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Famous Probability puzzle SHOOT 8 june

Famous Probability puzzle SHOOT

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?


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116 comments:

  1. He will shoot in air and not to any person.

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    1. But then one of the other guys might shoot him.

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    2. If you shoot in the air you have 50 50 chance.

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    3. no he'll shoot at the ground dumbo

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    4. wouldnt he just shoot a land mine behind mr. white and mr. gray???

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    5. land mine,,,,,, riteeeee

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    6. shoot in the air or shoot in the ground will have the same result

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    7. No Gray because he has like what the word less chance of makeing it know bing shoot and .still alive I did that for my class I they said
      I can't think of anything

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    8. whack them both with the gun

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    9. Dus no one think this riddle is a tad bit racist?! :D

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    10. if shoots gray,probability of survival is 2/3(1/2*2/3 +1/2*1/3)+2/3*1/2*1/3*1/2 =7/18
      if white p of survival = (1/3*1/3)+2/3(1/3*1/2+1/2*1/3)=8/18
      so better to shoot gray

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    11. i think he should shoot in a tube that goes at both and shoot twice

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    12. I think Mr. Grey, because... yea. I don't know.
      PS reply to Anonymous- its not racist because Mr. Black, Grey, and White are their LAST names, not their color.

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    13. if i was Mr. Black i would just shoot myself in the head

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    14. Mr. Black should shoot Mr. Gray because, then Mr. Gray would shoot Mr. White, if he doesn't get too mad that he was just shot by Mr. Black.

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    15. I think this riddle is just plain racist.

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    16. Oh, my last name's White, whoa I'm a racist.

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    17. I would hit Mr. White's gun, and if I miss, would hit him instead because he is holding the gun. So I would have a good chance of hitting him. If I actually hit the gun, I would aim at the handle, where his hands are. If you don't have hands, you probably can't shoot someone. Then Mr.Gray will want to copy, but since he has a better chance of hitting the gun, he would probably hit the gun. If he didn't hit the gun, then I would turn to one side. Most people would hit the end of the gun to create more force so the weapon will fly out of their hands, but if he misses he will just shoot straight to nowhere. Then if he hits my gun, I don't need to worry. The riddle said it was a cycle, so its pretty much taking turns. So then I have time to get my gun, and then I can try to shoot Mr. Gray's gun, at the handle specifically.

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    18. shoot to mr white n throw the gun to mr grey and when he gets up mr black goes and punch him

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    19. Actually it never said how long they get to shoot for! SO he could shoot at both of them.

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  2. This comment has been removed by the author.

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  3. If Mr. Black shoots the ground, it is Mr. Gray's turn. Mr. Gray would rather shoot at Mr. White than Mr. Black, because he is better. If Mr. Gray kills Mr. White, it is just Mr. Black and Mr. Gray left, giving Mr. Black a fair chance of winning. If Mr. Gray does not kill Mr. White, it is Mr. White's turn. He would rather shoot at Mr. Gray and will definitely kill him. Even though it is now Mr. Black against Mr. White, Mr. Black has a better chance of winning than before.

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    1. How is Mr. White vs Mr. Black give Mr. Black better chance of winning than before. One miss and he is dead for sure. Wouldn' t it be better if it were Mr. Gray vs Mr. Black for last?

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  4. correct me if i am wrong but it doesnt matter whom black person shoots first if he misses both shots,he is going to get killed anyway.

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    1. lol either dat or id shoot mr white and get mr gray 2 shoot him 2

      BTW 1 of my teacher is called mr white:P

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    2. y'know, if I were mr black then id screw rules and just run to grey and white and blast them to hell

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  5. Its probability quiz

    Soln "He should shoot at the ground.

    If Mr. Black shoots the ground, it is Mr. Gray's turn. Mr. Gray would rather shoot at Mr. White than Mr. Black, because he is better. If Mr. Gray kills Mr. White, it is just Mr. Black and Mr. Gray left, giving Mr. Black a fair chance of winning. If Mr. Gray does not kill Mr. White, it is Mr. White's turn. He would rather shoot at Mr. Gray and will definitely kill him. Even though it is now Mr. Black against Mr. White, Mr. Black has a better chance of winning than before."

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  6. you dont have to shoot because your already dead because mr white always shoots so you wont live anymore

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    1. But you go first, before Mr. White!

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    2. It have to be mr. black because mr.white has blue eyes

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  7. Mr.White because he gets to shoot all the time and Mr.Black will have a better chance of winning with Mr.Gray than with Mr.Black because Mr.Black gets to shoot all the time.

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    1. You shoot at white and get grey to shot at wihtes dead or alive body then kill grey

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  8. The ground, no one dies, so grey gets his shot, witch in most cases would be against white, then if white doens't get hit, grey will get hit by white because white see's him as a threat, then last shot belongs to black, since black already shot 1 and missed, and he hit's 1/3 of the time, leaving him with about a 1/2 chance of hit. Now say grey hit white, white's dead, blacks shot, but instead of against a 1/1 person he's against 2/3 witch is a better chance of survival

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    1. It is which not witch. That witch is the Halloween one ;)

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  9. This is GAME THEORY (or/and the prisoners dilemma)

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  10. Get them to stand in front of each other and shoot them both

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  11. the answer is wrong! Mr. Black would rather shoot at mr. white the first time, because there is a 33% chance he would hit. If he kills mr. white, then he still has a 33% chance Mr. Gray wouldn't hit him back. if he misses mr. white, mr. Gray would shoot at mr. white as well, making it a 50% chance between the two of them that mr. white dies. if mr. white dies, it will be mr. blacks turn again and would again have a 33% chance of hitting mr. gray first, while still having a 33% chance of survival if he misses.

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    1. No, because it Mr. Black actually kills Mr. White, then it is Mr. Gray's turn, and he will definitely aim for Mr. Black. If he doesn't shoot anyone, either Mr. White or Mr. Gray will be dead by the time he has his shot again, and no one will probably have shot at him. So it will be like it is his first shot, but with one opponent less. So he should miss on purpose the first time for the biggest chance of survival.

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  12. he should not shoot anyone because if he dosnt then its up to mr gray to decide. mr gray would most likely kill mr white beacause if he dosnt try to kill mr white, mr white turn is next and mr white would win.

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  13. I think they should count to three and pull the trigger

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  14. Mr. Black should shoot himself in the side At that range he shouldn't have a problem with aim and he can make it look like he is dead without actually killing himself. One of the other two will die and when they think they are the victor Mr. Black can sneak up behind the "vitor" and stab him in the back. Let's face it if Mr. Black isn't good with guns a knife just might be better.

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    1. Best answer evahhhh!!!

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  15. okay if Mr. Black shoots ant Mr. White then he has a better chance of living because, if he doesnt kill him it will be Mr. Grays turn and if he shoots at Mr. Black he will die so he will shoot Mr. White and if Mr. White dies he sill has a better chance of winning.

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    1. okay if Mr. Black shoots ant Mr. White then he has a better chance of living because, if he doesnt kill him it will be Mr. Grays turn and if he shoots at Mr. Black Mr. Gray will die by Mr. White so he will shoot Mr. White and if Mr. White doesnt die he it will be Mr. White's turn and he will go for Mr. gray so he will have a better chance of living and then Mr.Black gets to shoot again to increase chance of living and and if Mr. White dies he sill has a better chance of winning because he will be killing some one with a chance of miss.

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    2. Whoa that is way to complicated man. He actually shoots at the ground dumb dumb

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    3. yeah beacuse its goin to be Mr Grey turn and he shoot 2/3 of the time

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  16. he will shoot at the ground so that it is the next persons turn who will shoot at white guy and then it is his turn again so he will shoot at the last one standing. simple logic.

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  17. The reason why he shoots to the ground is that in the case he does kill someone then the remaining one, be it Mr. Gray or Mr. White, they are forced to take a shot at Mr. Black. This means Mr. Black would have a higher chance of dying.

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    1. if mr.black shot the ground then mr.gray will then shoot mr.white so he's gone. then its mr.blacks turn so he shoots mr.gray and then hes dead so mr.black won.

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  18. Well I'm only a kid but I am very very smart so I think he shoots at the ground.

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  19. But, if Mr Black shoots at the ground there is a 2/3 chance he will miss it. That stray bullet could kill one of the other guys. What if he shoots at himself? Shooting at himself leaves a 2/3 chance of survival! Then the other guys can shoot at each other.

