In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind.
"I'll arrange you three into a truel (three way duel)," he says, pointing at you and two other prisoners, "the survivor of which will be pardoned and released."
"In front of you are three guns," he continued,"a malfunctioning gun that hits target 20% of the time, a lame gun that hits 40% of the time, and a golden gun that hits 90% of the time. You must choose your guns and take turns to shoot at each other until only one survives."
"But," he chieftain adds with a wryly smile, breaking the eerie silence, "he who's the last one to choose will enjoy the privilege to determine the shooting order, i.e. who gets to shoot first, who shoots second and last. One more point, whoever chooses the malfunctioning gun can pass his turn without shooting, but the lame and the golden guns must always shoot in their turns."
The chieftain then turns to you and asks "I know you like solving puzzles, so would you like to choose first? Or do you want to wait and be the 2nd/3rd one to choose?"
You all know the chieftain is a man of his word, and everyone wants to maximize their surviving probabilities. Is it better for you to choose first or be the 2nd/3rd one to choose? What's your best strategy?
Always keep in mind your two opponents are no fools. This puzzle seems like the same kind as the simple good old truel puzzle at first glance, but that is very beguiling. There're a couple of really hard-to-discern mindset traps for you to fall into and land on a suboptimal strategy. Reason and calculate ultra carefully!