Mafia Strategy when Cop Claims...

Axelrod · Post Post #5 (isolation #0) » Sat Mar 12, 2005 2:27 am

If it's night two, as per your example, I can't see the Doc protecting anyone other than a confirmed cop. What's the alternative? Protecting a random person who probably won't be targeted anyway and might even be mafia? The benefit to be gained from this is greatly out weighed by the benefit of protecting a cop and guaranteeing them another inspection. And as long as the Mafia don't identify you as the Doc, you will be able to keep protecting him.

The only time this changes is when another role is revealed that might also merit Doc protection, then you have to ue your best judgment about who to protect (and then still probably protect the cop.)

Axelrod · Post Post #7 (isolation #1) » Sat Mar 12, 2005 3:45 am

Seol wrote:
Axelrod wrote:If it's night two, as per your example, I can't see the Doc protecting anyone other than a confirmed cop. What's the alternative? Protecting a random person who probably won't be targeted anyway and might even be mafia? The benefit to be gained from this is greatly out weighed by the benefit of protecting a cop and guaranteeing them another inspection. And as long as the Mafia don't identify you as the Doc, you will be able to keep protecting him.
If the Mafia know the doc is protecting the cop, then they won't target the cop. If the cop isn't being targetted, there's no point protecting him - you might as well protect a random townie and hope for no deaths. There's a delicate balance, though.

Well, yes, if you knew the Mafia wasn't going to target the Cop it would be pointless to protect him. But exactly when do you ever know this? What I'm saying is that the benefit to be gained from protecting a random person is outweighed by the benefit of protecting your cop. Just in case the Mafia is thinking like you are thinking. Bluffs and double bluffs are fine, but you should have a better reason for risking it than protecting someone at random. At least the way I see it.

Axelrod · Post Post #10 (isolation #2) » Sat Mar 12, 2005 4:24 am

Seol wrote:
Axelrod wrote:Well, yes, if you knew the Mafia wasn't going to target the Cop it would be pointless to protect him. But exactly when do you ever know this? What I'm saying is that the benefit to be gained from protecting a random person is outweighed by the benefit of protecting your cop. Just in case the Mafia is thinking like you are thinking. Bluffs and double bluffs are fine, but you should have a better reason for risking it than protecting someone at random. At least the way I see it.
This is where the game theory comes in. Assuming the cop isn't
infinitely
more valuable than the other townies (and he's not), it's
occasionally
worth the risk of targetting someone else, and it can be calculated how frequently that should be. If you pick the right frequency, the occasional times you lose the cop will be outweighed by the number of times you end up with no deaths. I'm not going to try and produce the numbers, though.

That's an interesting point, but it still seems to me that if you concede that protecting the cop is usually the correct play, then for all intents and purposes it should always be the play.

I'll use a blackjack analogy. Basic strategy dictates you hit when you have a 16 and the dealer is showing a 7, 8, 9, or 10. You know, when you take the hit, that you will probably bust, but you also know that, over the long haul, by taking the hit, you will win more hands than you would by standing. Basic Strategy doesn't say "you will win 25% of the time when you hit, and 10% of the time when you stand, therefore you should hit more than you stand (but still stand sometimes)", instead it says you should always hit.

The only exception to that is when you're counting cards and know the odds are actually tilted the other way. It doesn't seem to make sense to say that, if protecting the cop is right 85% of the time and wrong 15%, you should protect the cop in 85% of the cases and a random person 15% of the time. Chances are, you will do worse than if you just protected the cop every time.

Axelrod · Post Post #16 (isolation #3) » Sat Mar 12, 2005 11:34 am

Now observe as I embarass myself with my poor math skills.

If we assume that there is some kind of "optimal" strategy, by which I mean there is an ideal % that the Doc should protect the Cop. How does this play out? If you take a % at random, say the 85% figure I threw out before. If you play so as to protect the Cop 85% of the time and a random person 15% of the time, don't you come out worse than just protecting the Cop everytime?

Take the 85% of the times that you do protect the Cop. If this is the correct play 85% of the time, then your result is 85% x 85% or 72.25%. You must add to this the fact that 15% of the 15% of times you protect a random person it will be the correct play. This = .0225%.

72.25% + .0225% = 75%

So by "gaming the system," if you will, you end up with the correct result 75% of the time. Whereas if you just protected the Cop everytime you would be right 85% of the time.

I think this works with most sets of numbers as long as you assume that protecting the Cop is usually the correct play. If you throw out that assumption, however, then I guess anything goes. This is maybe the point I was trying to make with my original post.