Fermat and Pascal exchanged correspondence discussing the problem of points.
Here is a loose sketch of the problem:
Two players toss a fair coin. Player A gets a point, if it comes up heads, while player B gets a point, if it comes up tails.
They repeat this, until one of the player gets to 10 points.
At the start of the game, each player wagers $50 for a total pot of $100.
Suppose the game is interrupted at a certain point due to unavoidable reasons (say player A has 8 points and player B has 7 points).
How should the pot be divided?
At the start of the game, the odds are even, since the coin is fair. However, when the game is interrupted, player A has a higher chance of winning. How can we systematically take this condition into account?
A wonderful exploration of this problem written using "modern" terminology is available here. It outlines the problem, sketches Fermat's and Pascal's approaches, and generalizes the problem and solution.
The original correspondence (translated) is available here (pdf).
Here is a loose sketch of the problem:
Two players toss a fair coin. Player A gets a point, if it comes up heads, while player B gets a point, if it comes up tails.
They repeat this, until one of the player gets to 10 points.
At the start of the game, each player wagers $50 for a total pot of $100.
Suppose the game is interrupted at a certain point due to unavoidable reasons (say player A has 8 points and player B has 7 points).
How should the pot be divided?
At the start of the game, the odds are even, since the coin is fair. However, when the game is interrupted, player A has a higher chance of winning. How can we systematically take this condition into account?
A wonderful exploration of this problem written using "modern" terminology is available here. It outlines the problem, sketches Fermat's and Pascal's approaches, and generalizes the problem and solution.
The original correspondence (translated) is available here (pdf).
No comments:
Post a Comment