Philosopher Cats

Introduction

This is a party game, based on an old logic puzzle that goes something like this:

A logician walks into a room with 3 philsophers in it, and says "At least one of you has a smudge on your forehead". After a couple moments, all 3 philosophers wipe their foreheads at the exact same time. How did they know?

If only 1 philosopher had had a smudge, that philsopher would have known right away it was him by looking at the other two clean foreheads. Since nobody wipes off their smudge after a few seconds, they know at least 2 people have smudges. But then, both of those philosophers would be able to know they had smudges by looking and seeing that only 1 of the others has a smudge. So after a few more seconds, all of them know they have a smudge.

If the philosophers all reason at the exact same speed, they would all wipe the smudges off at the same time. The party game is to see how well this works with real people, with cards on their foreheads.

When my family plays this game, we use a deck of cards with cats on it. Also the people stare at each other's faces like cats. Hence the game is called "Philosopher Cats".

Players

5-8(ish) players.

Note: the game is harder the more people play, so 5 might be too easy for expert players, while 8 might be too much for new players. 6-7 seems to be a sweet spot, but it may depend on your group.

Components

* One deck of playing cards, ideally with cats on them
* a large supply of small red and black tokens of some sort
* another color of token to represent bonus points

Each token is worth 1 victory point at the end of the game.

Setup

Place the red and black tokens in two separate piles in the middle of the table, where each person can easily reach them. Choose a player to be the first Dealer. Each Dealer's turn consists of the following four phases:

1) Dealing
2) The Announcement
3) Deduction Phase
4) Scoring Phase

Dealing

The Dealer shuffles the cards and deals one face-down in front of each of the other players. Each player then places that card upon their forehead, in such a way that each player can see the cards on the other people, but not their own card. (If anyone accidentally sees their own card while picking it up, deal them a new one.) The Dealer does not get a card; their role is to make the announcement, and keep track of bonus points.

The most important thing about your card is whether it is red or black. The goal of the game is to correctly guess which it is, based on the actions of the other players.

(Of course, players should not explicitly tell the other players what color they have. The only exception is an Annoucement given by the Dealer.)

The Announcement

(Before making the announcement, the Dealer should begin by checking to see if any players are potentially eligible for the dominant cat bonus, described later. If so, the Dealer should make a mental note of this fact without saying anything to the players, because they may be required to adjudicate later which player guessed first.)

Once everyone has gotten a chance to see everyone else's cards, the Dealer, who can see everyone's cards, makes one of the following two announcements:

* "At least one of you cats is red!",
OR
* "At least one of you cats is black!"

The announcement must be true, but most of the time there will be players of both colors, so the Dealer will be able to freely select which of the two possible announcements they wish to make.

Deducing Your Color

After the Annoucement is made, the Deduction Phase begins immediately. At any time during this phase, each player (besides the Dealer) may guess that they are "red" or "black" by selecting a token of that color from the center of the table, and placing it in front of them. Once you have made your selection, you are not allowed to change your mind.

The players may take as long as they need to make up their minds. However, the players who make their selection faster are more likely to get bonus points. Thus, once you deduce which color you are, it is in your interests to guess that color immediately.

Scoring Phase

As soon as all players (besides the Dealer) have made their selection, the deduction phase ends and the Scoring Phase begins. Each player may now remove the card from their forehead, and examine it to see if they guessed correctly:

1) If the player was incorrect, they forfeit their token to the Dealer's score pile (who may therefore get several tokens in a single turn, if multiple people made errors).

2) If a player was correct, they keep their token, adding it to their own score pile, and may also be eligible for bonus points.

Dominant Cat Bonus

When cats compete for food and love, it is good to be the dominant one! Each player will recieve 1 additional bonus point for every cat that they dominate. Each cat in the deck can potentially dominate four other cats in the deck, namely:

* the cats with the same number in another suit (for example if there is a 7 and a 7♠, either cat might dominate over the other), OR

* the cat 1 number down in the same suit. (So an 5; could dominate a 4, or a J♣ could dominate a 10♣, but not vice versa. An Ace counts as both high (dominating Kings) and low (dominated by a 2).

The bonus is received only if you guess before the player with the card you can dominate. Thus to summarize, you can obtain a bonus point only if all 3 of these conditions are met:

(a) a player has a card that you can dominate, AND
(b) you guess before that player, AND
(c) you guess correctly.

(In order to collect the bonus, it does not matter whether the other player guessed correctly, only the timing of their guess is important.)

It is possible to gain the dominant cat bonus multiple times in a term, so long as there are multiple players with appropriate cards. For example, suppose there are three players with the same number card, e.g. Q, Q♣, and Q. Then among these 3 players, whoever guesses first will get 3 points (1 + 2 bonus) if they guess correctly, whoever guesses second will get 2 points (1 + 1) if they guess correctly, and whoever guesses last can get at most 1 point. Thus players are encouraged to guess as early as they can.

If the players guess incorrectly, their bonus points are forfeited (they do not go to the Dealer).

It is the Dealer's responsibility to determine which players guessed first, whenever it is relevant to the assigment of bonus points.

Continuing the Game

After the Dealer's turn is over, the deal passes to the player on their left. After everyone has dealt twice, the game is over, and the player with the most points wins.

If desired, the game may be played for a longer number of rounds, but to make it fair, everyone should have an equal number of chances to deal.

If Your Deck Contains Jokers

If your deck happens to have jokers in it, leave them in. The jokers count as whichever color is not called by the Dealer, during the Announcement Phase.

Strategy Hints

Meditate on the riddle in the Introduction. If everyone plays consistently, in principle it is possible for everyone to correctly deduce their color every single time! In practice, people often get it wrong but are still right more often than chance would predict.

The main information used to deduce your color correctly, is how long it takes other people to make their guess. The length of time before anyone makes the first guess is particularly important. In general, the more people there are with the color that was called, the longer it should take for anyone to make the first guess. For example, if black was the color called, the longer it takes for anyone to make their guess, the more likely you are to be black. But, the more poeple you see who have black, the longer you have to wait before you can be sure.

Normally, the first person to guess should guess the same color that the dealer called. The way you learn you are the opposite color, is if the other players guess they are the color called more quickly than you expected.

Different players play the game differently, and therefore their decisions may not be equally meaningful. A random guess by a low-skill player does not communicate the same information as a careful deduction by a highly-skilled player. If a player makes a mistake, try to figure out why they did so!

It is sometimes possible to gain information based on how frequently the other players are staring at you.

If you are the Dealer, you want your Announcement to confuse the other players as much as possible. If only 1 person has a particular color, it is usually rather unwise to call that color, since that can enable everyone to figure out their color almost immediately. In general, it is often better to call the color you see the most of. However, if the Dealer follows this strategy too consistently, shrewd players may be able to take that into account.

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