Actually, no, choosing randomally is not the optimal stratagy in RPS. The optimal stratagy is to sucessfully outguess or out-read your opponent. If either you or your opponent chooses randomally, you win 1/2 the time; the only way to do better then a 50/50 win ratio is to outplay opponents who do not act randomally by not acting randomally yourself. Some people are able to do this, though; they have regular rock-paper-scissors tourniments, and some players do manage to consistantly do better then a 50% win ratio.mathcam wrote:Well, I think you have to be more specific. If you assume the rationality of all players (which is indeed the assumption for most of game theory), and assure that the roles in the game are made public before the game starts, then yes, I feel pretty confident that there's an optimal strategy for each player.
Actually, no. For example, optimal strategy (at least in the sense of game theory) for rock-paper-scissors is to choose randomly every time. Re-doing draws, you'll expect to win 1/2 of the time. And now note that even if you are playing against a complete dimwit who picks his nose and picks rock every time, you still only expect to win 1/2 of the time. Your optimal strategyWhen playing against an irrational enemy with an optimal strategy, you should expect to win more than if they were being 100% rational. Right?guaranteesyou the most you can possibly be guaranteed. And often your optimal strategylimitsyou to this as well.
Back to the origional question...there is such a thing as optimal stratagy in mafia, I think, at least in a fuzzy sense (that is, it is likely there are many situations in a mafia game where there are multiple options, probably a large number of different options, that offer about equal chances of winning, and the margins of error involved are often fairly large).
However, what the optimal stratagy is depends very strongly on how well you know and can read the other players in the game, and predict how they will act in different situations.
Also, since mafia is kind of a team sport, in a way, I think that your optimal townie stratagy varies based on what the other pro-town people are doing; in basketball, for example, shooting 3 point shots can be a valid stratagy, but you don't really want a team that does nothing but shoot 3 point shots. So, in the same way, I think that there's a number of different "roles" that a townie can assume (agressive/analytical/defensive; emotional/logical/reasonable; loud/quiet; leader/follower, debator/table pounder/compromiser, ect), and that which role you should assume at any point of a game might depend on which roles the other people in the game are taking; a town where everyone is using the exact same method of finding scum isn't as likely to find all the scum, in my opinion, as a town where people are using more diverse stratagies.
Similarly, the optimal town stratagy and the optimal scum stratagy are often very close together; there are usually subtle differences, but generally it's within the margin of "fuzzyness" I mentioned earlier, ideally to the point where an outside observer can't easily tell the difference between what you are doing as scum and what you would be doing as town; a lot of mafia is a mental struggle between scum trying to slightly fudge the margins there a little and town trying to spot the very subtle difference between the two optimal playstyles. There are exceptions, though, points of a game where optimal town stratagy and optimal scum stratagy diverge widely (for example, 5 hours before deadline where there's one bandwagon on a claimed cop who really is a cop and one on your scumbuddy), and those are excellent points to go back and look at later when scumhunting.
Of course, in reality, the differences between town and scum will tend to be larger then they would be in optimal play, just because most people have only a limited understanding of exactally how they would play a situation as town, and because of different psycological tells and slips people tend to make, especally under pressure.