An Adaptive Kelly Betting Strategy for Finite Repeated Games

摘要

Kelly criterion is the optimal bidding strategy when considering a series of gambles with the wining probability p and the odds b . One of the arguments is Kelly criterion is optimal in theory rather than in practice. In this paper we show the results of using Kelly criterion in a gamble of bidding T steps. At the end of T steps, there are W times of winning and L times of losing. i.e. T= W + L. Consequently, the best strategy for these bidding steps is using the probability W/T instead of using p in Kelly Criterion. However, we do not know the number of W, to put it better the information of p, before placing the bet. We first derive the relation of profits between using p and W/T as the winning probability in the Kelly formula, respectively. Then we use the proportion of winning and bidding numbers before time step t, denoted as p_t, as the winning probability used in the Kelly criterion at time step t. Even we do not know the winning probability of p in a gamble, we can use this method to achieve the profit near the optimal profit when using p in the Kelly betting.