You live in Killville. Can you stay alive?

[bonanova]

You live in Killville - a town populated by 10 killers and 10 pacifists.

When a pacifist meets a pacifist, nothing happens.

When a pacifist meets a killer, the pacifist is killed.

When two killers meet, both die.

Assume meetings always occur between exactly two persons

and the pairs involved are completely random.

Are your odds of survival better if you are a killer? or a pacifist?

Or does it matter?

Regardless of whether you are a pacifist or a killer,

you may disregard all events in which a pacifist other than yourself is involved

and consider only events in which you are killed

or a pair of killers other than yourself is killed.

[phaze]

If there is an even number of killers all killers will eventually be eliminated. The only hope of surviving would be to be a Pacifist and keep your fingers crossed. If there is an odd number of killers the only way of surviving (there will be only 1) is to be a Killer and keep your fingers crossed. The real question is do you have more chance of surviving as a pacifist with 10 pacifists and 10 killers or as a killer with 11 pacifists and 11 killers?

[bonanova]

If there is an even number of killers all killers will eventually be eliminated. The only hope of surviving would be to be a Pacifist and keep your fingers crossed. If there is an odd number of killers the only way of surviving (there will be only 1) is to be a Killer and keep your fingers crossed. The real question is do you have more chance of surviving as a pacifist with 10 pacifists and 10 killers or as a killer with 11 pacifists and 11 killers?

Good question.

Let's start withe the obvious result that the killer's chance of survival is 1/11, cuz one killer must survive.

The question is a pacifist's chances with a 10-10 split. It's clearly not 1/10.

[mmiguel]

You live in Killville - a town populated by 10 killers and 10 pacifists.

When a pacifist meets a pacifist, nothing happens.

When a pacifist meets a killer, the pacifist is killed.

When two killers meet, both die.

Assume meetings always occur between exactly two persons

and the pairs involved are completely random.

Are your odds of survival better if you are a killer? or a pacifist?

Or does it matter?

Regardless of whether you are a pacifist or a killer,

you may disregard all events in which a pacifist other than yourself is involved

and consider only events in which you are killed

or a pair of killers other than yourself is killed.

everyone will die doesn't matter regardless whether you are P or K, if you meet a K, you will die. Your only hope is that all the other K's kill themselves. This will never happen since there are an even number of K's and they can only remove themselves in pairs. If there were an odd number of K's, then you would have a shot. The steady state of such a system would be one K left standing. If there are N K's and N P's and N is odd, then your chance of living would be 1/N due to assumed symmetry amongst all K's.

[mmiguel]

everyone will die doesn't matter regardless whether you are P or K, if you meet a K, you will die. Your only hope is that all the other K's kill themselves. This will never happen since there are an even number of K's and they can only remove themselves in pairs. If there were an odd number of K's, then you would have a shot. The steady state of such a system would be one K left standing. If there are N K's and N P's and N is odd, then your chance of living would be 1/N due to assumed symmetry amongst all K's.

edit: haha - i was wrong (after reading answer) - clever!

[joef1000]

Be pacifist, and hide in your house until the killers kill each other. If you HAVE to leave your house, travel with other pacifists so you have a higher chance of survival when there are killers about.