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  20. if its legal he would shoot both and kill them
    but if its illegal he should shoot the ground or air cause mr grey would want to kill mr white and if mr black shoots any one he will go to prison or the other guy will shoot him

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  21. your all idiots.... if mr white hits all the time and black is still alive than that means grey is already dead after the first round. he should shoot at mr white for the best chance of survival....

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  22. Shoot non:
    1/1 chance that Mr Gray stays alive and try to shoot White, 1/2 he hits = 1/3 vs 1/2
    1/2 he miss = 1/3 vs 1

    Shoot mr white:
    2/3 miss, mr gray shoots 1/2 he hits = 1/3 vs 1/2
    1/2 he miss = 1/3 vs 1
    1/3 hit, = 1/2 vs 1/3

    as 1/3 vs 1 = bad
    And 1/3 vs 1/2 = good
    As you have 1/2 change to survive first shot (1/2 vs 1/3) to make it 1/3 vs 1/2 we can say this is 50% bad and 50% Good.
    makes it no differences if u shoot Mr.White or non.

    Only works IF, Mr Gray & Mr White, choices the most dangerous target and not random

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  23. ...Um...it only makes sense to shoot at the ground, but we are in fact counting that Mr. Gray actually hits Mr. White.

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  24. Monkeys relax, black will shoot white first, black has a 33% (1/3) chance of hitting white, assuming he does, next up is gray. Gray has a 66%(2/3) chance of hitting black, so theres a 33% chance of him missing, assuming he misses, and black hits, he survives.

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  25. Mr b walks up to mr white puts his gun to his head and pulls the trigger so he can't miss and mr w is dead. Mr g might not point his gun at his head so he might miss so then mr b points his gun to his head and kills him

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  26. get a colateral in their heads lol

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  27. the correct answer is for mr black to shoot in the air, because the mr grey will shoot at mr white, the man who has a certain chance of hitting him, becuase he is more likely to shoot mr grey since he has the higher chance of killing him, if he isnt shot first. so after shooting in the air one of the two men will be dead, leaving him with a one in three chance of killing the other man since he's going next. why not shoot at someone instead of firing in the air? well if he killed the man with a two in three chance of killing someone, he'd be killed for sure since mr white has a certain chance of killing someone. and if mr black killed mr white first, the he's still left with someone to have a clear shot at him. so shooting in the air and missing will leave him with a one in three chance of not being killed all together. make sense?

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  28. mr black shoots mr white for better od. if he misses

    mr grey shoots at mr white which give odds 3/3 for mr white death. so now mr blacks odds to shoot mr grey are now 1/2

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  29. He shoots at the ground, Mr. Gray would shoot at Mr. White, because he knew he would win against just Mr. Black. If Mr. Gray misses, it would be Mr. White's turn. Mr. White would shoot at Mr. Gray, because, once again, he knew he would win against just Mr. Black.

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  30. Mr. Black should shoot himself..

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  31. SHORT VERSION:

    Black Misses Intentionally (preferred)
    22% White 1/3*2/3
    38% Grey 2/3*4/7
    40% Black 1/3*1/3+2/3*3/7
    100%
    Black Shoots at White
    15% White 2/3*1/3*2/3
    54% Grey 1/3*6/7+2/3*2/3*4/7
    31% Black 1/3*1/7+2/3*2/3*3/7+2/3*1/3*1/3
    100%

    LONG VERSION:

    To begin with, we must assume the people are logical and not subject to emotional irrationality. For example, White won't shoot at Black just because he's mad at Black for shooting at him first, or perhaps as the result of some comment Black made about White's mother.

    Now, since White is logical, he will always shoot at the opponent with the highest accuracy, because he wants to duel with the poorest shot, thus giving him the best chance of winning. Hence, Grey will always target White in response to this fact.

    Therefore, the only person with a choice is Mr. Black. If he happens to target Mr. Grey, he will either miss, or end up in a duel with Mr. White, and it's Mr. White's turn to shoot, a most undesirable situation for Mr. Black. Thus we are left with two choices: Should Mr. Black target Mr. White, or intentionally miss?

    I'm not going to derive everything, but I encourage you to check the numbers. The most difficult part is noticing that if Black and Grey duel, Grey has a 4/7 chance of winning if Black shoots first, and a 6/7 chance of winning if Grey shoots first.

