Bernie:
You want to wager on the outcome of a multi-game [best n out of 2n-1] series, but your bookie will only allow bets on individual games.
this should just be a high-school simple recusion problem
I don't think it's _that_ difficult, but anyway... Organize the problem, according to the number of wins needed by each side. Build a tableau like below. At row R, column C, put the amount you want to be ahead. When the series is over, you want to have a result of 1 or -1. Therefore: 0 1 2 3 4 5 --------------------------------------- 0 | 1 1 1 1 1 1 | -1 2 | -1 3 | -1 4 | -1 5 | -1 Each other cell is the average of its above and left cells. 0 1 2 3 4 5 --------------------------------------- 0 | 1 1 1 1 1 1 | -1 0 1/2 3/4 7/8 15/16 2 | -1 -1/2 0 3/8 5/8 25/32 3 | -1 -3/4 -3/8 0 5/16 35/64 4 | -1 -7/8 -5/8 -5/16 0 35/128 5 | -1 -15/16 -25/32 -35/64 -35/128 0 When you're at the state (R,C), bet (R-1,C)-(R,C) (which equals (R,C)-(R,C-1)). -- Don Reble djr@nk.ca