Mr. Hamman prefers contests with pure mathematical odds, like many casino games, but he will take a chance on almost anything.

So, the payoff for any given bet is less than what true mathematical odds would dictate.

The mathematical odds are the same: there will be an equal number of H's and V's resulting from the toss.

The bet is paid off at the true mathematical odds, but the 5% commission is paid as well, restoring the house advantage.

The mathematical odds against two such occurrences so close together were staggering.

First, Lansky and his connections had the technical expertise to effectively manage them based upon Lansky's knowledge of the true mathematical odds of most popular wagering games.

In practice, the mathematical odds against ever doing this are astronomical.

Like a gambler who works the mathematical odds instead of relying on lucky charms, these savvy individuals drive to beat the system.

It is possible to demonstrate that, even in a relatively stagnant society, the mathematical odds are heavily stacked against any couple achieving this ideal of parallel growth.

But no one can win thirty-eight thousand dollars on nineteen straight jackpots off one slot machine; it doesn't even have mathematical odds against its happening, Mr. Kostner.