    So if Black shoots at White first, the chances of White's survival are 2/3 (Black missing)* 1/3 (Grey missing) * 2/3 (Black missing after White kills Grey) = 4/27 Whereas Grey's chances of winning are 2/3 (Black misses White) * 2/3 (Grey hits White) * 4/7 (Grey wins the duel with Black going first)

    Summarized are the calculations below:

    o = Miss; x=Hit; '=Duel (BxG' = Black kills Grey in duel)
    Black Misses Intentionally
    .22 White 2/3 * 1 * 1/3 * 1
    Bo GoW WxG BoW' WxB'

    .38 Grey 2/3 * 4/7
    Bo GxW * GxB'

    .40 Black 2/3 * 3/7 + 1/3 * 1 * 1/3
    Bo GxW BxG' GoW WxG BxW'

    Black Shoots at White
    .15 White 2/3 * 1/3 * 1 * 2/3 * 1
    BoW GoW WxG BoW' WxB'

    .54 Grey 1/3 * 6/7 + 2/3 * 2/3 * 4/7
    BxW GxB' BoW GxW GxB'

    .31 Black 1/3 * 1/7 + 2/3 * 2/3 * 3/7 + 2/3 * 1/3
    BxW BxG' BoW GxW BxG' BoW GoW
    * 1 * 1/3
    WxG BxW'

    Therefore, Black actually becomes the most likely survivor if he misses intentionally. In addition, in both cases, White is least likely to survive.

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    1. I am explaining the odds associated with a duel between Mr. Black and Mr. Grey. No knowledge of calculus is necessary, though at least one concept is associated with calculus.

      If Mr. Black and Mr. Grey are in a duel, and Mr. Black shoots first, he will hit Mr. Grey with the first shot 1/3 of the time. 2/3 of the time he will miss, and the game is not over. Now, Mr. Grey shoots, and 2/3 of the time he has the chance to shoot, he will win. So Mr. Grey will win at least 4/9 of the time (since he wins 2/3 of the 2/3 of the time he gets the chance and 2/3 * 2/3 = 4/9).

      So in Round 1, Mr. Black wins 1/3 of the time, and Mr. Grey wins 4/9 of the time. Since 1/3 + 4/9 = 7/9, a winner will emerge after the second round only 7/9 of the time.

      2/9 of the time, this gun battle will move to Round 2. Again, of these 2/9, Mr. Black will win 1/3 and Mr. Grey will win 4/9 since nothing has changed in regards to order or skill. And 2/9 of these 2/9ths of the time, this contest will move to a third round.

      What emerges is a pattern. With the first round, we have three distinct outcomes, each with its own probability. These outcomes are: 1) Mr. Black will win, 2) Mr. Grey will win, and 3) the contest is undecided and moves to a next round. If we consider successive rounds, the probabilities of each of these change as the probability that the contest will remain undecided gets eaten away by the 1/3 chance that Mr. Black will win the new round, and the 4/9 chance that Mr. Grey will win the new round. So the 2/9 chance that the contest will remain undecided coming out of the first round becomes a 4/81 (2/9 of 2/9) chance coming out of the second round. Then a 8/729 chance (2/9 of 4/81) out of the third round, and so on. If we consider 1000 rounds, the chance that the contest will remain undecided becomes extremely small, specifically it is 2 to the power of 1000 divided by 9 to the power of 1000 (which is really really small). But, even after 1000 rounds, the probability that the contest will be undecided is different than it was coming out of the previous round, specifically it is smaller. It will get smaller after each and every round. Because it has this nature of getting smaller and smaller by a fractional constant, we say it approaches zero, and if we consider infinite rounds, the chance that the contest will remain undecided is 0. I don't know if this seems hard to believe; it did when I first studied calculus. I was all like, but if I multiply a fraction by itself over and over, it is never zero, it will always be that much bigger. In a way, this is right, but by the nature of attempting infinite rounds (which is beyond the human imagination to do) we have are representing a number that is infinitely close to zero with zero. You can say those are not the same thing, that infinitely close to zero and zero are not the same thing, but I will say, think of a number close to zero and I will think of one closer, and also, who cares, its tiny.

