Chance and Luck

The points which give a hand value are the presence of cards of the same denomination (as a pair, or two of the same denomination; triplets, or three of a kind; and fours, or four of a kind); a sequence -- that is, all the cards in the hand being in sequence, as 9, 10, knave, queen, king; a flush, or all the cards of the same suit. The lowest kind of hand is one which has none of these points; such a hand is estimated against others of the same kind by the highest card in it (the value of the cards being as in whist). Next in value is a hand with one pair in it; next a hand with two pairs (different pairs, of course); next a hand with three cards of the same denomination, called 'threes'; next a sequence hand; next a flush hand; then a full hand -- that is, a hand containing one pair and one triplet; then fours, a hand containing four cards of the same denomination; and, lastly, that is highest and best of all, a flush sequence -- that is, a sequence of high cards all of the same suit. In every case where two hands are of the same kind, the cards of highest denomination in the pair, triplet, four, flush, or sequence, wins. Thus a flush sequence of knave, 10, 9, 8, 7, beats a flush sequence of 9, 8, 7, 6, 5; four aces beat four kings or four queens; a full of three aces and two deuces beats a full of three kings and two queens, but a full of three aces and two threes beats a full of three aces and two deuces; a flush of king, 7, 5, 3, 2, beats a flush of queen, knave, 10, 9, 7; and so on. In cases of 'tie' the stakes are divided.

It is clear that the game itself is as good as many which are played in the domestic circle. In such a game as vingt-et-un, for 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.