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Two players, [itex]A[/itex] and [itex]B[/itex], are playing a sequence of matches of some game. In each match, one player wins (there is no draw game in any match). For winning the match, the player gets [itex]1[/itex] point, and for losing, [itex]0[/itex] points. The match ends when one of the players first gets [itex]6[/itex] points, and that player wins the match. At the beginning of each match, players invest the same amount of the stake.

Assume that the game is interrupted at the result [itex]4:3[/itex] for player [itex]A[/itex]. If the performance of both player are approximately good, what needs to be the ratio of stakes such that the split of stakes is righteous?

Two players, [itex]A[/itex] and [itex]B[/itex], are playing a sequence of matches of some game. In each match, one player wins (there is no draw game in any match). For winning the match, the player gets [itex]1[/itex] point, and for losing, [itex]0[/itex] points. The match ends when one of the players first gets [itex]6[/itex] points, and that player wins the match. At the beginning of each match, players invest the same amount of the stake.

Assume that the game is interrupted at the result [itex]4:3[/itex] for player [itex]A[/itex]. If the performance of both player are approximately good, what needs to be the ratio of stakes such that the split of stakes is righteous?

**Question:**How to approach this problem? What methods in probability are useful?