Micro 825: Only YOU Can Prevent Forest Fires VIII GAME OVER

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Post Post #75 (ISO) » Mon Sep 17, 2018 5:28 am

Post by Pine »

Two forests does seem like it would balance things.
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Post Post #76 (ISO) » Mon Sep 17, 2018 5:33 am

Post by FakeGod »

I think 1 pyro also balances things?
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Post Post #77 (ISO) » Mon Sep 17, 2018 6:58 am

Post by DrDolittle »

One pyro balances things in a wrong direction I think, because games would get more streaky depending on whether YOU is lucky and hits PYRO and whether PYRO is lucky at hits forrest. 2 of each is nice since it makes the game more 'mafia' and less luck.
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Post Post #78 (ISO) » Mon Sep 17, 2018 9:39 am

Post by Pine »

^This

We could give it a test run?
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Post Post #79 (ISO) » Mon Sep 17, 2018 10:23 am

Post by DrDolittle »

I realized that in the case where there is only 4 yous, pyro could potentially run the strategy of hunting all yous instead. That would also result in game. Note this is different from hunting forests since some YOU is public knowledge after shooting.
(i.e. in a night scenario, 5 people are alive: {smokey, you, forrest, forrest, pyro}, and a you is outted (presumably from shooting to get to the night phase), pyro should choose to shoot you.
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Post Post #80 (ISO) » Mon Sep 17, 2018 11:19 am

Post by DrDolittle »

running a random simulation under the following rules:
YOU kills randomly only among the alive players that are not YOU, FOREST, or SMOKEY if SMOKEY has killed already.
PYRO only hunts for forests (if some YOU shot, or smokey killed, pyro doesn't kill them)
The YOU that makes the first kill continues making kills (irrelephant's suggestion)
PYRO gets a final shot if no PYRO is alive.
[So we are assuming a very civil town...]

2/2/1/4 gives pyro advantage of 0.575.
1/2/1/5 gives pyro advantage of 0.742 (significantly less than I anticipated)
2/2/2/3 gives pyro advantage of 0.509 (so smokey is better than you in EV, I guess)
1/1/1/6 gives pyro advantage of 0.501 (almost fair)

However, 1/1/1/6, games last 1.025 days on average, while 2/2/1/4, games last for 1.65 days on average. Compared to the baseline, 1/2/1/5 games last 1.60 days (so 2/2/1/4 and 1/2/1/5 is roughly indistinguishable).

Here's some (poorly written) matlab code in case you want to run the simulation yourselves. To change the ratio, simply move the numbers 1 to 9 between the 4 groups of forest, pyro, smokey, and you.
Spoiler: code
%% Smokey the bear
pwin = 0;
for iter = 1:10000
forest = [1];
pyro = [3,4];
smokey = [5];
you = [2,6,7,8,9];
outted = [];
dead = [];

while isempty(forest) + isempty(pyro) == 0
if isempty(you) == 0
targets = [you(you~=you(1)),smokey,pyro];
for nottarget = [dead,outted]
targets(targets == nottarget) = [];
end
tgt = randi([1,length(targets)]);
kill = targets(tgt);
if ismember(kill,smokey) == 1
dead = [dead, you(1)];
you(1) = [];
outted = [outted,kill];
elseif ismember(kill,pyro) == 1
outted = [outted,you(1)];
dead = [dead,kill];
pyro(pyro==kill) = [];
elseif ismember(kill,you) == 1
outted = [outted,you(1)];
dead = [dead,kill];
you(you==kill) = [];
end
end
targets2 = [you,smokey,forest];
for nottarget2 = [dead,outted]
targets2(targets2 == nottarget2) = [];
end
kill2 = targets2(randi([1,length(targets2)]));
if ismember(kill2,smokey) == 1
if isequal(pyro,[])
break
elseif length(pyro) == 1
dead = [dead, pyro(1)];
pyro(1) = [];
outted = [outted,kill2];
targets2 = [you,smokey,forest];
for nottarget2 = [dead,outted]
targets2(targets2 == nottarget2) = [];
end
kill2 = targets2(randi([1,length(targets2)]));
end
elseif ismember(kill2,forest) == 1
dead = [dead,kill2];
forest(forest==kill2) = [];
elseif ismember(kill2,you) == 1
dead = [dead,kill2];
you(you==kill2) = [];
end
end

if isempty(forest) == 1
pwin = pwin +length(dead);
end
end

pwin/iter
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Post Post #81 (ISO) » Mon Sep 17, 2018 11:27 am

Post by DrDolittle »

made a mistake on game length - need to multiply that number roughly by 2...
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Post Post #82 (ISO) » Mon Sep 17, 2018 11:34 am

Post by DrDolittle »

Recomputed the average days till game end...

1.8434 for the 1/1/1/6 setup
2.7767 for the 2/2/1/4 setup
2.2267 for the 1/2/1/5 setup

[forest, pyro,smokey,you] if that wasn't clear.

