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e there are thirty-six possible throws, and six of these give ' seven' as the total. Thus the chance of throwing 'seven' is one sixth, and the chance of throwing 'seven' ten times running is obtained by multiplying six into itself ten times, and placing the resulting number under unity, to represent the minute fractional chance required. It will be found that the number thus obtained is 60,466,176, and instead of 1,000 guineas, fairness required that 60,466,175
guineas should have been wagered against one guinea, so enormous are the chances against the occurrence of ten successive throws of 'seven.' Even against nine successive throws the fair odds would have been 10,077,595 to one, or about forty thousand guineas to a farthing. But when the nine throws of ' seven' had been made, the chance of a tenth throw of ' seven ' was simply one-sixth as at the first trial. If there were any truth in the theory of the ' maturity of the chances,' the chance of such a throw would of course be greatly diminished. But even taking the mathematical value of the chance, Mr. Ogden need in fairness only have offered a sixth part of 1,001 guineas (the amount of the stakes), or 166 guineas 1Ts. 6d., to be off his wager. So that his opponent accepted in the first instance an utterly unfair offer, and refused in the second instance a sum exceeding by more than three hundred guineas the real value of his chance.
Closely connected with the theory about the range of possibility in the matter of chance combinations, is the theory of the maturity of the chances-' the most elementary of the theories on probabilities.' It might safely be termed the most mischievous of gambling superstitions.
As an illustration of the application of this theory, we may cite the ease of an Englishman, once well known at foreign gambling-tables, who had based a system on a generalization of this theory. In point of fact the theory asserts that when there has been a run in favor of any particular event, the chances in favor
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