ProbPoints Applet

       
            The Problem of Points was the math question Pascal was trying to solve when he started his research into the binomial coefficients.  Consider a two player game of chance where each round a point is awarded to one of the players; the game is won by the first person to have a lead of n points; as the game was played in Pascal's era, you had to have a lead of 12 points to win.  What if the game has to be stopped before someone gets to 12 points?  Is there a way to figure out what an 8 point lead should be worth?  What if the game of chance isn't a 50-50 proposition, but instead one player has an advantage?

            This program uses brute force to solve the problem instead of Pascal's clever methods; the user can change the probability of the player in question to win a point, how much of a lead the player has and the number of points needed to win.  The computer then runs a simulation, and when the number of unresolved games gets tiny enough, publishes the result.

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