Spoiler: updated code
%% Smokey the bear
pwin = 0;
deadd = 0;
for iter = 1:10000
forest = [1];
pyro = [3];
smokey = [5];
you = [2,4,6,7,8,9];
outted = [];
dead = [];
count = 0;
while isempty(forest) + isempty(pyro) == 0
if isempty(you) == 0
targets = [you(you~=you(1)),smokey,pyro];
for nottarget = [dead,outted]
targets(targets == nottarget) = [];
end
kill = targets(randi([1,length(targets)]));
if ismember(kill,smokey) == 1
dead = [dead, you(1)];
you(1) = [];
outted = [outted,kill];
elseif ismember(kill,pyro) == 1
outted = [outted,you(1)];
dead = [dead,kill];
pyro(pyro==kill) = [];
elseif ismember(kill,you) == 1
outted = [outted,you(1)];
dead = [dead,kill];
you(you==kill) = [];
end
end
targets2 = [you,smokey,forest];
for nottarget2 = [dead,outted]
targets2(targets2 == nottarget2) = [];
end
kill2 = targets2(randi([1,length(targets2)]));
if ismember(kill2,smokey) == 1
if isequal(pyro,[])
break
elseif length(pyro) == 1
dead = [dead, pyro(1)];
pyro(1) = [];
outted = [outted,kill2];
targets2 = [you,smokey,forest];
for nottarget2 = [dead,outted]
targets2(targets2 == nottarget2) = [];
end
kill2 = targets2(randi([1,length(targets2)]));
end
elseif ismember(kill2,forest) == 1
dead = [dead,kill2];
forest(forest==kill2) = [];
elseif ismember(kill2,you) == 1
dead = [dead,kill2];
you(you==kill2) = [];
end
count = count + 1;
end

if isempty(forest) == 1
pwin = pwin+1;
end
deadd = deadd + count;
end

deadd/iter
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Post Post #83 (ISO) » Mon Sep 17, 2018 12:22 pm

Post by FakeGod »

I was always curious on this point: if you are YOU but someone else prevented first, and the first preventer wants you dead. Would it be better for you to prevent before he could do so?
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Post Post #84 (ISO) » Mon Sep 17, 2018 12:23 pm

Post by RadiantCowbells »

Probably
2019 stats: Town WR 76.7%, overall WR 81.667%, 1 scum defeat involving a major mod error in lylo vs 8 scum wins.
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Post Post #85 (ISO) » Mon Sep 17, 2018 12:28 pm

Post by implosion »

It is probably better because it's sort of equivalent to a double day; it's hard to extend past a double day though, and it doesn't help if a YOU is about to prevent Smokey. And it might depend on some kind of parity.
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Post Post #86 (ISO) » Mon Sep 17, 2018 12:30 pm

Post by implosion »

Also probably depends a lot on the status of whether Smokey is known yet; if Smokey is public info, then it's significantly better, because there's no way that it accidentally outs smokey before pyros ignite smokey.
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Post Post #87 (ISO) » Mon Sep 17, 2018 12:31 pm

Post by DrDolittle »

doesnt this argument go down a slippery slope? If A wants to prevent B, and B is willing to prevent C, then C should prevent before B, before A
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Post Post #88 (ISO) » Mon Sep 17, 2018 12:32 pm

Post by RadiantCowbells »

You guys are doing a bad job of this. I will handle this.
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Post Post #89 (ISO) » Mon Sep 17, 2018 12:33 pm

Post by implosion »

In post 87, DrDolittle wrote:doesnt this argument go down a slippery slope? If A wants to prevent B, and B is willing to prevent C, then C should prevent before B, before A
The problem with this is that B isn't a confirmed YOU, so them saying that they want to prevent C doesn't prove that they can.
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Post Post #90 (ISO) » Mon Sep 17, 2018 12:36 pm

Post by DrDolittle »

does the same argument apply to that A is not a confirmed YOU so his threat is not credible (assuming we are still in day 1)
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Post Post #91 (ISO) » Mon Sep 17, 2018 12:41 pm

Post by implosion »

I was always curious on this point: if you are YOU but someone else prevented first, and the first preventer wants you dead. Would it be better for you to prevent before he could do so?
I was assuming based on the part where someone else prevented first that A is a confirmed YOU.
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Post Post #92 (ISO) » Mon Sep 17, 2018 1:40 pm

Post by DrDolittle »

realized that I could just simulate the scenario:

2/2/1/4 drops pyro advantage of 0.575 -> 0.517.
1/2/1/5 drops pyro advantage of 0.742 -> 0.697
1/1/1/6 gives pyro advantage of 0.501 -> 0.491

Honestly looks pretty solid.
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Post Post #93 (ISO) » Mon Sep 17, 2018 4:56 pm

Post by FakeGod »

I bet it gives you different results depending on the number of YOUs remaining.
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Post Post #94 (ISO) » Sun Nov 25, 2018 4:04 pm

Post by Micc »

:mrgreen:
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