# The Good, The Bad, and The Ugly

1. Nov 20, 2009

### BobG

A variation of this was posted about 4 years ago and provided some decent fun. This adds a little twist to the original puzzle.

Three gentlemen businessmen get into an argument over some gold that all claim belong to them. By the end of the argument, all three have exchanged challenges that have left them agreeing to a strange three-way duel.

Having somehow committed themselves to this duel, the ground rules are developed.

Blondie can shoot a hangman's rope at a 100 yards before a man's body can pull the rope taught. Unfortunately, he's endured a hard ordeal in the desert and his accuracy has been degraded to only a 95% chance of killing a man with any shot he takes. Angel Eyes is normally a very good shot, but has had his own ordeals and can currently shoot at a 50% accuracy rate. Job stress has turned Tuco into an uncoordinated alcoholic who can only shoot at a 25% rate.

Seeing as how Tuco is drunk and the worst shot, it's agreed that it's only fair that he be allowed the first shot. Since Angel Eyes is the second worst shot, he gets to shoot second. Blondie, being the best shot, has to shoot last. If more than one person is alive after the first round, each shooter continues to shoot in same order as the first round, skipping the dead player's turn once a player has been eliminated.

Being gentlemen, the three never lie. Being businessmen, they're capable of striking shrewd deals. Each player is allowed to shoot at any living opponent, any dead opponent, or to intentionally miss both opponents. He's also allowed to strike a deal with any living or dead opponent with the caveat that he can't lie. In other words, he has to follow through on any commitment he might make.

What's the best strategy for each to follow and which has the best chance of winning the duel? Which player has the worst chance of winning the duel?

2. Nov 23, 2009

### davee123

I never really considered this possibility back in the original problem, but is a player guaranteed not to kill anyone if they intentionally aim at a dead opponent or if they attempt to miss? Or is there some slight chance that they might TRY to miss, yet accidentally hit an unintended target (assumably not themselves)?

DaveE