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xed luck.) Half of the fifteen millions will deem themselves rather lucky, while the other half will deem themselves rather unlucky. None, of course, can have had even luck, since an odd number of games has been played.
Our 20,000,000 players enter on a fourth series of encounters. At its close there are found to be 1,250,000 very lucky players, who have won in all four encounters, and as many unlucky ones who have lost in all four. Of the 2,500,000 players who had won in three encounters, one-half lose in the fourth; they had been deemed lucky, but now their luck has changed. So with the 2,500,000 who had been thus far unlucky: one-half of them win on the fourth trial. We have
then 1,250,000 winners of three games out of four, and 1,250,000 losers of three games out of four. Of the 7,500,00() who had won two and lost one, one-half, or 3,750,000, win another game, and must be added to the 1,250,000 just mentioned, making three million winners of three games out of four. The other half lose the fourth game, giving us 3,750,000 who have had equal fortunes thus far, winning two games and losing two. Of the other 7,500,000, who had lost two and won one, half win the fourth game, and so give 3,750,000 more who have lost two games and won two: thus in all we have 7,500,000 who have had equal fortunes. The others lose at the fourth trial, and give us 3,500,000 to be added to the 1,250,000 already counted, who have lost thrice and won once only.
At the close, then, of the fourth encounter, we find a million and a quarter of players who have been constantly lucky, and as many who have been constantly unlucky. Five millions, having won three games out of four, consider themselves to have better luck than the average; while as many, having lost three games out of four, regard themselves as unlucky. Lastly, we have seven millions and a half who have won and lost in equal degree. These, it will be seen, constitute the largest part of our gambling community, though not equal to the other classes taken together. They are, in fact, three-eighths of the entire community.
So we might proceed to consider the twenty millions of gamblers after a fifth encounter, a sixth, and so on. Nor is there any difficulty in dealing with the
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