Geodesic
Calculation of efficiency indicators of some strategies in gambling
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 2, pp. 33-48

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This paper considers the case of making decisions under risk. The player is well-informed about all the possible states of nature, as well as the corresponding probabilities (or their statistical estimates) which help the nature implement the states. There is a finite number of games for the payoff matrix made. Moreover, its elements may vary depending on the outcome of each game. The paper offers some financial betting systems (strategies) such as a fixed bet, Kelly criterion, martingale method and some of its modifications. On small game intervals (3–5 games) there are calculations of performance indicators for these strategies. They are the calculations of performance indicators by Bayesian and the ones when the variance of winning is taken into consideration. In the final part of the paper the results of numerical experiments with elements of statistical modeling are given which allow us to give recommendations on the application of these strategies.
Keywords: games with nature, payoff matrix, Bayes criterion, empirical estimation. 
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     title = {Calculation of efficiency indicators of some strategies in gambling},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
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Mikhail V. Kryuchkov; Sergey V. Rusakov. Calculation of efficiency indicators of some strategies in gambling. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 2, pp. 33-48. http://geodesic.mathdoc.fr/item/MGTA_2015_7_2_a2/