The possible combinations of cards in a hand as dealt out by chance are truly wonderful. It has been established by calculation that a player at Whist may hold above 635 thousand millions of various hands! So that, continually varied, at 50 deals per evening, for 313 evenings, or 15,650 hands per annum, he might be above 40 millions of years before he would have the same hand again!
The chance is equal, in dealing cards, that every hand will have seven trumps in two deals, or seven trumps between two partners, and also four court cards in every deal. It is also certain on an average of hands, that nothing can be more superstitious and absurd than the prevailing notions about luck or ill-luck. Four persons, constantly playing at Whist during a long voyage, were frequently winners and losers to a large amount, but as frequently at 'quits;' and at the end of the voyage, after the last game, one of them was minus only one franc!
The chance of having a particular card out of 13 is 13/52, or 1 to 4, and the chance of holding any two cards is 1/4 of 1/4 or 1/16. The chances of a game are generally inversely as the number got by each, or as the number to be got to complete each game.
The chances against holding seven trumps are 160 to 1; against six, it is 26 to 1; against five, 6 to 1; and against four nearly 2 to 1. It is 8 to 1 against holding any two particular cards.
Similar calculations have been made respecting the probabilities with dice. There are 36 chances upon two dice.
It is an even chance that you throw 8. It is 35 to 1 against throwing any particular doublets, and 6 to 1 against any doublets at all. It is 17 to 1 against throwing any two desired numbers. It is 4 to 9 against throwing a single number with either of the dice, so as to hit a blot and enter. Against hitting with the amount of two dice, the chances against 7, 8, and 9 are 5 to 1; against 10 are 11 to 1; against 11 are 17 to 1; and against sixes, 35 to 1.
The probabilities of throwing required totals with two dice, depend on the number of ways in which the totals can be made up by the dice;—2, 3, 11, or 12 can only be made up one way each, and therefore the chance is but 1/36;—4, 5, 9, 10 may be made up two ways, or 1/8;—6, 7, 8 three ways, or 1/12. The chance of doublets is 1/36, the chance of PARTICULAR doublets 1/216.
The method was largely applied to lotteries, cock-fighting, and horse-racing. It may be asked how it is possible to calculate the odds in horse-racing, when perhaps the jockeys in a great measure know before they start which is to win?
In answer to this a question may be proposed:—Suppose I toss up a half-penny, and you are to guess whether it will be head or tail—must it not be allowed that you have an equal chance to win as to lose? Or, if I hide a half-penny under a hat, and I know what it is, have you not as good a chance to guess right, as if it were tossed up? My KNOWING IT TO BE HEAD can be no hindrance to you, as long as you have liberty of choosing either head or tail. In spite of this reasoning, there are people who build so much upon their own opinion, that should their favourite horse happen to be beaten, they will have it to be owing to some fraud.
The following fact is mentioned as a 'paradox.'