[extropy-chat] three coins in a fountain

spike spike66 at comcast.net
Sat Oct 22 01:17:39 UTC 2005

> bounces at lists.extropy.org] On Behalf Of Julian Assange
> Subject: RE: [extropy-chat] three coins in a fountain
> You are all wrong.
> Hence there is a 2/3 chance that the otherside of the coin will display
> heads.

The original question asked the chances of the other
side being tails.  Others have answered 1/3, which
is equivalent to your 2/3 chance of a head.  I agree
with you however, its 1/3 chance of a tail.  A digital
sim or even a physical experiment will verify this.

Recall that we have seen arguments that lead to
1/2, 1/3 and 1/4.  The game is not necessarily
to find the subjective *right* answer, but rather
to take into account that the head prole test maker
might be wrong and give one of the other answers.  It
is kinda like the newlywed game: you try to give not
necessarily the correct answer but rather to guess
what your bride will say.* 

Now of course you know from all these years that
I am brilliant, modest, etc, but that I have been 
wroong on occasion, so you are to distribute confidence
across the choices taking that into consideration.  So
if the choices are a)1/2, b)1/3, c)1/4 and d) none
of these, would you put all your chips on choice b?
You know of course that I as head prole could mistakenly
decide a) is the right answer, in which case you would
get a goose egg on the whole test and be beaten by the
monkey who gets a 1E-6 score.  You know that if you
put just 1% on each of the wrong answers, it costs you
only a negligible 3% of your total score.  But your
competitors may follow the same reasoning, and take
a chance by putting only 0.1% on each of the wrong
answers, thereby beating you by 2.7 percent.

So how do you distribute your confidence?  Does the
nature of the game matter?  If you know your competitors
are smart and motivated, does that change your strategy?


*My wife and I played the newlywed game at a social
gathering.  When asked how many drains were in our
home, we both responded "The correct answer is 14, but
I predict (s)he will say 12 because (s)he will forget
about the washing machine and the dish washer."  The 
audience loved it.  We were the only couple that matched
on that question.  {8^D

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