So here’s the answer to the three gunmen problem:
Gunman #1 should fire his shot into the air.
Want an explanation? Here’s the best one I received via email. Rob Cooper writes:
This calls into question Game Theory — which was a cold-war think tank strategy on how to wage and win in very dire straits. Each should fire towards the most likely target. If #1 shoots #3 and hits, then he’s second shot in a two way. If he aims at #2 and hits, he’s second shot and sure to lose. If he fires his gun into the air, #2 will fire at #3. If #2 misses, and #3 hits, #1 gets to go first. If #2 hits #3, #1 gets to go first. Ergo, fire into the air, let the bad guys duke it out until you are first shot in a two-way contest.
The worst thing #1 could do would be to aim at and hit his target in a 3 way contest — he’d most likely die. But if he aims and hits in a 2 way contest, he wins. In a 3 way contest — no one is shooting at him so it’s in his interest to keep it a 3 way contest until someone ELSE hits the other target.
Seems completely counterintuitive when you first hear the answer, but once you hear the explanation, it makes perfect sense.