IBM Ponder This #117 · January 2008

This month's puzzle concerns drawing balls from an urn. You know the urn contains 3 balls. You know each ball is white or black and that white balls are worth 1 unit, black balls are worth nothing. You know the urn is equally likely to contain 0,1,2 or 3 white balls. You have an opportunity to buy balls from the urn. Each ball costs c units (0<c<1). When you buy a ball one of the remaining balls in the urn is randomly selected and given to you. You may stop buying balls at any time based on the color of the balls you have received. Assuming you adopt the best strategy, what is your expected return as a function of c?

UPDATE, 1/3/08: You do not have to buy any balls. By return I mean the value of the balls you receive minus their cost.

Solution

Best opened after a real attempt

To be added.