The student is expected to apply modern martingale theory to various strategies in roulette. The profit/loss of any betting strategy in roulette follows a random walk with a negative drift and thus according to the law of large numbers, all strategies will ultimately end up negative. However, some strategies can be more appealing to others in terms of the distribution of the maximum (a better strategy has a higher distrubution of the maximum) and in terms of the distribution of the last exit time from the positive region (better strategies stay positive for a longer time). Finding the exact distribution requires quite solid understading of a discrete random walk (a more advanced course in probability theory), learning the theory of martingales and the ability to run Monte Carlo simulations. It is expected that some previously unknown relations are derived in this bachelor thesis.
Seznam odborné literatury
Dubins, Savage (2014): How to Gamble If You Must: Inequalities for Stochastic Processes, Dovers Book on Mathematics.
Lawler (2006): Introduction to Stochastic Processes, CRC Press.
- zadáno a potvrzeno stud. odd.