# The Ultimate Gaming Mathematics Guide

By Eliot Jacobson PhD.

The opportunity to play a casino game is a product that the consumer purchases with his gaming dollar. The view I take is that the player wants to have a certain experience when he sits at a game and is willing to pay for that experience by means of the inevitable bite the house edge takes.

To fully understand the product the player is purchasing requires a journey into the mathematics of casino games. Marketing must understand this material when developing effective strategies. Every part of a player’s interaction with a casino game has its own mathematics. Wagers have “odds” that determine how much to pay the player if he wins. The percentage of time the player wins is called the “hit frequency.” The “house edge” is the fraction of the player’s total initial wagers that the house expects to keep over the long run if the player uses perfect strategy. The “theo” or “theoretical” is the actual dollar amount the casino expects to win from the player. The “return to player” measures the fraction of the player’s total wagers the player is paid back in live casino play.