Three way Duel?

Question

you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?

Answer 1

The answer is the 100% one

Answer 2

Don't shoot at all. Your turn going first means you will definately live.



If you have to shoot, shoot at the 100% cyborg.



If you shoot at the other, a hit will guarantee your death when the 100% has its turn (100% won't miss you). If you miss, then they each have a chance of killing you: 1/4 + 1/2 probability (1/4 - the 50% will pick you instead of the other cyborg, then 50% chance it will kill you, and 50/50 chance the 100% picks you).



If you shoot yourself, you add a factor of 1/3 to that probability, since there is a 1/3 chance you will miss yourself. Granted, the chance of hitting the next cyborg who survives is technically 2/3 (when in reality it is still 1/3), but you won't survive past the second round if that is the case.

Answer 3

Aim at the 100% shooter on your turn. 33% chance of knocking it out. If you miss the 50% shooter should still go for the 100% cyborg because otherwise it WILL be out next go since 100% cyborg will go for 50% cyborg on its first go. (Maximises 100% cyborg's chance of winning.)



If you knock out the 100% cyborg on your first go, you still have a 50% chance of surviving the 50% cyborg's first shot.



If you miss the 100% cyborg and the 50% cyborg also misses, then you will only have the 100% cyborg to aim for when it's your turn to shoot again. If you miss then you will lose because the 100% cyborg will hit you with its second shot.



If you miss the 100% cyborg but the 50% cyborg hits the 100% cyborg, then you get a chance to knock out the 50% cyborg. The 50% cyborg is likely to win but you may get lucky!

Answer 4

You have 3 options to consider:

(1) Shoot at 50% guy. Death comes with: 72% likilhood (2) Shoot at the 100% guy. Death comes with: 63.64% likihood (3) Shoot into the air (purposely miss). Death comew with 58.33% likihood.

So, you shoot into the air and hope for the best

This is the correct solution.

Answer 5

Shoot at yourself, giving you a 67% chance of hitting one of the others.

Answer 6

you shoot your self then the other two would shoot at each other because they see each other more of a threat than you.

Answer 7

hehe are you using yahoo answers to try and figure out the answer to mine?



https://answersrip.com/question/index?qid=1006042127610



somebody above is indeed correct.