# Quantum Werewolf

This is the archive of the 2008 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.

## Introduction

Quantum Werewolf is a game invented by the creator of the puzzle Schrödinger's Wolves. It's not expected that puzzle solvers have any prior understanding of the game in order to solve the puzzle! The puzzle is to uncover enough of the rules of the game to work out the solution, by applying logic to the events revealed in the puzzle text.

For those interested in knowing how the game works, or even playing it themselves, the complete rules are given here.

## The Rough Idea

It's a basic game of Werewolf, but the roles aren't determined at the start. Instead, they're in a state of quantum uncertainty, and at any given time each player's character just has a certain probability of having each of the roles.

Each night, every character who could still be the seer gets a seer vision, and similarly multiple characters make a werewolf attack. The visions are only meaningful if that character turns out to be the seer, and the attacks are only fatal if they turn out to have been made by the dominant werewolf.

When a character is voted off, their death then causes the quantum wave function to collapse and determine their role precisely. As the game progresses this will make certain characters more and more likely to have each role until at the end each character has just one possible role.

The winners are those who finish the game (alive or dead) on the winning team of either good or evil. The game ends either when all the wolves are dead, or when the wolves have parity as well as it being completely determined who they are.

## The Rules

The game runs like a fairly normal Werewolf game. Each player takes on a character role. The roles are:

• One Seer.
• Some Wolves. There will be an alpha wolf, a beta wolf etc. The exact number of wolves, depends on the number of players, similar to normal werewolf.
• The rest of the roles are villagers.

## Voting

Each day, the players of all the characters who are still at least partly alive vote on who to burn. The character with the most votes is then killed, and their exact role is then randomly determined, in proportion to the chances of them having each role. An announcement is then made to all the players of whether the burned character was good or evil.

This may have flow on effects of determining other roles and causing other characters to die.

Although players of dead characters cannot vote, votes from quantum ghosts (characters whose fate is still undetermined when the votes are counted but later turn out to have been killed earlier) still count fully.

The usual variety of house rules can be used to break ties or allow multiple burnings.

## Wolves

Each night starting from night 1, the dominant werewolf makes a kill. The dominant werewolf is the alpha wolf until the alpha wolf dies, at which point the dominant wolf becomes the beta wolf, and so on. This will occur after the burning but before the seer's vision.

This means that each player who could be playing the dominant wolf needs to record a kill target. At each stage a charcter is given a percentage chance of being dead; this is the probability that they have been killed by a werewolf. If this reaches 100% then they will die. In this case their exact role will also be determined, which only means whether or not they were the seer, as they couldn't be 100% dead and still have any chance of being a werewolf themselves.

## Seer

Starting from night 0, the seer will receive one vision each night of a player of their choice as either good or evil. From night 1 onwards, this will occur after the werewolf killing.

This means that each player who could still be playing the seer must choose a target and will receive a vision. The vision is only accurate if they are really the seer, although it may still turn out to be correct by chance even if they are not.

The results of the vision are chosen randomly, in proportion to the probability of the target being good or evil, if the player having the vision really is the seer.

Players may also specifically elect not to receive a vision.

## Role Probabilities

Each morning, after the seer visions are returned, the state of the probability table is given for all to see. This will look something like:

Player 125%75%5%
Player 295%5%80%
Player 3  100%0%100%
Player 490%10%0%
Player 590%10%10%
Player 6100% 0%100%
Player 70%  100%  100%

Players will be told which player number they are (e.g. Bob is told he is "Player 4") at the start of the game, but do not know which numbers the other players are. This means the players know the chances of their own character being evil, and have information on how well determined the roles are each day, but don't who the other probabilities belong to (unless they figure it out somehow).

Players are not always told when specific roles they may have had are eliminated as possibilities, but if at any stage there is only one role a player can possibly have they will be informed of it.

## The Mechanics

The person running the game initially generates a table of every possible quantum game state (where "quantum game state" means an assignment of roles). A computer program can assist in generating and keeping track of game states.

As each action comes in, all game states which have become impossible as a result are eliminated. Actions can eliminate game states a number of ways:

• Each time a player receives a seer vision, every game state in which they are the seer and their target's role does not match their vision is eliminated.
• When a character dies for any reason, their exact role is fixed, and game states where they do not have that role are eliminated.
• When a character is voted off, any game state in which they would have been killed earlier is eliminated. In particular this means that as soon as someone that player X has attacked is voted off, player X can no longer have been the dominant werewolf on the night they made the attack.
• If a character attacks another character, any game state in which the attacker is the dominant wolf and the target is also a wolf is eliminated, as wolves cannot attack other wolves.

In some rare cases it's possible for the game to be over without it being determined who the winners are. For example, there could be two players left, and one of them is playing a wolf who has already killed the other player's character, but it could still be either player. When this happens, the wave function will be forced to randomly collapse and decide a winner.