14.50. The two players are of equal strength, i.e., they have equal chances of winning each game. They agreed that the prize would go to the one who first wins 6 games. They had to stop the game after the first player won 5 games, and the second player won 3. In what ratio should the prize be fairly divided?
14.50. Answer: $7: 1$. Let the players play three more games, i.e., the game is fictitiously continued even after the first player wins a prize. The second player will receive a prize if and only if he wins all three games. Since all $2^{3}=8$ outcomes of these three games are equally likely, the second player will receive a prize with a probability of $1 / 8$. Accordingly, the first player will receive a prize with a probability of $7 / 8$.