When an event happens which is very improbable, the person to whom it happens is considered lucky, and the greater the improbability, the greater his luck. If two men play a game, the winner is not considered particularly lucky; but if one wanted only two points to go out and the other wanted a hundred, the latter would be a very lucky man if he won.
It is a remarkable fact that luck is the only subject in the world on which we have no recognised authority, although it is a topic of the most universal interest. Strictly speaking, to be lucky simply means to be successful, the word being a derivative of gelingen, to succeed. There are a few general principles connected with luck which should be understood by every person who is interested in games of chance. In the first place, luck attaches to persons and not to things. It is useless for an unlucky man to change the seats or the cards, for no matter which he chooses the personal equation of good or bad luck adhering to him for the time being cannot be shaken off. In the second place, all men are lucky in some things, and not in others; and they are lucky or unlucky in those things at certain times and for certain seasons. This element of luck seems to come and go like the swell of the ocean. In the lives of some men the tide of fortune appears to be a long steady flood, without a ripple on the surface. In others it rises and falls in waves of greater or lesser length; while in others it is irregular in the extreme; splashing choppy seas to-day; a storm to-morrow that smashes everything; and then calm enough to make ducks and drakes with the pebbles on the shore. In the lives of all the tide of fortune is uncertain; for the man has never lived who could be sure of the weather a week ahead. In the nature of things this must be so, for if there were no ups and downs in life, there would be no such things as chance and luck, and the laws of probability would not exist.
The greatest fallacy in connection with luck is the belief that certain men are lucky, whereas the truth is simply that they have been lucky up to that time. They have succeeded so far, but that is no guarantee that they will succeed again in any matter of pure chance. This is demonstrated by the laws governing the probability of successive events.
Suppose two men sit down to play a game which is one of pure chance; poker dice, for instance. You are backing Mr. Smith, and want to know the probability of his winning the first game. There are only two possible events, to win or lose, and both are equally probable, so 2 is the denominator of our fraction. The number of favourable events is 1, which is our numerator, and the fraction is therefore ½, which always represents equality.
Now for the successive events. Your man wins the first game, and they proceed to play another. What are the odds on Smith’s winning the second game? It is evident that they are exactly the same as if the first game had never been played, because there are still only two possible events, and one of them will be favourable to him. Suppose he wins that game, and the next, and the next, and so on until he has won nine games in succession, what are the odds against his winning the tenth also? Still exactly an even thing.
But, says a spectator, Smith’s luck must change; because it is very improbable that he will win ten games in succession. The odds against such a thing are 1023 to 1, and the more he wins the more probable it is that he will lose the next game. This is what gamblers call the maturity of the chances, and it is one of the greatest fallacies ever entertained by intelligent men. Curiously enough, the men who believe that luck must change in some circumstances, also believe in betting on it to continue in others. When they are in the vein they will “follow their luck” in perfect confidence that it will continue. The same men will not bet on another man’s luck, even if he is “in the vein,” because “the maturity of the chances” tells them that it cannot last!
| GAMES. | ODDS. |
|---|---|
| One | 1 to 1 |
| Two | 3 to 1 |
| Three | 7 to 1 |
| Four | 15 to 1 |
| Five | 31 to 1 |
| Six | 63 to 1 |
| Seven | 127 to 1 |
| Eight | 255 to 1 |
| Nine | 511 to 1 |
| Ten | 1023 to 1 |
If Smith and his adversary had started with an agreement to play ten games, the odds against either of them winning any number in succession would be found by taking the first game as an even chance, expressed by unity, or 1. The odds against the same player winning the second game also would be twice 1 plus 1, or 3 to 1; and the odds against his winning three games in succession would be twice 3 plus 1, or 7 to 1, and so on, according to the figures shown in the margin.
| GAMES. | |
|---|---|
| 1st | 2nd |
| 1 | 1 |
| 1 | 0 |
| 0 | 1 |
| 0 | 0 |