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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