The History of Probability as it Related to Games of Chance

One of the most interesting and instructive things that one can look at is how disciplines start. The origins and the history of a specific skill or trade are going to help to put it in the proper perspective with regard to time and environment. This allows some appreciations of the developments in the field that the subject has had since it began. This generally applies to all fields, including the field of probability. Maybe some of the initial episodes in its history will shed some light on why it is a good subject to study.

So this may not come as a big surprise to you, but probability originated from the study of games of chance in gambling. Gambling has always historically existed, but it is one of the oldest documented instances of a specific mathematical question being used. It deals with a way that can divide the stakes from a game. This originated in the 15th century. A monk was born in Tuscany in 1445 and was a person who worked with and knew Leonardo da Vinci. He wrote on a lot of subjects with regard to math and is known as one of the originators of the two column accounting system.

One of the problems that he tried to solve revolved around a specific game of chance that was known as balla and it had to do with a problem of points. Two players generally play this game of balla which will last a few rounds. The first player to get six rounds in his or her belt is going to win the game and the stakes that have been bet throughout the entire process. Halfway through the game someone else interrupts and the game has to be stopped. So now player 1 has won around five rounds and player 2 has won three rounds. So what should happen with the stakes? How should they be divided between the two players?

It makes the most sense for player 1 to get a larger share of the winnings than player 2. He is only one round away from a total victory in the game and player 2 is not. Player 2 does have some stake in this though because it is entirely possible that he could have won three rounds in a row. So how do we divide this based on the likelihood of one of the two players winning the game? How should this be calculated?