Resistance I - London Calling - Page 22

On January 02 2012 19:53 Blazinghand wrote:
In the event of 1 spy on the d1 team:
33% chance of Blazinghand
33% chance of Palmar
33% chance of Radfield

What are (randomly) the odds of 1 spy on d1 team?
there's a 1/3rd chance for the first guy to be a spy, right? so assuming that, for the other two not to be spy, there is a 3/4ths chance to not pick the 2/8 ppl who are spies, then a 5/7ths chance not to pick the 2/7 people who are spies, meaning there is a 1/3*3/4*5/7 = 0.1786 of the first guy being a spy

"but wait blazinghand" you say "what if the first guy is town, then the second guy is spy?

well don't worry man, i can help you with that. Check this:
the odds of the first guy being town is 2/3rds, right? well ok if the second guy is a spy there's a 3/8ths chance of getting him as spy, then if the third guy is a town, there's a 5/7ths chance of him being town... which comes out to 2/3 * 3/8 * 5/7 = 0.1786 of the second guy being a spy

"oh shoot blazinghand" you say "how does that work?"

well, we're just multiplying probabilities, so the order doesn't matter, right? The one thing we can determine for sure is that it should be the same probability of a single person on that team being a spy. That makes sense, yes?

Adding these three probabilities together, the probabilities come out to 53% chance of exactly 1 spy on N1 team! That still leaves a lot of room for the possibility of 2 spies N1.

What are the odds of 2 spies on the d1 team?
The odds of there being 2 spies means that after there has been picked a spy (1/3rd chance) there is another spy pick, either immediately (1/4 chance), and then the third spy ISN'T picked (6/7) chance or there is a town pick then a spy pick (the other 3/4 of the time, there is a 2/7 chance of a second spy). (1/3) * (2/8) * (6/7) = 0.0714, and with three combinatorial routes, this leaves us with a 21% chance of 2 spies on D1.

Well, what about the remaining 26% chance?
There is a small but non-zero chance that there were no spies D1 (which wasn't the case, but for completeness sake) and the odds of that would be 2/3rd * 5/8 * 4/7 (order irrelevant) which gives us a 23% chance. There's also a very small chance that the mission actually contained 3 spies, which would be a 1/3rd * 2/7 * 1/6 = 1.5% chance. Very small.

Now you're probably thinking "Wait why would there be 3 spies N1, Blazinghand? that sounds horribly unlikely and sub-optimal for the spies, doesn't it?"

Why yes, reader, that DOES?

See, the thing a raw probability calculation like this leaves out is that in every situation, there's a chance that the spy is Radfield, rather than Blazinghand or Palmar. See, if Blazinghand or Palmar is the spy, that has no impact on whether the other dude (Blazinghand or Palmar) is the spy. However, if Radfield is the spy, he's the dude who put together the team. He could easily chose to include 1, 2, 3, or 0 spies regardless of probability.

This makes things much more interesting.

Now imagine you're Radfield. This means you are a spy and are totally devious and smart etc etc. So you lucked into a d1 captainship, and you get the feeling people are gonna sheep all over you. You posted a question and some people have made some vaguely scummy d1 posts (Zona, Blazinghand both made posts prior to Greymist's warning about posting anything that could be used as spy meta). What's an optimal strategy?

Well, as Radfield, you'd pick your scumbuddy Palmar, who has been judiciously silent, and Blazinghand. Blazinghand, being the mad nerd baller that he is, will nayvote the team, looking even scummier, but luckily the (now probably not) scum Jackal comes in and hammers the vote.

Now, you get into a big long argument with Blazinghand and Palmar sort of chills. Townies, operating under the assumption that there was 1 spy N1 (when really there were two-- you sabotaged and palmar did nothing, so it looked like there was only 1 spy), are not going to select an "only new dudes" 4-man team. They don't want to select Blazinghand, because you've made a case against him. And, despite (or because of) your best efforts, Blazinghand has made a case of sorts against you.

Naturally, the pick Palmar. You wait until a team of 3 townies plus Palmar gets suggested, and of course it passes-- nobody wants a team with Blazinghand on it, and you are vaguely suspicious to some.

Palmar sabotages, and now things are looking scary. People immediately assume it's not Palmar, even though he's the common article between the two missions. Some people are like "Well radfield isn't confirmed town any more" and some people are suspicious of Palmar, but Blazinghand is still on everyone's scum list...

and then your Third man swoops in, Zona, who busts out this big "Blazinghand and Rad are working together" theory and it doesn't really make sense but people buy it because people will buy things when they're desperate. Zona took a hit earlier during the "is this a scum strat being said" deal, but things start to make sense. Radfield/Blazinghand/Zona? could be. Radfield/Blazinghand/someone else? maybe.

But these people aren't paying attention to the facts and the facts are that Radfield is scummy and the ONLY REASON HE WOULD BRING ME D1 when I looked scummy would be to entrap me as he has! it's an elaborate plot