      So then if we establish that the chances of the contest remaining undecided are zero, then there are only two distinct possibilities: Mr. Black wins or Mr. Grey wins. After the first rounds, Mr. Black has a 1/3 chance of winning, as we said, and Mr. Grey has a 4/9 chance of winning. Now, we will call the chance that the contest moves to a successive round "the leftovers." After the 1st round, Mr. Black will win 1/3 and Mr. Grey will win 4/9 of the leftovers. And we see that after each and every round, for every 1/3 chance Mr. Black gains out of the previous round's leftovers, Mr. Grey will gain 4/9. So there is a ratio of Mr. Black to Mr. Grey winning of 1/3 : 4/9, which is the same as 3:4, or 3/4. These are the odds that Mr. Black will win versus Mr. Grey will win. To get the probability, we just have to recognize, that if for every 3 rounds Mr. Black wins, Mr. Grey will win 4, then Mr. Black will win 3 of every 7 rounds, or 3/7.

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  32. If Mr. Black shoots at one of the person, then the other person who is not shoot will shoot Mr. Black but if he should in the air, one of the person will shoot the other person but not Mr. Black

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  33. Having Mr. Black shooting at the ground first is a nice reasoning. But it misses one point: Mr. Gray and Mr. White can also choose to shoot at the ground (leading to a stalemate).
    The problem is: if one guy (B, G or W) shoots and kils another one we will be left with 2 guys and it's the turn of the guy who did not shoot. Obviously this is very bad for the guy who initiated the shooting.
    The best strategy for any of them is to shoot at the ground.
    If B shoots at the ground then G must be stupid to aim at W, because if he hits he gives B a free shot at himself. Consequently the best G can choose is shoot to the ground as he knows that W acts rationally.
    Further, W must not shoot G if he acts rationally. He should also shoot to the ground. Otherwise he gives B a free shot to himself.
    Everybody should pass the decision to shoot to the next one. That's how they keep their best chances to stay alive. But that leads to a stalemate.
    My question about the proposed solution is: why G has to aim to W when B is allowed to shoot to the ground? G shoud do the same!
    Is this problem well formulated? Or just a flaw?

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  34. Mr.black will shoot at Mr grey and hit Mr. white Mr grey will shoot mr.black

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  36. he must shoot Mr, white because if he kill's him and Mr, gray's turn comes with his 2/3 accuracy Mr,black's chance to survive is (1/3). and if didn't kill Mr, white and Mr,gray's turn comes the second may choose Mr, white IF HE IS SMART! so black's survival chance is (2/3), so when the assassin's turn comes (if he is alive) Mr,black's chance to survive is (1/2), and now... IT'S HIS TURN >_<

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  37. between mr. black and mr. grey is a 3/3 chance to kill the best marksman mr. white, which leaves mr. black with a better chance at nailing his target mr. grey.

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  38. i am also a kid but i think he will shoot at the ground!
    by the the way i made up this riddle with by french and british parents

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  39. ALL will shoot at the ground until they run out of ammunition, as these are men capable of statistics and probability, they should be able to ascertain that the highest chance of survival (100%) is for no one to kill anyone. Works 3 for 3 every time. I mean, you are already making the assumption that the other people are shooting by probability of their own survival right?

    Don't try to be slick by copping out and shooting the ground with ONLY one person. Pick someone to shoot and do the damn probability problem, otherwise we can make assumptions all day long... like, with the assumption that NO shot misses, Black will ALWAYS die. Or that White, who apparently CAN do probability percentages, would know better than to join this duel, since apparently everyone will shoot the better shot.

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  40. Easy enough.

    If Black shoots at Gray and hits him, it's White's turn to kill Black immediately. => certain death, so he won't try to fire at Gray.

    If Black shoots at White and hits him, it will be Grays turn who has a 2/3 chance to kill Black immediately.

    If Black misses, only one of White and Gray will be alive (as they would always shoot at each other first), and it will be Black's turn again. At least he survives one turn longer for sure.

    If "missing intentionally" is not allowed, then Black should rather shoot at White.

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  41. Black should shoot the air or the ground. He has a 1/3 chance of hitting whatever he shoots, so this gives him a 2/3 of "accidentally" hitting Gray or White.

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  42. Black shoots at white with 1/3 chance of hitting but misses. Gray shoots at white and kills him. Blacks turn comes again so 1/3 chance from first turn adds to 1/3 chance this turn, making blacks chance of hitting grey 2/3, so he will most likely hit grey, but if he doesn't, it only asked who he should shoot to have the greatest chance of survival; he doesn't NEED to survive. BTW, im only 12 years old.

