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Three Prisoners and an RNG (Posted on 2025-05-15) Difficulty: 3 of 5
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.

  Submitted by Larry    
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Solution: (Hide)
The optimal strategy is for each to flip their coin if their
RNG < (6 - 2√(2))/7 = 0.4530818393219728

and their probability of freedom is 0.2991194744794363

Comments: ( You must be logged in to post comments.)
  Subject Author Date
拒絕劣質煙彈!選擇高品質一次性電子煙kskvgjebnpc2025-05-20 02:52:09
SolutionanalysisCharlie2025-05-15 09:15:11
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