increases by a twentieth the probability of the simple event which it favors. If this event is heads, its probability will be ½ plus 1/20, or 11/20, and the probability of throwing it twice in succession will be the square of 11/20, or 121/400. If the favored event is tails, the probability of heads, will be ½ minus 1/20, or 9/20, and the probability of throwing it twice in succession will be 81/400. Since we have at first no reason for believing that the inequality favors one of these events rather than the other, it is clear that in order to have the probability of the compound event heads heads it is necessary to add the two preceding probabilities and take the half of their sum, which gives 101/400 for this probability, which exceeds ¼ by 1/400 or by the square of the favor 1/20 that the inequality adds to the possibilities of the event which it favors. The probability of throwing tails tails is similarly 101/400, but the probability of throwing heads tails or tails heads is each 99/400; for the sum of these four probabilities ought to equal certainty or unity. We find thus generally that the constant and unknown causes which favor simple events which are judged equally possible always increase the probability of the repetition of the same simple event. In an even number of throws heads and tails ought both to happen either an even number of times or odd number of times. The probability of each of these cases is ½ if the possibilities of the two faces are equal; but if there is between them an unknown inequality, this inequality is always favorable to the first case. Two players whose skill is supposed to be equal play on the conditions that at each throw that one who loses gives a counter to his adversary, and that the game continues until one of the players has no more counters. The calculation of the probabilities shows us that for the equality of the play the throws of the players ought to be an inverse ratio to their counters. But if there is between the players a small unknown inequality, it favors that one of the players who has the smallest number of counters. His probability of winning the game increases if the players agree to double or triple their counters; and it will be ½ or the same as the probability of the other player in the case where the number of their counters should become infinite, preserving always the same ratio.