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Whether to switch


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22 replies to this topic

#21 plasmid

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Posted 10 May 2013 - 04:09 AM

It doesn't matter what random number generation method you use, the results will be the same. And there's no need to code the program if you can tell by looking at it what the results would be.
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#22 bushindo

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Posted 10 May 2013 - 05:50 AM

It doesn't matter what random number generation method you use, the results will be the same. And there's no need to code the program if you can tell by looking at it what the results would be.

 
I think I see where we agree and where we diverge now. This two-envelope paradox has two variants,
 
A) There are two envelopes, both of which are unopened. We reach the same conclusion on this one.
 

Spoiler for

 
B) One of the envelope is opened and has $1000. This is where we disagree
 
Spoiler for


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#23 plasmid

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Posted 10 May 2013 - 01:56 PM

I had been considering the scenario where the amount of money in the envelopes could be any real number. In that case, if you have no information about the probability distributions, both an integration of your post 13 over the entire range of possible values in the envelope and the experiment of making random probability distributions shows that there is no gain for switching.

However, I'm still not sure I can make an adequate math - to - english translation of those results; in particular showing how this is fundamentally different from a game where you are given $1000 and asked whether you want to flip a coin to either double or half your winnings (which is a no-brainer) in a way that makes intuitive sense.

If the amount of money in the envelope is restricted to integers, that's a whole new can of worms because being even or odd gives information. I'll have to mull over post 7 again and decide which of those two conclusions I like the best.
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