Three mathematicians are imprisoned in a dungeon. The evil dungeon master decides to give them a chance for freedom. He gives each prisoner a fair coin, and a random number generator which produces a number which is Uniform [0,1]. They cannot communicate with each other in any way. But they are all clever mathematicians who realize the random number generator may be a useful tool in forming a strategy.
They each must decide whether or not to flip their coin.
If no one flips any coin, they remain imprisoned.
If any flipped coins come up Tails, they remain imprisoned.
But if all flipped coins are Heads, they all go free.
What is their optimal strategy and what is their probability of freedom if they use that strategy.
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