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# You live in Killville. Can you stay alive?

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## Question

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.

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Let's assume this problem runs for an infinite amount of time. Since there are an even number of killers they will all die eventually. This holds true because Killers can only die at the hand of another killer. Leaving the pacifists out of the mix you can easily see how the killers will start crossing paths and offing one another. If there were eleven killers then there would be 5 gun fights (sooner or later) ending in the death of 10 of those killers while the remaining killer off'd the Pacifists.

Although it may be a very small probability, the pacifists are the only one's capable of ultimate survival.

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Killville Script -- It records the total number so you can see percentages (must have javascript enabled)
Edited by marchawg
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Killville Script -- It records the total number so you can see percentages (must have javascript enabled)

I would jsut move and save myself the trouble of thinking it through all the way.

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Killville Script -- It records the total number so you can see percentages (must have javascript enabled)

Hi marchawg and welcome to the Den.

Nice job.

Can you do this for an odd number of killers?

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killers will eliminate themselves after 5 meetings and the only chance for survival of anyone is for one or more pacifists to have not been met by killers before they have elimintated themselves... if the first five meetings are between killers then all pacifists live but once all pacifists die, the killers will still continue until they have elimated each other. If there were an odd number of killers the the final solution would be a single killer to survive... If I wanted to be the survivor I would want to increase my odds by being a pacifist and try to limit my number of meetings in general

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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.

Pacifist has better odds at survival.

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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.

if you are the pacifict, the chance of meeting another pacifist is 9/19

if you are a killer, then the chance of meeting a pacifist is 10/19

With the first meeting, if you are a killer, the following happens:

If you meet a pacifist, then the probability of meeting another pacifist is 9/18.

if you meet a killer, you die.

If you are a killer then each time you meet a pacifist, you decrease the chances of survival. This is because you make the chance to meeting a killer higher than the chance of meeting a pacifist, and sometime soon you will meet a killer.

It is better to be a pacifist. I would be one anyway too!

Edited by Raoul
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If you are a killer then you can meet 9 other killers that will kill you and ten pacifists

If you are a pacifist then you can meet 10 killers that will kill you and 9 pacifists

So it is better to be a killer in that town, you have more chances to survive

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If you are a killer then you can meet 9 other killers that will kill you and ten pacifists

If you are a pacifist then you can meet 10 killers that will kill you and 9 pacifists

So it is better to be a killer in that town, you have more chances to survive

That's after one encounter. How about after unlimited encounters?

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Hi marchawg and welcome to the Den.

Nice job.

Can you do this for an odd number of killers?

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Since Killers die in pairs at some point 10 Killers will die.

The surviving Killer will kill any remaining Pacifist.

Love the script.

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we have 19! state of meeting.a pacifist in 10^10 of these meets will die;but a killer will die just in 9! of these meets.10^10 is bigger than 9!.so if you be a pacifist you have a better chance to survive;)

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killer

if your a pasavist then you can meet 9 out of the 19 people other than you and live

if your a killer then you can meet 10 out of the 19 people other that you and live

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2 answers i have depending on what is meant by survival.

1. if the meeting is only once to encounter (10 ppl meet 10 ppl) and few of them coming alive:

If I am a killer:

meeting a killer: 9/19 (chance of dying) = 0.472

meeting a pacifier: 10/19 (chance of survival) = 0.526

If I am a pacifier:

meeting a killer: 10/19 (chance of dying) = 0.526

meeting a pacifier: 9/19 (chance of survival) = 0.472

Chance of survival is higher if i am a killer.

2. If it is down to the last man standing (survivors from previous meetings pit together again, till no more killers in town)

No matter what i am, i have to face only pacifiers, all the rounds. my last round ideally be me( K | P) vs P. However, i cannot be the lone killer in pack to be left, as killers exist in pair (or die in pairs). So, there got to be 4 ppl alive in previous round, which are 2 killers and 2 pacifiers.

K v K && P v P

or

K v P && K v P, then K v K

If i am a pacifier, i have atleast a remote chance of survival, however being a killer, there is NO WAY of survival.

so, the only chance of survival is, when i am pacifier.

