WINNING CHANCES

Ellesmere Guardian, Volume LIII, Issue 13, 16 February 1932, Page 7

WINNING CHANCES

GAMBLING MATHEMATICS.

ODDS AGAINST FLAYER

What are your chances of winning one of the £30,000 prizes in the Irish Hospitals Sweepstake, is the question put in an article in the London Sunday Dispatch.

You may be lucky, but mathematical science says that the chances are so overwhelmingly against you that if you are a wise man or woman you will forget all about the ticket you have been so carefully guarding, and write off the ten shillings you paid for it as a bad debt. In cold, harsh figures, if, as is expected, £1,500,000 is distributed in prizes it means, since 25 per cent, of the takings go to charity, and a large sum is absorbed by expenses, that £2,500,000 has been received for the sale of tickets. Five million tickets will have been sold. In addition, two free tickets are allotted to the sellers of every ten. In a lottery offering £1,500,000 in prizes the chances of an individual ticket winning the first prize is one in 5,500,000. As the stake money is divided into fifteen units of £100,000, the odds against winning one of the £30,000 prizes are precisely 366,666.6 to 1. If you live for 366,666.6 years and the conditions remain the same you may be reasonably certain of winning a first prize in the last year of that period. You may win on the first trial, or you may win on the 366,666.6 th time you have risked your annual 10/-, but if you keep on for 366,666.6 years and ultimately win you will lose money, for all the time two-fifths of your stake has been absorbed by the Irish hospitals and the cost of running the lottery.

And this deduction for costs is the fundamental reason why no one can win money by persistent gambling. If a gambler stays long enough at Monte Carlo he will come away minus the commission he has paid to the owner of the casino for running the house. Mathematical science can measure luck as accurately as it can do a sum in simple multiplication. Take a game of dice. A single dice has six sides, numbered from one to six. When thrown, it may stop with any one of the sides up. Supposing a bet is taken that the five will turn up. The odds are five to one against that happening; and if nothing is deducted for commission a player will eventually come out even.

If a pair of dice are used, then for each side of one the other may turn up in six different ways. What chances are there of throwing a seven? The cambinations may be 6 plus 1, 1 plus 6, 5 plus 2, 2 plus 5, 4 plus 3, 3 plus 4. There you have six different ways of throwing seven spots out of a possibility of thirty-six ways..

In a game of cards, what are the chances of getting four aces in a hand. In a pack of fifty-two cards there are four aces. The chance of getting the first one is four in fiftytwo. In the remaining fifty-one cards there are three aces. The chances of a second ace is three in fifty-one. Similarly the chance of a third is twoin fifty, ana of a fourth one in fortynine. The chance of getting four is the product of all the separate chances — one in 270,725! Whether a person risks 10/- in an Irish sweepstake ticket or not, he is gambling all the time. His life is gambled every time he walks across the street, but the law of probability is so accurate that an insurance company is willing to act as bookmaker against the risk with a certainty, if it obtains enough clients, that it will make a profit.

Ah insurance company is like a bookmaker. It it has plenty of money to meet contingencies and the luck goes against it, it will pay out. If not, like the insolvent bookmaker, it will welsh.

If a company has a capital of £1,000 and issues # a premium for £1000, and if the insured person is killed by a taxicab, the company is at an end by the loss of its total capital.

THE REAL GAMBLER. But suppose the company has 5100,000 capital and insures 100 peo-

pie in different places for £1000 each, the chances of their all dying at once before the company has had time to build up a reserve are 100 to 1 against. If the company insures 1,000,000 people the chances of the whole million dying at once are 1,000,000 to 1 against, so that if proper premiums are charged the laws of probability remove the element of gambling from its side of the business. The gambler is the premium payer, who has no means of avoiding a fatal collision with a recklessly driven motor car except by staying in bed. Even there the chances are not insignificant that he will come to a violent end.