Knights and Knaves Cards

 

Raymond Smulyan (May 25, 1919 - February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher. He studied with Alonzo Church and was a friend of Martin Gardner.

Raymond Smulyan played a major role in popularizing Knights and Knaves logic puzzles. 

Raymond Smullyan

The idea behind Knights and Knaves Cards is that information from Knights is always true and information from Knaves is always false. There are thousands of puzzles and related discussions about statements made by Knights and Knaves.

 

I imagine card games where the Back of the card is identical to the Front, so other players can see what the other players have. These are Knight cards. They always tell the truth. But only about half of the cards are this way. The other half shows one image on the Back but the actual value of the card, on the Front, is another. These are Knave cards. They always lie.

 

The idea is to produce the decks and let players choose their favorite games, whatever games they choose.

 

The deal is made from a deck of 104 cards, 52 for Knights where the Front and Back match, and 52 where the Front is one thing and the Back is another. The number of cards dealt depends on the game played. We don't know how many of our cards are from the Knights' deck or how many cards are from Knaves' deck; they have been merged and shuffled together.

Here is an example of the Knight version of the four of Spades. The Back is what other players see and the Front side is viewed by the player holding the card.

 

 

The Knave Card example shows the Three of Hearts whose Backside falsely shows the Jack of Diamonds. The Jack of Diamonds is a lie. The Frontside shows the Three of Hearts, the actual value of the cards, with a small Jack of Diamonds image in the center, so that the player holding the hand can see what the other players see. