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THE DOCTRINE OF CHANCES. 5
senting the probability multiplied into the sum exDected. 







Again, if from the respective expectations which the players have upon the whole sum deposited be subtracted from the amount of their stakes, the remainder will be the advantage or disadvantage of either, according as the difference is positive or negative.
When the obtaining of any sum requires the advent of several events, independent of each other, the value of the expectation is found by multiplying together the several probabilities of happening, and again multiplving the product by the value of
b'2 
