On the Analysis of Kelly Criterion and Its Application

摘要: We analyze the return of a game for gambler after bidding \( T \) time steps. Consider gamble with known odds and win rate, optimal solution is to use Kelly criterion which determines fraction in each step. In this paper we show that logarithm when {\text{KL}}\left( {{\text{R}}||{\text{P}}(b)} \right) - {{\text{R}}||{\text{P}}} \), where {\text{R}} proportion winning\losing outcome steps, {\text{P}}\left( b risk-neutral probability corresponding {\text{P}} gambler’s individual belief about game. This argument shows that, fixed odds, KL divergence win\lose proportion, say portion losing amount. On other hand, profit determined by irrelevant \). Any improvement not obtainable even estimated precisely advance.