Last game there were two people on the first mission and I was positive retep was innocent, even though I decided to use a RNG to pick him. Now there's three people, and I'm not sure if any of them are innocent at this point.

@mrxak, on 27 July 2012 - 02:30 PM, said in GTW 40:

Looking at SoItBegin's probabilities, they don't even especially make any mathematical sense. Am I the only one who noticed that?

Not that it matters. Probability only gets you so far, you need to establish trust with people.

OK, Mr. Vibrant-objections-to-everything. How's my math wrong, and what names would you pick this time?

The question of there being at least one sleeper agent on a team of three is logically the opposite of saying there are no sleeper agents on a team of three. It's a simple marble problem. Take a marble out of the jar, then take a second one, then take a third one, without ever replacing the marbles you've taken out.

So, the odds of the first person being innocent is 5/8. The second person being innocent is then 4/7. The third is 3/6.

5/8 * 4/7 * 3/6 = ~17.86%

100 - 17.86 = 82.14% chance of there being at least one bad guy.

Now, if one is innocent, as one must always presume oneself to be, the odds of two other people being innocent are 4/7 and 3/6. That comes out to be about 28.57%. Which means, if one is innocent on a team with two others, the odds are 71.43% that there's at least one bad guy in there with them.

I have really no idea where you came up with:
3/8 * 100% + 5/8 * (11/21) = 70.8%

But, as previously stated, probabilities don't matter much, because this is not a game of chance, it's a game of trust and strategy. There are variables we simply don't have, such as the willingness of the three traitors in the game to not fail a mission they are put on.

Now, I'm going to go ahead and assume you are innocent, for the sake of argument here, and as an innocent, you are now forming a mission team in the hopes of maximizing the innocents and minimizing sleeper agents. You are dealing with the prospect that a bit over a quarter of all games you play of size eight, the three people on the first team were all innocent. Those aren't great odds, but those are decent odds. This game is best won with streaks, establishing a workable group, and running with it.

You apparently trust retep998 enough to put him on the team again. It makes sense, after all, he was just on a team with you that succeeded, and he didn't make any forceful statements, a sign of trying to control the game like this mrxak fellow. Fair enough.

But if you trust yourself, and you trust retep998, the odds are such that there's a 50% chance I'm a good guy too. If you picked me, and got lucky on the fourth guy (40% odds), we could sweep this game and win it in three rounds.

People get too hung up on the probabilities here, it seems. Probabilities are nice, to understand just how risky something is, but it all comes down to trust. I have greater reason to trust myself, SoItBegins, and retep998, than anyone else in the game, because none of us have sabotaged a mission yet, given an opportunity to do so. I would want to have all three of those people on a team together. Then, I'd add somebody reasonable, somebody like darth_vader. Maybe even croc. I would avoid prophile, who is apparently laying low. I would avoid JacaByte and Crow T. Robot who seem to have an issue, even now, with the way the first round was conducted.

darth_vader, mrxak, retep988, SoItBegins. Risky, sure, but the most likely of the bunch to be trustworthy so far. I would take a gamble on that group. If we're lucky, the game will end by round three, if we're unlucky, we'll have two extra rounds to figure things out.

@mrxak, on 27 July 2012 - 10:29 PM, said in GTW 40:

So, the odds of the first person being innocent is 5/8. The second person being innocent is then 4/7. The third is 3/6.

5/8 * 4/7 * 3/6 = ~17.86%

100 - 17.86 = 82.14% chance of there being at least one bad guy.

Now, if one is innocent, as one must always presume oneself to be, the odds of two other people being innocent are 4/7 and 3/6. That comes out to be about 28.57%. Which means, if one is innocent on a team with two others, the odds are 71.43% that there's at least one bad guy in there with them.

I have really no idea where you came up with:
3/8 * 100% + 5/8 * (11/21) = 70.8%

OK, I did make an error.

The odds of the first person being innocent are 5/8.

So, 5/8 of the time:

There are 21 ways to choose 2 people from 7. (7 nCr 2)

There are 6 ways to choose 2 people from 4 (4 nCr 2), that is: from the group of 7 with the traitors removed.
(my error was here— I did 2 from 5 by mistake.)

This makes 5/8 * 15/21 = 25/56.

3/8 of the time, the first person is a traitor so the group always contains traitors.

25/56 + 3/8 ≈ 82.14%.

So, shouldn't mrxak propose a group that has less of a chance (that is, fewer people from the first group) of being evil?

EDIT: I don't trust retep. Not with those odds. I'm just floating up a balloon so we can see who rejects it when the proposal fails.

This post has been edited by SoItBegins : 27 July 2012 - 10:55 PM

Really all I'm doing is grate on your nerves, because you've been awfully suspicious during this game and I want you to snap. If it were up to me I'd put myself, SIB, retep and Darth Vader on a proposal. SIB and retep because they've been on a successful mission, DV because he's probably not a traitor, considering that he's brand new to this game, and myself because I'm innocent, of course.

@soitbegins, on 27 July 2012 - 10:54 PM, said in GTW 40:

So, shouldn't mrxak propose a group that has less of a chance (that is, fewer people from the first group) of being evil?

If you're just picking at random, you're not going to better your odds, no matter what. That's why you shouldn't pick at random. If you can find a random selection of four names that betters the odds over the three of us plus one, mathematically, I'll gladly vote for it. That, however, is impossible. The group you've picked has a 92.9% chance of having at least one bad guy on it from an outsider's perspective (not being on the team), because you're choosing at random.

My picks were based on trusting the people who have already been trustworthy (all three of us), plus one or two who have been reasonable in the game so far, as good guys acting in good guys' best interests.

