble is that you call too many big bets on mediocre hands.” He bowed up at me, saying, “I know you guys are trying to run me out of those big pots!”