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Topic: ZOMGbies! (A 1 person board game)
Replies: 1   Last Post: Mar 15, 2013 12:29 AM

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Phil Carmody

Posts: 2,219
Registered: 12/7/04
Re: ZOMGbies! (A 1 person board game)
Posted: Mar 15, 2013 12:29 AM
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<fc3a501@uni-hamburg.de> writes:
> Da Rulez!
> 0. All rules may be pimped for moar lulz.
> 1. You play on a m*m torus square grid board.
> 2. The cells are in one of three states:
> human, zombie or asleep.
> 3. Initially all cells are asleep.
> 4. Your move is "awakening" k cells.
> 5. On awakening, the cell will become human
> with probability p. (Alternatively, the state
> is preset but unknown to you, like in Minesweeper).


And they become zombies otherwise?
Or do they fall back asleep again?

> 6. A zombie cell will infect all "sleeping" cells
> in its vicinity (The usual LIFE 8-cell neighborhood).
> Already woken humans carry a chainsaw and are immune. :-)
> (The infection is computed after the awakening, but
> see Rule 0.)
> Protect mankind!
>
> Some analysis:
> - For k>=8, your job is trivial: awake all the neighborhood
> of any zombie.
> - Still, k=4 is enough to stamp out any breakout if zombies
> appear only sparingly. See self-explaining sketch:
>
> 444
> 4z33
> 11z3
> 1z23
> 222
>
> - With k=2 and a woken human anywhere, you can protect a
> whole half-plane (since the infection spreads with v=1
> to both sides and your protective wall too). Oops, did I say
> we play on a torus? Goto 0 :-) Also, I assumed there is
> just one zombie hidden on the board.


No you didn't. You assumed "3. Initially all cells are asleep."
combined with "2. The cells are in one of three states: human,
zombie or asleep." that means there are no zombies on the board.

> So, any strategies for k=1 and a board starting with one
> awoken zombie (and no more hidden)?
>
> P.S.:
> oo. Anyone making a browser game out of my idea and not
> sharing the million$ will meet Cindy, the rusty chainsaw :-)


You can't kill what's already dead!

Phil
--
"In a world of magnets and miracles"
-- Insane Clown Posse, Miracles, 2009. Much derided.
"Magnets, how do they work"
-- Pink Floyd, High Hopes, 1994. Lauded as lyrical geniuses.



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