No Photo

Happy Mutant Profile

JDW

Puzzle: three-way pistol duel

September 21, 2007 6:23pm

Ooh, interesting! Common sense says shoot Mr.100 first, but those saying intentionally missing first are correct.

If you shoot the ground on your first shot, you have over a 40% chance of winning.
(33% chance of hit from 50% chance of Mr.50 missing = 16.5%, around 24% chance from Mr.50 hitting Mr.100 and going one on one with him with you having the first turn--estimated, I didn't work out the whole regression.)

Unintuitive, but here's why: if you aim at Mr.50 and hit, you die. If you aim at him and miss, you've basically got the "miss intentionally" scenario now--66% of 40% = around 27% chance of winning.

If you aim at Mr.100 and hit, now you have 50% chance of surviving Mr.50, then 24% chance in the one-on-one battle = .24*.5*.33 = 4%

If you aim at Mr.100 and miss, now you have the "miss intentionally scenario" .66*.40 = 26.4%

Total odds of winning by aiming at Mr.50: 27%.
Total odds of winning by aiming at Mr.100: 27%
Total odds of winning by shooting the ground: 40%.

No friends yet.