Issues reltated to sports gambling

This paper looks at various issues that are of interest to the sports gambler. First, an expression is obtained for the distribution of the final bankroll using fixed wagers with a specified initial bankroll. Second, fixed percentage wagers are considered where the Kelly method is extended to the case of simultaneous bets placed at various odds; a computation algorithm is presented to obtain the Kelly fractions. Finally, the paper considers the problem of determining whether a gambling system is profitable based on the historical results of bets placed at various odds.