Problem of Points

Problem of Points is a classical problem in Probability.

The setting of the problem is a game played between two. Each round of the game has an equal likelihood of any player winning. It is agreed upon before the fame that the first player to win a certain number of rounds wins the game. The proceeds, equally contributed by both players, is given in its entireity to the winner.

Now, the question is, if the game were to be interrupted for some reason, how can the pot be divided fairly.

Pascal and Fermat worked on this problem to come up with a solution. The tenets of which is what forms the basis of expected value in probability.

To keep it simple, the solution involved calculating the odd of each player winning for the subsequent rounds that were to be played. And splitting the pot based on that. While Fermat provided a logical solution to compute the final split of the pot, Pascal came up with a solution that could easily compute the pot if they were to play a certain number of rounds.

This activity involved drawing up a decision tree to map out all possibilties and their odds in an efficient way. This gave birth to whats now known as the Pascals Triangle.