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Prisoner's Gambit: Difference between revisions

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Alluding to the famous game theory situation known as the [http://en.wikipedia.org/wiki/Prisoner%27s_Dilemma Prisoner's dilemma], in a [[Mafia game]] this is typically an [[Endgame]] scenario where a single powerless [[Townie]] is left with a [[Serial Killer]] and a single [[Mafia]]; each player's normal play in this case will end up disastrous. For example:
The '''Prisoner's Gambit''' is a scum gambit that tends to crop up in [[Dilemma]] scenarios. Aptly named after the Prisoner's Dilemma from game theory, it is perhaps best explained with an example.
* If the [[ProTown]] player helps [[Lynch]] one of the [[Scum]], then the other one will kill them that [[Night]]. Therefore their only real option is to vote for [[No Lynch]] and wait to see what happens at night.
* If both [[Scum]] vote to lynch the [[Townie]], then they are each left with only one [[Night Choice]], killing each other and ending in a [[Draw]]. Therefore, they should either lynch the other [[Scum]], or go for [[No Lynch]].
* Assuming rational play, then, all three players have made it to [[Night]]; but now each [[Scum]] has a choice: kill the [[Townie]], or eliminate their rival?
** If one of them kills the [[Townie]], and the other targets them for death, then they hand victory to their opponent.
** However, if they ''both'' kill the [[Townie]], then the two Scum survive until the next [[Day]], and depending on the [[Game Moderator]], they may both win, or be faced with killing each other anyway.
** Finally, if they each kill the other [[Scum]], then they hand victory directly to the powerless [[Townie]].


The entire situation is predicated on trust and self-interest; thus far, no one has found a foolproof way to assure their own victory when this situation arises.
The game state has three players alive - one [[Townie]], one [[Mafioso]], and one [[Serial Killer]].  The Townie has no incentive to lynch anyone, and votes No Lynch.  The Mafioso knows that they have to kill the Serial Killer this Night, and vice versa.
 
At this point, one or both of the scum may gambit by offering to shoot the [[Townie]].  If both scum shoot the [[Townie]], then they may draw - not as good as a win, but better than a loss.  On the other hand, if they both shoot each other, the Townie will win (often unjustifiably given the Town's play if the game got to this point).  What is often left unsaid is that if, say, the Mafioso shoots the Townie and the SK shoots the Mafioso, the SK wins outright.
 
It is mathematically best to always shoot the other scum.  But then again, the other scum knows that too, and they're supposed to be aiming at you, so it's probably better to persuade them to shoot the Townie... regardless of what you choose to do in the end.


[[Category:Gambits]]
[[Category:Gambits]]

Revision as of 04:40, 22 August 2011

The Prisoner's Gambit is a scum gambit that tends to crop up in Dilemma scenarios. Aptly named after the Prisoner's Dilemma from game theory, it is perhaps best explained with an example.

The game state has three players alive - one Townie, one Mafioso, and one Serial Killer. The Townie has no incentive to lynch anyone, and votes No Lynch. The Mafioso knows that they have to kill the Serial Killer this Night, and vice versa.

At this point, one or both of the scum may gambit by offering to shoot the Townie. If both scum shoot the Townie, then they may draw - not as good as a win, but better than a loss. On the other hand, if they both shoot each other, the Townie will win (often unjustifiably given the Town's play if the game got to this point). What is often left unsaid is that if, say, the Mafioso shoots the Townie and the SK shoots the Mafioso, the SK wins outright.

It is mathematically best to always shoot the other scum. But then again, the other scum knows that too, and they're supposed to be aiming at you, so it's probably better to persuade them to shoot the Townie... regardless of what you choose to do in the end.

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