From: hector@sci.ccny.cuny.edu (Hector Garcia)
Subject: Help me with MH puzzle, also, a new puzzle.
Organization: City College of New York - Science Computing Facility
Date: Tue, 12 Jan 1993 18:01:36 GMT


From: hector@sci.ccny.cuny.edu
Subject: Re: Help me with MH puzzle, also, a new puzzle.

In article <1993Jan6.213351.29174@ll.mit.edu> mikem@ll.mit.edu (Michael Maciolek) writes:
mk>In article <1i7cb6INNe0@mirror.digex.com> adric@access.digex.com (William Johnson) writes:
mk>wj> When playing Russian Roulette, each member has a revolver with 6 chambers
mk>wj> and 1 bullet (may have been 2 bullets, I don't think it changes the answer,
mk>wj> just the likelihood of death).  Each member then fires the gun twice into
mk>wj> his/her own head.  Members may spin the revolver before each shot.  Which
mk>wj> option gives the best chance of survival:
mk>wj>     A) Spin shoot spin shoot
mk>wj>     B) Spin shoot shoot
mk>wj>     C) Shoot spin shoot
mk>wj>     D) Shoot shoot.
mk>ltb> A: P(survive) = 5/6*5/6= 25/36
mk>ltb> B: P(survive) = 5/6*4/6= 20/36 Second shot only 4 empty chamber left.
mk>ltb> C: P(survive) = 3/6*3/6= 9/36  Don't spin after preceding round.
mk>ltb> D: P(survive) = 3/6*2/6= 6/36

mk>Whoa!  Hold on!  Why is first probability in C and D only 3/6?  What assumption
mk>are you making about the state of the gun prior to the first shot?  What is the
mk>basis for your making this assumption?

No assumption is needed. I view of the absence of more specific information prior to
firing the gun for the first time, you are forced to express P(survive) according to
what you know. All you know is that you have a gun! Hence, the probability of 
surviving after shooting the first time depends on whether the chamber fired 
contains the bullet or not. The bullet is either there or not there.
Therefore the P(survive)=P(bullet in chamber)=1/2.
Why (ltb) expresses this probability as 3/6 is beyond me.

mk>The missing piece of information in this puzzle is whether you know anything
mk>about the state of the gun before you choose an option.  But the puzzle does
mk>not fill in this missing information.  It's therefore not complete, and you
mk>can't answer it based on the information provided.

Actually, it is this missing information that makes this an interesting puzzle.
Again, prior to firing the gun for the first time you don't know who put the
bullet in the gun, or how, or if the person had intentions to kill you or not.
All you know is that you have a gun, and that the bullet may or may not be in
the chamber that is about to be fired, (ie P=1/2).
Remember that in the absence of information, all events are assumed to be
equally likely. After the first shot without spinning, assigning
P(survive) anything different from 1/2 will be a sign of PRIOR knowledge about
whether the current chamber has or does not have the bullet.

The SPIN operation has two distinct purposes:
1-)In between shots, it makes them independent events.
2-)At the beginning of the game it gives the bullet an equal likelihood of 
   being in either of the six chambers. And hence P(survive)=5/6

You can always argue as to the completeness of the problem if you want to be
unreasonably picky. For example, nothing is said as to how much angular
momentum is involved in the spin operation, yet we all assume that it is 
enough to give all chambers equal likelihood of being fired next. In reality, 
however, the presence of the bullet in one of the chambers makes it more likely 
to end up at the bottom due to gravity. And of course the inclination of the
hand of the person is always important, bla, bla, bla.

mk> Bad puzzle!  Bad, bad puzzle!  No biscuit!

Excellent puzzle! very good puzzle! Here, have two biscuits.
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Hector C. Garcia	hector@sci.ccny.cuny.edu	City College
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