Chapter 10: Brainteasers 359
The Answers
Russian roulette
I have a revolver which holds up to six bullets. There
are two bullets in the gun, in adjacent chambers. I am
going to play Russian roulette (on my own!), I spin the
barrel so that I don’t know where the bullets are and
then pull the trigger. Assuming that I don’t shoot myself
with this first attempt, am I now better off pulling the
trigger a second time without spinning or spin the barrel
first?
(Thanks to pusher.)
Solution
This is a very typical, simple probability Brainteaser.
It doesn’t require any sophisticated or lateral thought.
Just pure calculation.
Whenever you spin the barrel you clearly have a two
in six, or one in three chance of landing on a chamber
containing a bullet.
If you spin and pull the trigger on an empty chamber,
what are the chances of the next chamber containing
a bullet? You are equally likely to be at any one of the
four empty chambers but only the last of these is adja-
cent to a chamber containing a bullet. So there is now a
one in four chance of the next pull of the trigger being
fatal. Conclusion is that you shouldnotspin the barrel.
After surviving two pulls of the trigger without spinning
the barrel the odds become one in three again, and
it doesn’t matter whether you spin or not (at least it
doesn’t matter in a probabilistic sense). After surviving
