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/sci/ - Science & Math

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11079766 No.11079766 [Reply] [Original]

A vampire can attack two people every night.
Every time a vampire attacks a human, there is a chance [math]C[/math] they will kill the human.

A human attacked by a vampire but who was NOT killed will instead turn into a Servant of the vampire.
A Servant can attack one human every night.
Every time a Servant attacks a human, the Servant will attempt to turn the human into a fellow Servant. This process has a [math]0.9[/math] chance of succeeding, i.e. there a [math]0.1[/math] chance of the process failing and the human dying. Humans who die after being attacked by a Servant stay dead.

A human who was killed by the vampire has a [math]0.01[/math] chance of coming back to life as a ghoul. Given a sample of 100 such eligible corpses killed by a vampire, it would take [math]t_{1\backslash2}=30[/math] days for 50 of them to rise up as a ghouls. A ghoul will then feast on the flesh of the dead to grow in power. Every night, there is a [math]0.5[/math] chance of a ghoul encountering another ghoul. When two ghouls meet, one eats the other and gains the other's total power. It takes the combined power of 666 ghouls for a ghoul to turn into a proper vampire.

Once a ghoul turns into a vampire, he will seek out his "parent vampire" and defeat him. Let us define [math]S_{total}[/math] to be the number of Servants the original vampire has at the time of his defeat.

Express [math]S_{total}[/math] as a function of [math]C[/math].

>> No.11079955
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11079955

Bumping for interest.

>> No.11080000

> Every night, there is a 0.5 chance of a ghoul encountering another ghoul.

Do you mean there is either 0 or 1 meeting per night? Or do you mean every ghoul has it's own independent 0.5 chance of meeting another ghoul?

> It takes the combined power of 666 ghouls for a ghoul to turn into a proper vampire.
Do you mean at least 666 or exactly 666?

>> No.11080032

>>11080000
Every night, there is a coinflip chance some two ghouls meeting each other.

A ghoul needs to have the combined power of AT LEAST 666 ghouls (inc. his own inherent power) to become a vampire.

>> No.11080076
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11080076

>>11080032
>Every night, there is a coinflip chance some two ghouls meeting each other.
I'm pretty sure that for sufficiently high C the probability of some ghoul eventually becoming a vampire goes to zero.
And with sufficiently high I mean something like 40% should be enough. Quite possibly less.

>> No.11080077

>>11080076
Yes, it's part of the question. It's actually much lower than 40%.

>> No.11080218

>>11080076
>>11080077
I don't see how the probability can be 0. As long as C > 0, this scenario should be possible.

After 666 days, 666*2 humans killed by vampire. All corpses became eligible, and immediately rose. Every night, ghoul number one kills another ghoul.

>> No.11080219

>>11080218
>ghoul number one
That's where you're wrong.
If it were always the same ghoul, the problem is trivial.
The problem is that two randomly chosen ghouls fight. There are eventually too many ghouls to choose from, so the chances of getting to 666 go to zero.

>> No.11080229
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11080229

>>11079766
>>11079955
>>11080000
>>11080077
The proportion of [math]repeating digits[/math] in this thread fascinate me

>> No.11080231

>>11080219
It has a non-zero chance of being chosen over and over.

>> No.11080712

>>11080231
Yeah, but the number of ghouls grows really fast.

>> No.11082030

Bumperino.

>> No.11082533

Bump