I know that I'm getting senile, and I'm growing to accept that, but... this little problem has been driving me *NUTS*. The problem whizzed by on another mailing list as a programming problem and I wasn't particularly interested in the programming aspect [which was actually simple enough given the right algorithm] but in the derivation of the algorithm... But I just *can't* do it, and so I'm looking for some help. I *must* be missing something because it just can't be as hard as I'm finding it. Here's the problem: 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. For a one-game series, this isn't an issue, obviously. But what I was surprised to see was that: For a best two-out-of-three, if you wager half what you want to risk [call that 'R'] on the first two games, then either the series is over and you've gotten the result of wagering R on the series, or the series is tied *and*you're*even*, so you just wager R on the last game and you're done. No matter what happens in the invidual games of the series you win or lose R. For a best three out of five series, it is actually easy enough to do a similar analysis brute force: Bet B on the first two games. If the teams split the series is now best two-out-of-three, and you're even, so use the above strategy. If either time wins both, then you're either ahead or behind by 2B. To make your overall position be 'R' if the same team wins the third game and sweeps, you need to bet R-2B on the third game. If the series goes on, it is now 2-1. But 2-1 in which a five game seeries is the *same* as 1-0 in a three game series and we know how the bets go in that: when a three-game series is at 1-0, you should be ahead [behind] by R/2. Since your current standing is [+/-](4B - R), you just set: R/2 = 4B - R and you solve for 'B' and find out that your first bet in the three out of five series should be 3R/8. It seems that this should just be a high-school simple recusion problem, but it is sure beating me -- I can't even find the brute-force solution for a best 4-out-of-7, much less the general formula for an arbitrary series. It is easy enough to show that all you need is to know the *first* bet -- given just the first bet for a particular series it is easy to figure out ALL the bets for that series, but I'm stuck on how to do that. Insight would be appreciated! :o) /Bernie\