An even split seems like the safest choice. Here, however, the best strategy creates one perfect opportunity and concentrates the remaining risk in the other urn.
The prisoner and the two urns
Riddle statement
A prisoner is given 50 white balls and 50 black balls.
He may distribute all 100 balls between two urns in any way, provided that neither urn is empty.
The jailer then:
- chooses either urn at random, with probability \(1/2\) for each;
- draws one ball uniformly at random from the chosen urn.
If the ball is white, the prisoner goes free. If it is black, he dies.
How should he distribute the balls to maximize his probability of survival? What is the maximum probability?