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Topic: strategy for escape of osama and saddam (Read 1036 times) |
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inexorable
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strategy for escape of osama and saddam
« on: Dec 14th, 2005, 7:52pm » |
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Osama and saddam, who are prisoners under the supervision of warden GWB, are in separate rooms and cannot communicate with each other. GWB meets with them individually, gives each a penny, and offers to free them if they succeed in the following task.
On the next day they are to appear together in GWB's office, and each is to hold out a closed fist which either contains, or does not contain, the penny. They open their fists simultaneously and anyone holding a coin must flip it. They will be released if there is at least one flip and if all flips are heads.
What strategy should osama and saddam follow to maximize the probability of success?
Ps:-you can assume that each know that other one is smart, and approaches problem probabilistically
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| « Last Edit: Dec 14th, 2005, 11:37pm by inexorable » |
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Neelesh
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Re: strategy for escape of osama and saddam
« Reply #1 on: Dec 14th, 2005, 11:51pm » |
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What if both of them caarry the coin and close the fist in such a way that on opening it, tail is up, and then they flip the coin so that head is up?
I am sure I am missing something.
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inexorable
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Re: strategy for escape of osama and saddam
« Reply #2 on: Dec 15th, 2005, 6:11am » |
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on Dec 14th, 2005, 11:51pm, Neelesh wrote:What if both of them caarry the coin and close the fist in such a way that on opening it, tail is up, and then they flip the coin so that head is up?
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flip here means tossing the coin.
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rmsgrey
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Re: strategy for escape of osama and saddam
« Reply #3 on: Dec 15th, 2005, 9:01am » |
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I reckon their ideal strategy is:
| hidden: | | independently calculate the value, p, which maximises their probability of escape if each of them independently produces the penny with probability p. Doing so is easy enough - the probability of escape is a quadratic in p - and gives p=2/3 |
Probability of escape: 1/3
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inexorable
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Re: strategy for escape of osama and saddam
« Reply #4 on: Dec 16th, 2005, 6:39am » |
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can this be generalised to n prisoners?
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JocK
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Re: strategy for escape of osama and saddam
« Reply #5 on: Dec 16th, 2005, 10:20am » |
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No, although Saddam seemed to have a number of duplicates, there s only one Saddam and one Osama... (just the thought of it!  )
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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JocK
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Re: strategy for escape of osama and saddam
« Reply #6 on: Dec 16th, 2005, 10:59am » |
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So: n prisoners appear together, and each is to hold out a closed fist which either contains, or does not contain, the penny. They open their fists simultaneously and anyone holding a coin must toss it. They will be released if there is at least one toss and if all tosses produce heads.
The optimal strategy for each of them is to hold a penny with probability P = (21/(n+1) - 1) / (21/(n+1) - 1/2).
The resulting probability for release is (1-p)n-1.
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| « Last Edit: Dec 16th, 2005, 11:07am by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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