A few books:"How To Gamble If You Must" Dubbins and Savage (classic on subfair gambling)"The Science of Winning" Fabricand (not much maths. but an interesting angle)"An Introduction To Probability Theory and Its Applications" Feller contains the orientation and analysis for several gambling problemsSome articles mostly available on the web:- start at
www.bjmath.com for downloadable pdf files with classic 'featured articles' ranging from Kelly's original paper to Thorpe's "The Kelly Criterion in Blackjack, Sports Betting and The Stock Market" (better than "Beat The Dealer" which is more of a general description of method rather than the maths.) - "Bound's On Gambler's Ruin Probabilities In Terms of Moments" Ethier/Khosnevisan (new, recent solution)- "Optimal Control of Favourable Games with a Time Limit" Kulldorff (the complement to Dubbins and Savage for superfair games)- "Reaching Goals by a Deadline" Sid Browne (for those who can't wait long enough for Kelly to work!)Hope that helps.