“That the strait pass was damm’d.”
Cymbeline. Act V., Scene 3d.
The study of the theory of probabilities for the playing of poker, i.e.; how to win at it, may be very good in its way. The examination of the chance laws is a most interesting one. For practical use they are of no value. No one save a genius, in the possession of an exceptional memory, playing like an automaton, could carry these laws into actual practice, and such a gifted individual does not usually sit at a poker-table.
Everybody knows that before the draw one pair is more commonly held than two pairs; and that after the draw, to receive another pair is more usual than to get a third card, which makes threes. The progression of difficulties is at once understood when the scale of winning combinations is examined, and for the rarity of such combinations the laws of chance may be studied.
For those interested in such mathematical problems, the laws of chance relative to poker are presented in this volume, due to such authorities as Pole and Proctor. “Cavendish” has also written a learned paper on this same topic, but we do not print it, as being too abstract for common use.
There are some very simple, common-sense facts in poker in regard to the advantages of position, which positions are, of course, always changing.
The hand after the age, designated as C, after A the dealer, and B the age, has the worst position. If he has anything he comes in first, and has to stand the entrance or the possible raises of all who are after him. C then is in the position of a man running the gauntlet. For, position the advantage lies with the last man, who is the age. He winds up the performance. If he happens to hold a good hand, anything above the average - as a pair of aces, or two pairs - he should raise before the draw is made. The chances are that he has the best hand, or even if he has not, that he forces out some of the others. They will not see his raise, and he carries off the pool.
If all the other players go out, the dealer with a low pair has a good chance of winning against the, blind. It is the exact reverse of the position of C, who plays when he enters against four. A, the dealer, plays only against B, the blind. The chances are that the blind has nothing, and gives up.
For the first player, after the age, or C, to raise is a stupidity. All he can do is then to win the age’s half ante; for if he has not a fair hand, the age will give it up. This raise too at the beginning drives out all the others, unless they hold good hands. C must always play a waiting game. If he has a strong hand, he sees the raises or may raise in his turn.
If C comes in it is not wise for D to raise, because E and A and B are after him. The blind, who is never given credit for holding anything, is in the best position to raise, not alone because he is the last, but for the reason that his raise is the most unexpected. It is, therefore, good tactics if he has a pair over the average to raise. But the age still remains the most wasting, as to chips of all the positions.
If a player were to retain the age through a whole game, there are ninety-nine chances in a hundred that he would lose. A great many chips are lost by the age by the mere fact of his doubling his ante, or making his blind good, relying on his holding one small pair, lower than the average. Taking three minutes as the average time to finish one round at poker, when five are playing, within an hour the ante-man will have put up twenty chips. If he, plays three hours, he has offered up sixty chips. If he has made his blind good, that would be one hundred and twenty chips. The chances would be, that as age he held originally some fair hands. The probabilities, if given all in his favor, would be when he won with some of his hands. But calculating all to his advantage, it is quite, certain that if he comes in with a small pair he will lose in the three hours ninety chips.. To have the age and to bluff with a small pair is very great folly, and this adds to ruin.
For the age to raise induces the players to believe that there is a bluff in the air, and it looks, from a study of the game, as if the age were more constantly called than any other hand.
The dangers of the age cannot be too much expatiated upon. It is the finest and the worst position at the same time. Steady, experienced players,. when more than one come in, often make it a rule to abandon their chip if they hold a pair lower than tens. C, if he knows what he is, about, will never come in first with less than tens; and D ought to have even better. The percentage against C’s winning then is very great.
“All in the draw.” When a person who holds the age believes in that, it is ruin. Suppose you do go in with two nines, and draw a third, making three nines. The chances are just as good for another player to have taken in another ten, or another jack, queen, king, or ace, and then you are beaten. You started too low, and your improvement is only so much the worse for you. It requires no explanation to understand that your adversary’s two pairs, made during the draw, with their jacks up, are better than yours, with tens up.
To straddle is a weakness. It confers no possible benefit. You assume for the moment the apparent advantages of the age, and then when you want this advantage the most – that is, to bet last – you have, according to the rule, to give it up. You have simply doubled the ante. This may or may not intimidate the rest of the players. It ought never to frighten out the age if he has a pair. The age, if he has a single pair, will see the straddle, with good chances of winning. The person who straddles often forgets that the active condition of the game is something, entirely different from the passive one.
Entrance into the game by the last player, A the dealer, when C, D, and E are in, unless he has a good, pair, is folly.
When players meet frequently, they all know that a wild player, if there is such a one among them, is certain to lose in the long run. Steady play – conservative poker – is absolutely sure to worst him. He may have occasional flights of luck, and draw “a tan-yard from a shoe-string”; but that kind of thing does not last long. He may win largely once in awhile, and all the rest of the time lose quite as largely.
It may be denied, but experienced players rarely enter without a pair of jacks or better. It is even under exceptional circumstances that they draw for a straight or a flush. At the first to go in, after the blind, they let the straights and flushes severely alone. If they have the age they will draw on straights and flushes and may or may not raise. If there are many players, then old players take their chance with a flush or straight to draw to.
With all these explanations for playing, founded on common-sense principles, there are numerous exceptions. These exceptions do not arise from the laws of chance, but have to do with the idiosyncrasies of the players, Most of the money lost at poker comes from seeing. Curiosity is fatal,. All the money saved arises from want of curiosity. Still, take the player who has won twice hand running, his hand having been called, if he makes a high bet a third time with a new hand, there are many chances that he is bluffing. It is not likely that he will have three times consecutively the best cards.
