Smart Gambler's Calculator allows one to calculate the main parameters for fixed-size and fixed-fraction betting. The main input parameters are grouped into several groups. The first group contains data about the properties of a single bet: probability of winning the bet, and the payoff (prize-to-bet ratio). The second group contains parameters of the gambler's "comfort zone": bankroll, number of games to play (or number of bets to place), and desired profit or prize-to-win in these games/bets. The calculator shows the expected value (profit/lose in the long run) and standard deviation (variability) of this gambling or investment opportunity. For the fixed bet, the probabilities of reaching the goal and of losing the bankroll are calculated. For the fixed-fraction betting strategy, the optimal fraction (percentage) of bankroll is determined. In contrast to Kelly's system, in which it is assumed that a player is a risk-averse person (so not a gambler) and which is applicable only to games with positive expected values, this system has none of these restrictions. The optimality is determined in the following way. First of all, the optimal fixed-fraction bet should minimize the probability of ruin. In theory, if money were "infinitely divisible," the probability of ruin in fixed-fraction betting is zero. The second objective/criterion is to maximize the probability of reaching the established goal, and the third objective/criterion is to maximize the expected value of the player's bankroll, subject to restrictions set by the previous criteria. |
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