Puzzle #60: Mexican standoff
From New Scientist #3283, 23rd May 2020 [link] [link]
The Good, the Bad and the Bumbling have decided the only way to resolve their differences is with a three-way duel, aka a Mexican standoff. They stand in a triangle, each armed with a gun and unlimited ammunition. As you might expect, Good has the deadliest shot: he kills his target 99 per cent of the time. Bad is more hit-and-miss: his success rate is 66 per cent. And Bumbling, in his role as the comedy relief, only fatally hits the mark 33 per cent of the time. On a count of three, each will draw their gun and, using the best strategy they can, will keep shooting with the aim of being the last spaghetti westerner standing.
Roughly what is the chance that Bumbling will survive?