: The Truel : the answer

: Your best bet is to fire your first shot into the air and let the other contenders
: deal with themselves first. Here's out things will then play out :

: It's best to not hit either of your opponents in the first round, as if you hit/killed
: either of them, your chances would be 50% or 0% of surviving the next shot
: (depending on if you killed the expert or the 50-50 shooter).

: By firing into the air, you force the 2nd shooter to address his most serious
: threat: the expert-shot. If the 2nd shooter misses, then the expert will shoot
: and kill him. If he hits, then you can take your chances with the 50-50 shooter.

: After the first round, one of the your two opponents will have been taken out
: of contention (either the 50-50 shooter succeeds in hitting the expert-shot, or
: the expert-shot takes out his most threatening opponent, the 50-50 shot).

: At the beginning of the second round, you're either face sure death with the
: expert-shooter, or 50-50 chance with the 2nd shooter. Either way, you've
: survived one round (not necessarily guaranteed otherwise). At the beginning
: of the second round, the outlook is decidedly better for your ultimate survival,
: as you only have one contender to deal with. Still, it's not a situation you might
: fancy myself in, as there's a good chance you won't make it out alive.

: © 2001, Aaron Clauset

: Disclaimer: This puzzle is not of my devising. It was posed in the 40th issue
: of the AWADmail as a classical mathematical example of a 'trilemma.'