How Probability Can Be Used to Design Games of Chance

One of the origins of of probability as a field in mathematics was solving games of chance. The famous correspondence between Fermat and Pascal in 1654 was one of the earliest accounts on how to use mathematics formally in order to solve a fair game of chance.

In this post, we are going to design a game that will demonstrate the power of probability. We will use probability to create a game that looks like as if it favors the player, while in reality, it favors the casino. Although most casino games actually obviously favor the casino, the game below is a bit more conservative (or should I say ‘deceptive.’)

The dice to be used in the game below is the standard 6-sided die whose number of dots are from 1 to 6. This means that the smallest possible sum is 1 + 1 = 2 and the largest possible sum is 6 + 6 = 12. Below are the instructions on how to play the game.  » Read more