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From: Stathis Papaioannou <stathispapaioannou.domain.name.hidden>

Date: Thu, 14 Oct 2004 17:35:37 +1000

Brent Meeker and Jesse Mazer and others wrote:

Well, lots and lots of complex mathematical argument on the two envelope

problem...

But no-one has yet pointed out a flaw in my rather simplistic analysis:

(1) One envelope contains x currency units, so the other contains 2x

currency units;

(2) If you stop at the first envelope you choose, expected gain is: 0.5*x +

0.5*2x = 1.5x;

(3) If you open the first envelope then switch to the second, your expected

gain is: 0.5*2x + 0.5*x = 1.5x - as above, just in a different order,

obviously;

(4) If, in a variation, the millionaire flips a coin to give you double or

half the amount in the first envelope if you switch envelopes, expected gain

is: 0.25*2x + 0.25*0.5x + 0.25*x + 0.25*4x = 1.875x.

In the latter situation you are obviously better off switching, but it is a

mistake to assume that (4) applies in the original problem, (3) - hence, no

paradox.

Is the above wrong, or is it just so obvious that it isn't worth discussing?

(I'm willing to accept either answer).

Stathis Papaioannou

_________________________________________________________________

Searching for that dream home? Try http://ninemsn.realestate.com.au for

all your property needs.

Received on Thu Oct 14 2004 - 03:38:09 PDT

Date: Thu, 14 Oct 2004 17:35:37 +1000

Brent Meeker and Jesse Mazer and others wrote:

Well, lots and lots of complex mathematical argument on the two envelope

problem...

But no-one has yet pointed out a flaw in my rather simplistic analysis:

(1) One envelope contains x currency units, so the other contains 2x

currency units;

(2) If you stop at the first envelope you choose, expected gain is: 0.5*x +

0.5*2x = 1.5x;

(3) If you open the first envelope then switch to the second, your expected

gain is: 0.5*2x + 0.5*x = 1.5x - as above, just in a different order,

obviously;

(4) If, in a variation, the millionaire flips a coin to give you double or

half the amount in the first envelope if you switch envelopes, expected gain

is: 0.25*2x + 0.25*0.5x + 0.25*x + 0.25*4x = 1.875x.

In the latter situation you are obviously better off switching, but it is a

mistake to assume that (4) applies in the original problem, (3) - hence, no

paradox.

Is the above wrong, or is it just so obvious that it isn't worth discussing?

(I'm willing to accept either answer).

Stathis Papaioannou

_________________________________________________________________

Searching for that dream home? Try http://ninemsn.realestate.com.au for

all your property needs.

Received on Thu Oct 14 2004 - 03:38:09 PDT

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