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  43. The puzzle does not give appropriate instances for accurate calculations. For example, If Mr. Black hits a
    target one out of three times, then it has to explain
    which one of the three is the good shot, because if he makes good on his first shot, and misses the next two,
    then it makes no sense for him to waste his first shot
    by firing at the ground, because his next two shots will
    not hit anything. In which case, he should shot at Mr. White first, hoping this is his good shot.

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  45. He should shoot at the ground.

    If Mr. Black shoots the ground, it is Mr. Gray's turn. Mr. Gray would rather shoot at Mr. White than Mr. Black, because he is better. If Mr. Gray kills Mr. White, it is just Mr. Black and Mr. Gray left, giving Mr. Black a fair chance of winning. If Mr. Gray does not kill Mr. White, it is Mr. White's turn. He would rather shoot at Mr. Gray and will definitely kill him. Even though it is now Mr. Black against Mr. White, Mr. Black has a better chance of winning than before.

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  46. Shooting in the air/ skipping his turn is actually Mr. Black's SECOND BEST choice.

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  47. Well, you said 1/3 of the time he hits. You never said how many bullets he shoots. So shooting at both could work

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  48. If he shoots the ground he will look easy and the other guys will go after him but he has an ok chance of killing mr. White so go after him and the other guys probably going to shoot white too and then gray and black can be friends! Ok not really he probably won't live but he has the best dance of living using this method

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  49. mr.white will shoot at air. then mr. black point mr. grey and mr grey points mr black because mr. white has no bullet so he cant shoot others. mr. black and white as bullet so they have to point each other to save thier life.

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  50. If Mr. Black points his gun at the ground and shoots, and he only hits 1/3 of his shots, there is only a 33.3% chance of him actually hitting the ground. If he misses the ground and hits Mr. Gray, Mr. White will kill Mr. Black. If he misses the ground and hits Mr. White he is still at a disadvantage with a 1/2 chance while Mr. Gray has a 2/3 chance and it's Mr. Gray's turn to shoot.

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  51. mr. black used to shoot first in air , then eventually , mr.white kills the mr. gray and mrb black take benfit of it and kill mr.white

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  52. then he falls to the ground and allows the others to shoot one another

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  53. ...and if one is left standing he swipes the guys leg

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  54. If he shoots at the ground he has 67% chance to stay alive.
    If he shoots at Gray he has a 44% chance to stay alive.
    If he shoots at White he has a 50% chance to stay alive.
    That's it. He better shoot at the ground.

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  55. Why dont they just play cards instead.....

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  56. Shouldn't he shoot Mr. White because even if Mr. Black shot Mr. Gray and he happened to kill him, Mr. White would shoot him and get him. If Mr. Black shoots Mr. White and happens to get him, then there's a chance that he might survive, because Mr. Gray misses one of three shots.

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  57. It's all about who the order and changes in probability. If Mr Black Shoots Mr White and gets him Mr Gray gets first shot at Mr Black. However if Mr Black shoots at unrelated target like a random can he probably misses but his chance of hitting the next shot goes up from 1/3 to 2/3 the same as Mr Gray. Mr Gray will probably get Mr White giving Mr Black 1st shot at Mr Gray with a 2/3 chance of hitting him this being his second shot plus he goes first being next in the cycle. Plus if Mr Gray hits a Mr white which is 2/3 probable his chance of hitting the next shot goes down to 1/3 giving Mr Black the next shot and advantage over Mr Grey.
    If Mr Gray misses Mr Black still has raised his shooting percentage to 2/3 and Mr White will definitely eliminate Mr Gray seeing him as more of a threat. So when he goes against Mr White his chance of hitting him is higher.The most favourable option for Mr Black is to shoot at unrelated target.

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  58. My friend said ,
    "look
    u never know
    if im gray
    id be like
    nigga
    i thought we gon team up on white
    why u shooting the sky
    fuck life ima kill u first
    u just never know man"

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  59. If he doesn't shoot at all, then the others can't shoot at all. Therefore he can go home and find another family to piss off.

