A mathematical model of a casino game is built to accurately calculate
the maximum percentage return to the player. The
model also provides hit rates, volatility and confidence intervals.
Percentages never lie. (…) You can lose faith
in everything, religion and God, women and love, good and evil,
war and peace. You name it. But the percentage will always stand
Fools Die, Mario Puzo (1978)
- The percentage return is the percentage of the collected
money the game will return to the players in the long term.
- The hit rate is the average number of games before a
- The confidence intervals for the percentage return provide
a range in which the percentage return will be (with a certain degree
of confidence) after a set number of games.
A casino is a mathematics palace set up to separate players from their
Casino: Love and honor in Las Vegas,
Nicholas Pileggi (1995)
- Finally, the volatility is a measure of the amount
of fluctuation in the prizes.
The probability model takes into account every possible outcome (or path
to an outcome) of the game.
Games can have many different features: line wins, scatters, holds
and nudges, free spins, gambles, progressive jackpots, other bonus
games... see the Slot Design page.
Some of these features require us to calculate the optimal strategy to know
what is the best the player can do and, therefore, the minimum house edge.
To model these processes we use either Excel spreadsheets or C++, depending on which is
more appropriate in each case.
See our Game Portfolio for a list
of games in which we have worked.