This is why algorithms are so important in computer science. They can save a lot of calculations,
You have a 2/3 chance that B will hit C (who he should rationally target), and then you have a 1/3 chance that you will hit B. So 2/9 chance you survive and win on your second shot, plus some minor odds that a sequence of misses between you and B will end with you hitting. (I’ll leave that for the smart people.)
Interestingly, your chance of survival would be greater if B were a better shot. Against two perfect sharp-shooters, you’d go all the way up to 1/3 chance.
[quote=“frauenfelder, post:1, topic:89437”]Math problems are more interesting when they are posed as horror stories.[/quote]This calls for a gruesome re-imagining of the Dining philosophers.
Like, they’re all participating in a ritual to desperately forestall the awakening of Cthulu, and they must not stop chanting until morning.
Am I correctly being irritated by his (I believe) incorrect pronunciation of Josephus?
If B misses C (1/3 chance), then C will kill B (as the greater threat), but you then have a 1/3 chance to hit C, so there’s an additional 1/9 on top of the 2/9 you identified, and we’re up to 1/3, so B being a perfect shot doesn’t help you…and then there’s the chance you mention of B hitting C and then you and B trading shots until you win—I get something like 6% in a rough pass–that can’t happen if B is a perfect shot.
B being just an infinitesimal bit better than 1/3 still ends up getting you a 1/3 chance of winning by your second shot (the first real one), but your chance of winning future exchanges of shots with B is better.
You could make it almost 1/1 and not even have to shoot. Talk to them both privately before the duel…
“So, I paid for B to take marksmanship classes, you best shoot him first.”
“So, I paid for C to take marksmanship classes, you best shoot her first.”
Just focus on the math.
Well, I do understand that it’s a word problem, but in my army, if you would die either way - I suggest fighting your way out.
“To subdue the enemy without fighting is the acme of skill.” ~ Sun Tzu
“Trick others into attacking your enemy.” ~ Sun Tzu
Use a machine pistol.
This whole story might explain why the people of Jerusalem pelted Josephus with dung as he called on them to surrender to the Romans. Of course they also knew that he had been in charge of the unit which had chosen death rather than surrender to the Romans. Sorry, had mostly chosen death rather than surrender to the Romans.
And Josephus said they had used the method of drawing lots (if I remember right). But I wouldnt be surprised if he was not entirely truthful about this episode.
It’s a flat circle.
First, assume a spherical cow …
The theme of this election season has been picking one’s second favorite option, and then as that ones eliminated as a choice, go down to the next worse choice until everyone is more or less equally disgusted. So in keeping with that vibe, I’d urge you to consider that the second-best chair in the circle is always the same, and it always conveys the same advantage: whoever sits in chair two doesn’t have to watch any of his comrades die.
W being 2L+1 also works when the excess, L, is zero, of course.
Just run the other 40 guys over with the trolley.
As the only shooter with less than even odds, I picked a hell of a time to start acting rationally.
Hats off to his brilliant teacher.