An employer engaged two young men, A and B, and agreed to pay them wages at the rate of £100 per annum. A enquires if there is to be a “rise,” and is answered by the employer, “Yes, I will increase your wages £5 every six months.” “Oh! that is very small; it’s only £10 per year,” replied A. “Well,” said the employer, “I will double it, and give you a rise of £20 per year.” A accepts the situation on those terms.
B, in making his choice, prefers the £5 every six months. At the first glance, it would appear that A’s position was the better.
Now, let us see how much each receives up to the end of four years:—
| A | B | ||
| 1st year | £100 | 50} | 1st year |
| 2nd " | 120 | 55} | |
| 3rd " | 140 | 60} | 2nd " |
| 4th " | 160 | 65} | |
| 70} | 3rd " | ||
| 75} | |||
| 80} | 4th " | ||
| 85} | |||
| £520 | £540 | ||
A spieler at a Country Show amused the people with the following game:—He had 6 large dice, each of which was marked only on one face—the first with 1, the second 2, and so on to the sixth, which was marked 6. He held in his hand a bundle of notes, and offered to stake £100 to £1 if, in throwing these six dice, the six marked faces should come up only once, and the person attempting it to have 20 throws.
Though the proposal of the spieler does not on the first view appear very disadvantageous to those who wagered with him, it is certain there were a great many chances against them.
The six dice can come up 46,656 different ways, only one of which would give the marked faces; the odds, therefore, in doing this in one throw would be 46,655 to 1 against, but, as the player was allowed 20 throws, the probability of his succeeding would be—
20
46,656
To play an equal game, therefore, the spieler should have engaged to return 2332 times the money deposited.