kelly makes a series of n bets, each of which she has a probability p of winning, independently. initially, she has x0 dollars. let xj be the amount she has immidiately after her jth bet is settled. let f be a constant in (0, 1), called the betting fraction. on each bet, kelly wagers a fraction f of her wealth, and then she either wins or loses that amount. for example, if her current wealth is $100 and f = 2p -1, which is known as the kelly criterion.