@jacabyte, on 27 July 2012 - 11:01 PM, said in GTW 40:

Really all I'm doing is grate on your nerves, because you've been awfully suspicious during this game and I want you to snap. If it were up to me I'd put myself, SIB, retep and Darth Vader on a proposal. SIB and retep because they've been on a successful mission, DV because he's probably not a traitor, considering that he's brand new to this game, and myself because I'm innocent, of course.

Can you think of a game of GTW where I have snapped? Hint: I'm not Mackilroy ;). Can you think of a game of GTW where I've behaved differently based on my role, like at all? You only think I'm suspicious because you apparently have a very short memory, or just a general mistrust of me based on nothing to do with this game.

You're using justification for SoItBegins and retep998 that applies just as equally to me.

You're using justification for darth_vader that is nonsensical in the face of a randomized role selection process.

You know, there is one thing that differentiates me from SoItBegins and retep998 right now. By SoItBegins separating me from the other two in his selection, it's quite possible the bad guys have determined I am not one of their cohorts. For example, let's say SoItBegins is a sleeper agent. In the first round, his two fellow sleeper agents would have been informed by Mackilroy that there's one sleeper agent in the first team proposal. SoItBegins comes along, and boots me out of the dream team. His other cohorts get notification again that there are now two sleeper agents in the proposal. This would indicate to a sleeper agent like JacaByte that either retep998 or SoItBegins is a sleeper agent, one of the two new guys is a sleeper agent, and I was not. Now that I've been eliminated as a possible cohort the sleeper agents want to discredit me, and make sure I stay off of any teams in the future. That way, in the last round when we require a perfect team selection, all my fellow innocents think I'm a bad guy, and take a chance on somebody who's actually a bad guy in my place.

So, JacaByte, know something about SoItBegins and retep998 that the rest of us don't?

Playing passively at the start as an innocent seems like a pretty solid strategy to me, particularly when the first subcommittee proposal contains mrxak immediately pulling his McCarthy thing.

Do we know if we are waiting for any votes still?

@mrxak, on 28 July 2012 - 02:11 AM, said in GTW 40:

Can you think of a game of GTW where I've behaved differently based on my role, like at all?

The last time you were we traitor you were much more aggressive than you are when you're innocent. Like the way you're acting right now.

@crow-t--robot, on 28 July 2012 - 09:15 AM, said in GTW 40:

Do we know if we are waiting for any votes still?

I'm waiting on one vote.

@jacabyte, on 28 July 2012 - 10:21 AM, said in GTW 40:

The last time you were we traitor you were much more aggressive than you are when you're innocent. Like the way you're acting right now.

I see you've answered the question you wanted to answer, and ignored the one you didn't want to answer.

Anyway, you've got a rather short memory.

In the last ten games, I've been accused of undue aggression while I've been innocent, in:
Game 30
Game 31
Game 35

In Games 32 and 33, I died in the first round from bad guys. No time to be accused of anything. I did not participate in Game 34. I hosted Games 36 and 39. Game 37 I was a traitor, you seem to think I was aggressive in it, so be it. In Game 38, I was certainly aggressive, though nobody had the time (or cared) to accuse me of it, since my aggression led to a swift victory for the good guys.

So, faced with the actual facts do you still want to say I'm more aggressive as a bad guy?

I'm looking forward to Game 41 when I get to point to this game as yet another case where I've acted the same in every game, when you inevitably accuse me again of aggression.

@mrxak, on 28 July 2012 - 02:37 PM, said in GTW 40:

I see you've answered the question you wanted to answer, and ignored the one you didn't want to answer.

I understood it as a rhetorical question. People aren't supposed to answer rhetorical questions.

Your McCarthyism is going to be the doom of us all.

Now I see you're ignoring the facts, and resorting to name-calling ;).

You know, I'd much rather be having a conversation about strategy in name selection. Why you're defending SoItBegin's poor choices by attacking me is certainly curious. You're not even on his list. So what, got a PM from Mack saying somebody else is?

I didn't call you any names, I simply said you're employing McCarthyism.

I no longer see any point in listening to you. I shall ignore you until the game ends. Good day.

If all these games have such drama, I'll phone Hollywood. They'd be interested in this as a reality show.

It's not really drama. JacaByte just suddenly decided that even though he agreed with me in the first round, and the first round was successful, he's now going to attack me over... I have no idea? He wanted to "make me snap", I guess, but apparently I broke him instead once I listed off actual facts :p.

What might actually make me snap is if the mystery 8th person doesn't freaking vote today.

If the last vote doesn't come in by noon PST today, I'm counting their vote as an abstain.

Mission #2 subcommittee by SoItBegins
SoItBegins
retep998
prophile
Crow T.Robot

Approve
SoItBegins -- 4:00
Crow T. Robot -- 6:58
retep998 -- 10:25

Reject
JacaByte -- 10:43
croc -- 11:45
mrxak -- 11:49
prophile -- 8:46

Abstain
darth_vader -- 14:00

Result:
Three approvals, four rejections, one abstain. The motion fails.

The committee proposal consisting of SoItBegins, retep998, prophile, Crow T.Robot has been rejected. retep998 is the new speaker, and may choose another four players to form the committee. After five committee rejections, the terrorists win.

Well then, considering mrxak and SoltBegins have a tiny bit of evidence going for them from the first round, even though they could just as well be traitors, I do believe the best way to determine whether they're innocent is by simply doing the same thing again. This leaves a single spot open for someone new.

Therefore I propose the following:
retep998
SoItBegins
mrxak
darth_vader

Just as predicted.

I reject this motion as well