Date:         Wed, 26 Jan 2000 21:09:17 GMT
Reply-To:     Kyle Dane <kyledane@MY-DEJA.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Kyle Dane <kyledane@MY-DEJA.COM>
Organization: Deja.com - Before you buy.
Subject:      Re: an interesting game

  Kyle Dane <kyledane@my-deja.com> wrote:
> The interesting thing is that you do improve your chances of winning
if
> you recognize this as a strategy.  Over a large number of repetitions
a
> strategy of switching about half the time improves your chances of
> winning from 1/3 to 1/2 over never switching.  However, you do not
> improve your chances if you switch *every time*.  If you switch every
> time, you're right back to 1/3 again.

This is great, I have to correct myself.  In fact, your chances of
winning never were 1/3 (or 2/3 for that matter).  They are and always
will be 1/2, regardless of the strategy you use with regard to
switching.  Your chances of picking the correct one on the first shot is
1/3, but your chance of winning is always 1/2, equal whether you switch
or not.  I will demonstrate later how this works and why so many
simulations, like the one posted already today, fail to produce this
result.  I'll also post a simulation of my own that does produce it.

--
Kyle Dane
Programmer/Analyst - UCSF Division of Geriatrics
kdane@medicine.ucsf.edu -   415-514-0714


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Before you buy.