Question

Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?

Answer 1

@dan815 @ganeshie8 @ParthKohli

Answer 2

Mr. White, who is the prime target, and basically wins if he gets a shot in.

Answer 3

actually, my bad. shoot yourself to purge your inaccuracy from this earth.

Answer 4

try again joe take into account the repercussions of each action taken by Mr. Black

Answer 5

are they fighting in a duel? whats a truel :P

Answer 6

duel*

Answer 7

Mr black --->Mr Gray --->Mr white
there is 1/3 chance My gray will miss and mr white will kill you
There is 2/3 chance you will miss Mr Gray the first time but
there is 2/3*2/3 you will miss him twice so 4/9 < 50%
and 1/3rd chance he will miss you, so your prob even goes up slightly more

Answer 8

in the end you have the highest prob of winning out of the 3 atleast, but lets see if there is better prob arrangement for him

Answer 9

actually there is another solution if they are allowed to shoot anyone they want

Answer 10

ok no im going with my old answet then!! my black my gray mr white

Answer 11

well lets look at it! Mr. Black has the option to shoot either Mr. Gray or Mr. White. Reasoning would say to shoot at Mr. White because he never misses however, it is mathematically in your favor to shoot at Mr. Gray. You will most likely miss Mr. Gray therefore out of fear, Mr. Gray will in turn shoot at Mr. White because he is his biggest threat. If Mr. Gray misses then Mr. Black will shoot and kill Mr. Gray. Now it is Mr. Black vs Mr. White and his odds are now better than before.

Answer 12

maye if my black choses to miss my gray on purpose first try... his prob will increase even more

Answer 13

Mr white will kill Mr. gray*

Answer 14

ah ok

Answer 15

If Mr. Black were to shoot at Mr. White then Mr. white would most likely react accordingly and shoot Mr. Black out of spite

Answer 16

Mr. Black wants to pit the two good shooters against one another in hops of taking one out, increasing his odds

Answer 17

xD thats kinda iffy solutions lol, thats based on psychology not pure math