Chris Croft's Personal Blog

April 19, 2010

Three way gun fight

Filed under: News and Politics — chriscroft @ 5:25 pm

There’s a great maths puzzle about the three way gun fight, where one of the gun-slingers, lets’ call him Posh Gammon Robot never misses, and the second one, let’s call him Grumpy Maths Bear, is 75% accurate, while the third one, let’s call him Smarmy Egg, is only 10% accurate, in fact pretty much rubbish.  Who will win?  Surely PGR??

But no, because Posh Robot will shoot Grumpy Bear, and take his chances with SmEgg, while Bear’s best chance is to try to take out the deadly Robot.  So Egg just has to stand there and let Robot and Bear shoot each other.

But of course if they don’t shoot each other because they have decided to convince the onlookers that they are nice people, and if Egg crows too much about still being alive, there is a risk that Gammon and Grumpy will both turn on Egg and then he’s a goner.

Remind you of anything?



  1. The first case assumes that the transit time of the bullet is less than the difference between the times at which PGR and GMB shoot. If that is not so, then there is a 50% chance that PGR slays GMB immediately, and a 37.5% chance that GMB slays PGR immediately.

    So, even if PGR and SmEgg don’t decide to make cuddly, there’s going to be at least one of them standing after the first shot is fired – and maybe two – unless SmEgg kills one of them. But SmEgg has only a 10% chance of hitting anything with his first shot – and barely 5% of hitting something that wasn’t going to be killed anyway by one of the others.

    So after one round of shooting, there’s approx:
    — 5% probabilty that SmEgg is the only man standing.
    — 12.5% probability that neither of GMB and PGR kills the other, and the whole thing goes to round two.
    — > 80% probability that SmEgg finds himself one-on-one with a vastly superior shot.

    Whether or not GMB and PGR pretend to love each other, the prospects for SmEgg are not good.

    Comment by Martin Herrington — April 19, 2010 @ 10:15 pm

  2. The show-down is irrelevant as the Impending Doom gang are riding into town and will annihilate our sad little duelling heroes. Only chance is for them to cover each other’s back and work together to fight off the bad guys and save the town from being shot to pieces.

    Fat chance.

    Citizens prepare for the worst.

    Comment by Kate Hartigan — April 21, 2010 @ 4:22 pm

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