Three men stand in the center of this clearing where the dead grass is stained a rusty brown from the blood of combatants. It appears the tradition will continue: all three men hold a flintlock pistol.
A small crowd has gathered. One of the busier on-lookers sidles up to you and asks if you wish to place a bet.
“What on?” you ask.
“The Triangle Duel,” the bookie answers. “It’s the biggest event of the year. Alphonse, Bertram, and Cuthbert have each mortally offended the other two men, so they’ve decided to hold a three-way duel until only one man is left. They’ll take turns shooting, it’s very civilized. The only catch: Alphonse never misses, Bertram hits his target only 80% of the time, and Cuthbert misses his mark half the time.”
“That does sound a little unfair,” you offer.
“It certainly is! How is an honest bookie supposed to figure the odds? Why, I’d give an obol to anyone who could tell me who has the best chance of surviving… Four obols to someone who could tell me the exact odds of each duelist’s survival!”
You think for a moment. “Who is to shoot first?” you ask.
“They’ll draw lots just before they start,” replies the bookie, “but I need to know the odds now. I can tell you one thing, though: these guys are smart. They know what their best strategy is, and you can count on them to follow it when they shoot.”
Solve the bookie’s problem by submitting a solution…
… or continue on your journey