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fects the average proportion of heads or tails coming next after the series. Thus I have before me the record of a series of 16,317 tossings, in which the number of sequences of tails (only) were rendered; and I find that after 271 cases in which tails had been tossed 5 times in succession, the next tossing gave in 182 cases heads, and in 139 cases tails. Among the 16,317 tossings, two cases occurred in which tail was tossed 15 times in succession.
MARTINGALES; OR, SURE (?) GAMBLING
SYSTEMS.
IN previous pages I have considered, under the head of 'Gamblers' Fallacies,' certain plans by which some fondly imagine that fortune may be forced. I have shown how illusory the schemes really are which at first view appear so promising. There are other plans the fallacy in which cannot be quite so readily seen, though in reality unmistakable, when once the conditions of the problem are duly considered.
Let me in the first place briefly run through the reasoning relating to one of the simpler methods already considered at length.
The simplest method for winning constantly at any such game as rouge-et-noir is as follows :--The player stakes the sum which he desires to win, say 11. Either he wins or loses. If he wins he again stakes 1l., having already gained one. If, however, he loses, he stakes 21. If this time he wins, he gains a balance of 1l., and begins again, staking 1t., having already won 1l. If, however, he loses the stake of 21., or 31. in all (for 11. was lost at the first trial), he stakes 4l. If he wins at this third trial, he is 11. to the good, and
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