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r instance, where the players are all against the dealer, there is about the same element of chance and about the same room for the exercise of judgment that there is in a game of poker which is to end with a call. But the bluffing element, which is what gives the game its real value to the gambling fraternity, is independent of any qualities possessed by poker as a card game. Where there is no ' limit' (that is, no stated sum beyond which no bet must go), one can bluff as well, and almost as safely, over a bad hand as over a good one--if one possesses the requisite qualities of a false face and a steady nerve.
But I wish just now to consider the qualities which this game possesses as an exercise of the judgment. No judgment is shown by one who sits down to gamble at poker; but in the game itself there are points depending a good deal on judgment, and especially on a knowledge of the laws of chance. Here, oddly enough, the professional poker-players have made, for the most part, little progress. We have before us the reasoning of one who claims to teach, calling his book ' The Complete Poker Player,' and we find not only much that is
incorrect in theory, but an absolute failure to understand the real value of the principles of probability to the poker proficient, and indeed to all who gamble. He deliberately tells us, in fact, that while theory shows the odds to be such and such, experience points to other odds, the real fact being that experience and theory are in most perfect accord in all matters of probabilities.
In the first place, the problems connected with the decision, whether to stay in or retire on a given hand, are very pretty. The case is entirely different from that to be dealt with in such a game as vingt-et-un, where only the dealer has to be considered, each player being as it were in contest with him. In poker a player has to consider, not the chance of having a better hand than some particular adversary, but the chance that he holds better cards than any of the others. This modifies the chances in a very interesting manner. Not only are they different from those existing where each player is matched against the dealer, but they vary according to the number of players. Where the players are few a moderately good hand may be trusted to win against the company, in the average of a great number of trials; but where there are many players there is more chance of a strong hand lying somewhere to beat it, and therefore, the hand in which the player should decide to trust must be a better one. For instance, with few players a pokerist might safely decide that he would not go in on less than a high pair, as kings or aces, and adhering to that rule throughout the play would be likely to come out without heavy loss. But if there
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