Once you've had a chance to think about it, mouse over this to see my solution.
The solution is to shoot yourself in the foot. Here's why.
Presumably, your chances of shooting yourself in the foot are better than 33%. Even if they're not, you have a 33% chance of getting a non-fatal wound and avoiding any other injury.
It's safe to assume that with Mr. 100% in the game, Mr. 50% isn't going to shoot at you. If he takes out Mr. 100%, you have one more chance to stay alive (this time shooting at Mr. 50%). If he misses Mr. 100%, Mr. 100% will take out Mr. 50%, giving you another 33% chance to take out your foot before Mr. 100% takes a 100% accurate shot at your skull.
But how would Mr. 50% behave? Would it be any different? Knowing that the logical step for Mr. 33% is to shoot himself in the foot or at you, the fact that you even get a shot means that Mr. 33% took himself out already, or shot at you and missed. In any case, Mr. 100% shoots next and he's looking at you to make your move.
It seems the proper thing for Mr. 50% to do is shoot himself in the foot (particularly if he's a better than 50% shot when aiming at himself-- since then, Mr. 33% most likely took himself out already). If Mr. 33% is still in the game, and you hit Mr. 100%, Mr. 33% gets another shot at you. If you miss Mr. 100%, his next step is to take you out. So your strategy as Mr. 50% appears to also shoot yourself in the foot.
What's the strategy for Mr. 100%? Easy. Become a podiatrist. Your shot accuracy ensures you'll have customers.
Presumably, your chances of shooting yourself in the foot are better than 33%. Even if they're not, you have a 33% chance of getting a non-fatal wound and avoiding any other injury.
It's safe to assume that with Mr. 100% in the game, Mr. 50% isn't going to shoot at you. If he takes out Mr. 100%, you have one more chance to stay alive (this time shooting at Mr. 50%). If he misses Mr. 100%, Mr. 100% will take out Mr. 50%, giving you another 33% chance to take out your foot before Mr. 100% takes a 100% accurate shot at your skull.
But how would Mr. 50% behave? Would it be any different? Knowing that the logical step for Mr. 33% is to shoot himself in the foot or at you, the fact that you even get a shot means that Mr. 33% took himself out already, or shot at you and missed. In any case, Mr. 100% shoots next and he's looking at you to make your move.
It seems the proper thing for Mr. 50% to do is shoot himself in the foot (particularly if he's a better than 50% shot when aiming at himself-- since then, Mr. 33% most likely took himself out already). If Mr. 33% is still in the game, and you hit Mr. 100%, Mr. 33% gets another shot at you. If you miss Mr. 100%, his next step is to take you out. So your strategy as Mr. 50% appears to also shoot yourself in the foot.
What's the strategy for Mr. 100%? Easy. Become a podiatrist. Your shot accuracy ensures you'll have customers.