Being a pacifier also helps keep other pacifiers alive, whoever i encounter them, for these last rounds. The more they are left, the more prob. i have in later stages of meeting them.

There is a good reason why bible says

" the meek will inherit the world"

and sayings like "those who live by sword, die by it" (in long run)

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I think it will be unfair and straight forward if we pit (11K && 10P) or (11K && 11P) or even (1K && 10/11P). A round will be missed (where 1 will sit out idle in 1st or 2nd round). If that is allowed, then hypothetically the last meeting [K,P,P] can always become [P,P] while K sits out and all 3 can play stalemate.

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It doesn't matter.If you are a pacifist you have 50% chances of getting killed and 50 % of staying alive becouse there are only 2 metting chances in witch you can get evolved.Same with killers.

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Basically, it's the odds of if you will meet a killer.

A pacifist could meet 10 killers or 9 pacifists

10/19

A killer could meet 9 killers or 10 pacifiests

9/19

I couldn't agree more, yes it is a 50/50 chance for the most part but u have to remember you are someone too and you will not kill ur self (hopefully) and there fore if u are a killer u have slightly a better chance of survial. there really is no better answer

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I think it's simple.

How long can the game go on? A finite time, and at the end, either; no one survives, or some number of pacifists survive.

From that alone, it's better to be a pacifist.

No killers can survive - why? Let's suppose a game where ALL the pacifists have met a killer at some point, they're all gone. Then we have K -K and they'll all go. No one left. On the other hand, a pacifist stands a small chance of not encountering a killer before all the killers are gone.

I've not looked at the probabilities in terms of the probability of a given killer/pacifist surviving n encounters, but this looks very similar to an urn problem I've seen earlier. abilities in terms of the probability of a given killer/pacifist surviving n encounters, but this looks very similar to an urn problem I've seen earlier.

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I think it's simple.

How long can the game go on? A finite time, and at the end, either; no one survives, or some number of pacifists survive.

From that alone, it's better to be a pacifist.

No killers can survive - why? Let's suppose a game where ALL the pacifists have met a killer at some point, they're all gone. Then we have K -K and they'll all go. No one left. On the other hand, a pacifist stands a small chance of not encountering a killer before all the killers are gone.

I've not looked at the probabilities in terms of the probability of a given killer/pacifist surviving n encounters, but this looks very similar to an urn problem I've seen earlier. abilities in terms of the probability of a given killer/pacifist surviving n encounters, but this looks very similar to an urn problem I've seen earlier.

I agree, be a pacifist and lock yourself in your house and wait until the killing is finished ! Better than killing people only to be killed yourself. Don't you guys know the saying, " Who lives by the sword (gun) dies by the sword (gun)"

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I would go for pacifist...

it may seem like the killers have a better chance of survival..

but.. actually..

there is an even number of killers.. assuming that meeting always happen..

that means sooner or later the killers will kill each other anyways..

so the killers have a zero chance of survival..

and the pacifist.. have a small chance of survival.. depending whether the killers kill each other first.. or meeting with pacifist first..

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well if you think about it, a pacifist would have more chance of survival because there are three possible scenarios:

1. Pacifist meets Pacifist - No One Dies

2. Pacifist meets Killer - Pacifist Dies

3. Killer meets Killer - BOTH Killers Die

Assuming the meetings occur in this order there would be 3 pacifists remaining by the end, but we have been told the meetings are random.....

I think I'd choose a Pacifist because there is only one meeting at which ONE pacifist dies and there is one meeting at which TWO killers die therefore you'd have a better chance of surviving

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Either way your chances are equal.. working out at 0.00001082508 chance of survival

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EQUAL CHANCES UNTIL EVERYONE DIES!!!

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I'm guessing Pacifist for one simple reason, when two Pacifists meet they both live, when two Killers meet they both die. Odds are two Killers will meet, kill each other, then you have more Pacifists than killers which gives you a better chance of meeting a Pacifist although you still need a lot of luck.

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Pacifist

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