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From: colonel@sunybcs.UUCP (Col. G. L. Sicherman)
Newsgroups: net.puzzle
Subject: Re: infinite poker chips
Message-ID: <2655@sunybcs.UUCP>
Date: Tue, 24-Dec-85 12:36:52 EST
Article-I.D.: sunybcs.2655
Posted: Tue Dec 24 12:36:52 1985
Date-Received: Sat, 28-Dec-85 00:44:48 EST
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> I don't see how you have proved your hypothesis, that it doesn't make
> sense to discuss random numbers in an infinite domain.  First, the number
> of points in the range 0-1 is the same as the number of points in the
> range -oo to +oo. Secondly, lets play another little game:
>   [description of same game, only finite]
>           Since we both have a 2/3 chance of winning, by your reasoning
> we must conclude that it makes no sense to discuss random numbers on a
> finite domain.   Right.
>     What this really means is that the reasoning is faulty.  The game can
> be broken into two random acts: first the selection of the disk, second
> the orientation of the selected disk.  Since each disk has a winning side
> and a losing side, they are all equivalent. Thus only the orientation
> matters.  Seeing the number imparts no information about this, so the odds
> are just fifty/fifty, which is what you would expect.

It's not enough to produce a proof of the "correct" result.  You must
find a flaw in Hayes's original Bayesian proof of the "incorrect" result.
And I don't think you can do it....

Of course, the "incorrect" proof doesn't really carry over to the finite
case.  Each side no longer has a 2/3 chance of winning, because there
are so many more 10s than 1s in the game.
-- 
Col. G. L. Sicherman
UU: ...{rocksvax|decvax}!sunybcs!colonel
CS: colonel@buffalo-cs
BI: csdsicher@sunyabva