maximize probability of survival in a shootout

Your name is Ten. You’re standing in a wide field with two enemies called Thirty and Sixty. Each individual has a gun and limitless ammunition. Each of you can see each other and you’re all in each other’s firing range.

You want to maximize your chances of survival. You’re called Ten, because unfortunately, you only have a 10% chance of killing whoever you shot at. Thirty has a 30% chance and Sixty has a 60% with their respective shots. You take turns at shooting in the following order: You, Thirty, then Sixty. You keep going until only one person remains on the field.

You’re up first. Who do you shoot at and why?

 

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