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  60. But if he aims at the ground he has only a 1/3 chance at hitting it. But if he aims at something other than the ground he has a 2/3 chance of hitting the ground. Then again there are more things then just not the ground or the ground. If there are 4 things ( white grey ground air) not including black, he only had a .5/3 chance of hitting the ground if he aims at something other than the ground. Therefore this whole riddle and solutions is impossible and wrong :D

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  61. Why wudn't Mr Black shoot Mr White first ... irrespective of whether he succeeds or not it wud be Mr Grey's turn next - isn't it?

    So, what's the point of shooting at the ground?

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  62. The best answer for this riddle is for Mr. Black to not shoot the gun at all, thereby not giving any of the others a turn to shoot resulting in 0 deaths, 100% chance of survival.
    Mr. Gray and Mr. White also have the option of shooting nothing resulting in 100% chance of survival.
    If Mr. Black did have to fire the gun his chances of survival will be exactly the same unless his shot hits either Mr. Gray or Mr. White resulting in significantly lower percentage.

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  63. your all wrong hell shoot himself

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  64. For the best chance of survival shoot the guy that is most racist.

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  65. Mr. Grey hits his shot 2/3 of the time, while Mr.White hits the shot ALL the time. So, the logical resonce would be to kill off Mr. Grey. However, because Mr.Black only hits his shot 1/3 of the time, it may not be likely to hit Mr.White. If it did, however, then it would be Mr. Grey's turn. Mr.Grey hits his target most of the time, but now since the area has gone down to 2/2 (1) Mr.Grey would hit his shot ALL the time (hypothetically speaking, of course). If we are talking literal fractions, then it wouldn't make a difference, and Mr.Grey could still miss, but it's unlikely. So, in other words, Mr.Black is screwed.

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  66. I think they shoud all NOT shoot each other or all of them kill themselves or Mr. Black hides and when white and grey fight the victor will not be able to find Black and Black shoots the victor from there and becomes the real victor and then gets locked up for 10 years in jail for killing an innocent man or gets away as a criminal mastermind.

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  67. I think you shoot mister white first he never misses, and then you take your chances with mister gray which hits his mark 2/3 of the time

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  68. In "Mr. Black, Mr. Gray, and Mr. White are fighting in a truel",
    Considering Mr. Gray and Mr. White always choose to aim at either of the alive opponent (with same odds)...
    I calculated the exact probabilities of Survival for Mr. Black to be-
    25/189 -> in case he aims Mr. Gray
    34/189 -> in case he aims Mr. White
    25/126 -> in case he aims ground
    Please reply in case you have numbers which agree or disagree...

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  69. Imagine you're Mr. White, it's your turn to shoot, and everyone is still alive. If you kill Mr. Black, then Mr. Gray has a 66% chance to kill you. However, if you kill Mr. Gray, Mr. Black only has a 33% chance to kill you. So, if you are Mr. White, it is logical that you shoot Mr. Gray.

    Now, if you are Mr. Gray, knowing that Mr. White is going to kill you if you don't kill him, you know you have to try to kill him.

    So, either Mr. Gray kills Mr. White or Mr. White kills Mr. Gray. Either way one of them is dead. Now, if you (Mr. Black) shoot at one of them and hit, there is no one left to shoot back. So, your best first shot is to shoot at nothing, shoot the ground, shoot up in the air, whatever. Just don't shoot at one of the other people

    Otherwise, if in the first round you shoot at one of the others and you manage to hit, there will be someone left and they will have no one else to shoot at but you.

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  70. Probability is not predictive. Rolling a die and getting a 3 has a probability of 1/6, since there are 6 possible outcomes. Still, rolling a 3 on consecutive tries is not at all excluded by probability. The 1/6 result occurs after a very large number of tries.

    SO... Just because Black has a probability of 1/3 successful hits doesn't mean a hit on his first attempt necessitates a miss on the second or third attempt. The only significance of each man's probability for this puzzle is to determine which opponent to aim at. Black should aim for White on his first turn since White has no probability of missing. Shooting at the ground only wastes a chance.

    The result of any successive turn is not dictated by the result of any previous turn. Black and Gray have a chance of hitting or missing at every attempt; each attempt still has the same probability of 1/3 or 2/3 successes respectively.

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  71. For anyone still struggling I wrote a simulator for the three way duel puzzle and a rigorous mathematical treatment:
    Three way duel puzzle

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  72. Just don't shoot!! That is how you don't die!! since it won't be the other guys turn!! 100% chance of no death

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