Calculating the Odds : Gambling and Betting to Win

How To Calculate the Odds

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broker by the constant influx of fresh victims.

In the series of transactions imagined above the stockbroker, without risk, secures more than the victim would have gained if there had been no brokerage. tie would have secured the same percentage had the investments been all ten times greater, or a hundred times greater, or a thousand, or ten thousand. Always he pockets freely and without risk; always, even the luckiest speculator pays freely, and the unluckiest speculator has to pay in like manner, besides losing heavily. Apart from success or failure in the speculations themselves and in the long run these are bound to balance




themselves pretty equally unless the speculator gets ' tips,' in which case he is sure to lose heavily in the long run--the broker always makes a sure and large gain, the speculator always has a sure and large loss, in brokerage alone.
Of course the example I have just considered will not be regarded by the average speculative gambler as typical. He expects to win very much more than he loses, or to win always and not lose at all. In reality, he has no more right to expect a considerable balance of gain than a farmer has to expect exceptional weather. Assuming fair bargains, as I have pointed out in the preceding sections, the gambler in stocks has no right to expect to gain more than he loses. Of course he does expect to gain, or he would not speculate. But if he has a particle of common sense, he will see that at the best he can only gain on some transactions rather ,more than he loses on others. Hence such a result as I have considered above is about what might be expected to occur in the case of a lucky speculator.

Taking a more general view, a speculator would have reason to regard himself as exceptionally fortunate if his gains were to his losses in the proportion of nine to eight. Suppose now that a speculator went on for a whole year at this rate, gaining on the average 50/. a week; and suppose, further, that his gain, when he has gained, has averaged the amount of cover invested, his loss, when he has lost, being always the cover paid in. It will be seen that his full weekly gain has been 450/.,




his full weekly loss being 400l.; so that the total amount invested as cover has been 850/. weekly, the stock represented being 85,000/. The brokerage on this at 1/16 per cent. amounts to 53/. 2s. 6d.; so that in this case, with a seeming gain of 50/. weekly, the unfortunate speculator loses 31. 2s. 6d., the broker pocketing all his client's gains and 31. 2s. 6d. beyond.

 

 

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