FAIR AND UNFAIR WAGERS,

Otago Witness, Volume 26, Issue 2419, 26 July 1900, Page 37

FAIR AND UNFAIR WAGERS,

3lr R. A. Proctor writes: Suppose thai the just odds against a horse in a race are 9 to 1. /By this I mean that so far as the two bettors go— that is, from all that they kuovv about the chances of the horseit is nine times more likely that iLe hor?? will not win the race than that he will. Now it is nine times more likely that a particular ticket among 10 will not be drawn at a single trial than- that it will. So the chance of this horse is correctly represented by the chanco of the prize ticket being drawn in a lottery where there are 10 tickets in all. -If -Javo persons anange such a lottery, and A pays in £1 to the pool, while the other, B, pays in £9, making £10 in all, A gels a fair return for his money in a single draw, one ticket out of the 10 being marked for the prize. A represents, then, the backer of the horse who risks £1 ; B the layer of the odds who risks £9. The sum of the stakes is the prize, of £10. If A ris'ks'less than £1, while B" risks £9, the to Lai prize -is diminished. In either case the wrong done to the other bettor amounts precisely to the amount by which the total is diminished. Tf, for instance, A only wagers 18s against B's £9, the case is exactly the same as though A and B, having severally contributed £1 and £9 to a pool, one ticket out of 10 having been marked, and A to have one chance of drawing it (which we have just seen would be strictly fair), A. abstracted 2s from the pool. If B only wagered £7, instead of £9, against A's Si, the case would be just the same as though, after the pool had been made up as just described, B had abstracted £2. Take another case. The odds are 7to 3 against a horse. The chance of it winning is the same as that of drawing a marked ticket out of a bagcontaining 10, when three are marked and seven N are unmarked. We know that in this case two players, A and B, forming the lottery, must severally contribute £3 and £7 to the x^ool, and if on a single drawing on* of the three marked tickets appears, then A wins the pool, or £10, whereas B takes it if one of the seven unmarked liokets are drawn. If the backer of the horse, instead of wagering £3, wagered only £2 against £7, he would beprecisely in the poaiton' of a player A, who, having paid in his £3 to the pool of £10 in all, should abstract a pound therefrom. Ifi the layer of the odds wagered only £5 against £3, he would be in the position, of a- jjJa^MJ^

B, "who, having paid nig £ft to tha pool of £10 in all/ should abstract £2 therefrom. In reality, however, though quite possibly some -' among the foolish bettors riot only win money, tut even keep what they win, refraining from trying their luck afresh, it must not be supposed that, the fraudulent bettor exposes himBelf to the Tick of lose, in the long run. He plays a safe game. Every one of his bets is a partial swindle ; yet he in each case runs the risk of loss. His entire series of bets is l a complete swindle, in which he runs no risk .whatever of loss, but insures a certain gain.

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