wedrifid comments on Solving the two envelopes problem - Less Wrong

32 Post author: rstarkov 09 August 2012 01:42PM

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Comment author: wedrifid 13 August 2012 08:45:27PM 0 points [-]

There are two envelopes in which I, the host of the game, put two different natural numbers, chosen by any distribution I like, that you don't have access.

Now, before everything I said happens, you must devise a strategy that guarantees that you have a greater than 1/2 chance of winning.

Well natural numbers and simple greater than satisfying makes it easy. "If one THEN swap ELSE keep."

Comment author: Omegaile 13 August 2012 09:33:57PM 2 points [-]

Maybe I didn't express myself well, but this strategy should work regardless of the distribution I choose. For example, if I choose a distribution in which 1 has probability 0, than your strategy yield 1/2 chance.

Comment author: wedrifid 14 August 2012 01:53:11AM -1 points [-]

Maybe I didn't express myself well, but this strategy should work regardless of the distribution I choose. For example, if I choose a distribution in which 1 has probability 0, than your strategy yield 1/2 chance.

If that kind of selection of distributions is possible then there is no free lunch to be found.

For any strategy of envelope switching a hostile distribution selector who knows your strategy in advance can trivially select distributions to thwart it.

Comment author: Oscar_Cunningham 14 August 2012 02:45:16PM *  1 point [-]

Have you looked at the "solution"? There really isn't a counter-strategy that reduces it to 1/2 chance, although there are strategies moving it arbitrarily close to 1/2.

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