Triangle Of Death
Three
men: Fermat,
Galois, and Hilbert,
decide to fight a pistol duel.
They'll stand at the corners of an
equilateral triangle, and each man, in
order, will aim and shoot wherever he pleases.
They choose randomly who will be shooting first,
second, and third, and will continue in order until two
of them are dead. All three know Fermat always hits his
target, Galois is 80% accurate, and Hilbert hits his mark half
the time. Assuming that all three adopt the best strategy and that
nobody is killed by a wild shot not intended for him, who has the best
chance to survive, and why? Find the survival probabilities for each man.