Personal Comment: Sent in by Ricky Duval!

The Prisoner's Dilema Enigma

What we know:A prisoner is given 2 bowls, 100 red balls, and 100 white balls. He is told to put the balls into the bowls any way he wishes, as long as there's at least 1 ball in each bowl. The Executioner comes in and will reach into a random bowl and draws out a ball. If it is RED, the prisoner DIES. If it is WHITE, he goes FREE.

Enigma: How should the prisoner arrange the 200 balls so that he has the greatest possiblilty of going free?

Solution He should put ONE WHITE BALL in one bowl and ALL OF THE REST in the other.

WHY??

If he puts all of the white ones in one bowl and all of the red ones in the other, he only has a 50/50 chance to survive. Similarly if he puts 50 of each into each bowl.

SO ... If he puts one white one in the first bowl, then there is a 100% chance that (IF it is chosen) he will go free.

If he puts all of the rest in the other bowl, he has ALMOST a 50% chance (49.749... 99/199) of surviving.

There's a 50% chance the Exocutioner will choose the first bowl, and

50% x 100% = 50%.

Add to that the second --

50% x 49.749% is approximately 25%.

So 50% + 25% = a 75% chance that he'll go free.

See who got this right

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