Whether to draw for a straight or a flush depends not only on position but how many cards your adversaries take. If you see the blind, and have, say, four hearts, or four clubs, spades, or diamonds, your four cards ending with a queen, king, or ace, and the other card being a queen, king, or ace, you have a pair. Are you to retain a pair or draw for a flush? If the majority of those before you draw one card, they may also be drawing to a flush or straight, but at the same time they may have two pairs or threes. If the majority of the adversaries draw one card, what should you do? We would not advise throwing away the queens, but to draw three cards. If you make two pairs or three queens, your hand is above the average. But we would throw away a pair of tens. Having a straight to make, the same plan is recommended. If the flush is made, or the straight, of course the advantages of this hand are immense. The temptation to raise on a straight to be made or a flush to be made is very great, as it is likewise for players having the making of these two cornbinations to see the raises. They look, when one card is drawn, like two pairs or threes in hand. The player raising on a flush or straight in the future is bound to bet on it, and mostly wins, providing other players have only two small pairs. It is here that the bluff must be pushed home.
How to draw on threes, whether by taking two cards or by dispensing with their presence, asking for one card is only a question of expediency. Poker, in order to be well played, must be ever changing in its methods. Deceit is the constant element. It is quite unlikely that when C is raised by D, and that C only takes two cards, that he has not a bona, fide triplet. If you have raised on two pairs, you had better treat the matter mildly, and if he raises, go out. Even four of a kind maybe disguised by the drawing of one card, or by standing pat.
In fact, whether there is anything in a hand or not, can never be known until it is called; with threes, is it then better to draw two cards or one If two cards were drawn, the chances of making a four are possible; but at the same time, the value of the hand is given away to the players. The probabilities of having fours are 4,164 to 1; of a full, 693 to 1. Many players having threes, discard, invariably, the lowest card. They believe that the higher cards have been retained by the other hands coming in. The only thing in regard to the discard of the lowest card is, that once begun it must always be continued.
Theoretically, calculations as to what should happen with cards do not avail against what actually does take place. Luck is a perverse jade, and refuses to be bridled. In theory, in 10,900 games of poker there ought to occur at least fours ten times. In an actual game, fours never came out but once, and yet at one sitting, on three occasions fours have appeared and during the same time two straight flushes. More straights per contra by fifty per cent. were dealt in an actual game than should have been theoretically present. There were sixty dealt, while there should have been but forty, according to the books. Strangely enough, the threes tallied with the theory, and in two pairs and single pairs the players and the theorists were wonderfully close.
A player ought in a certain way to equalize his chances, and do the same thing over and over again. This equalization of his chances, and the advantages of it, may not be apparent during one, game, but only during a series of games. Win to-day, lose to-morrow, is the maxim. It is not the cards that change, it is human nature.
When a player takes but one card, it is a rule among conservative players to see his bet, if they have a good hand, but not to raise him. This rule is applied when only two are in. Two falls may meet each other in this dull way. But it is foreign to the game of poker, and, belongs to the automatic way of playing.
It is impossible to estimate the value of a hand. The heaviest losses may be made on four kings. Never think how much you may win on a good hand, but how much you can lose. There is no such thing as cowardice at poker. A player has stood on a pat, ace, king, flush, and, raising, seen without raising another flush which had drawn on four cards, with an ace, king, queen, flush, and thereby the holder of the pat hand saved innumerable chips - it having cost him no more than if he had had two pairs, ace high. Those who pity “your poor play” are by no means willing to share your risks.
Jack-pots have very much changed the character of the game, and in one respect to its detriment. On the other hand, it has equalized poker. It is really at best but a show of hands. A great deal depends in jack-pot on the character of the game, whether it is a high or a low one. Among conservative players, the first player, C, will not open on jacks; the risk is too great. If all, pass to the dealer, he is safe to open on jacks. Some players will never open themselves or come in afterward without two good pairs, at the lowest kings up, or threes.
The losses at jack-pot, where the limit is reached every time, are heavier, it should be remembered, than at any other period during the game. Bluffing in the play of jack-pot should be eschewed -nothing is more dangerous. The chances are, that starting in with good hands, the bluff will be seen. A conservative player is never tempted in a jack-pot, with a flush or straight to be drawn to. To raise the opener of a jack-pot requires a good hand. If the player after the opener raises, and the opener raises in his turn do nothing more than call, unless a superlative hand is there.
A trick in the jack-pot, when all have passed up to E and E opens, is for A, the last to come in, to raise him. All the others are weak, having passed out once, and it is likely that E will drop. But this is, like all things in poker, uncertain.
In all these hints as to playing poker, the supposition is, that there is a limit. In fact, this treatise on poker is written only for those who play with a limit. To play poker without a limit is ruin. The game without a limit brings to the front all the rascals. It is a temptation to fraud.
It is rather difficult to state what shall be the limit. Penny-ante, with a limit of 20 cents, suffices for all amusement. The losses may be $5; with a $1 limit, $10; with a $2 limit, $75, with a $5 limit, $250. It is the limit which largely increases the losses. A player may lose $5 and go to bed happy. But with a loss of $250, it is pretty certain that the player does not sleep sweetly. A heavy game is destructive of poker. No purse is big enough to stand it. In fact, harmless as is poker when played with reason, when unreasonably indulged in it ends with desolation and dishonor.
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