🚀 go-pugleaf

In article <1i7cb6INNe0@mirror.digex.com> adric@access.digex.com (William Johnson) writes:
wj> When playing Russian Roulette, each member has a revolver with 6 chambers
wj> and 1 bullet (may have been 2 bullets, I don't think it changes the answer,
wj> just the likelihood of death).  Each member then fires the gun twice into
wj> his/her own head.  Members may spin the revolver before each shot.  Which
wj> option gives the best chance of survival:
wj> 	A) Spin shoot spin shoot
wj> 	B) Spin shoot shoot
wj> 	C) Shoot spin shoot
wj> 	D) Shoot shoot.
wj> 

In article <1i8at3INNjbl@iskut.ucs.ubc.ca>  leon@unixg.ubc.ca (Leon ter Beek) writes:
ltb> A=C if you didn't spin before you start the next round. 

Wait a minute.  What's this about starting another round?  The problem states,
"Each member then fires the gun twice into his/her own head."  Twice.  Two shots.
That's it.  Nothing more.  Furthermore, each member has his/her *own* *gun*, so
the result of any other player's move is irrelevant too, since you use your own
gun, not the gun just fired by another player.

ltb> Spinning makes the events independent, ie. next shot same probability as
ltb> first shot if you survive the first one.

I'll go along with that.

ltb> A: P(survive) = 5/6*5/6= 25/36
ltb> B: P(survive) = 5/6*4/6= 20/36 Second shot only 4 empty chamber left.
ltb> C: P(survive) = 3/6*3/6= 9/36  Don't spin after preceding round.
ltb> D: P(survive) = 3/6*2/6= 6/36

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

wj> Ok, it seems obvious to me that the two options where you shoot twice
wj> without a spin in the middle are worst.  Because assuming you survive
wj> the first shot (because if you didn't, it's over), you have now reduced
wj> your chances of surviving the next chamber.

Makes perfect sense to me.

wj> But I don't see the difference between A and C, unless in case C you know
wj> in advance that where you put the bullet either was or was not in the
wj> next chamber to be fired.  This may have been the answer, but I don't think
wj> so, because reading their answer sheet, the probabilities weren't as clear
wj> cut as that.  Any suggestions?

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

Bad puzzle!  Bad, bad puzzle!  No biscuit!

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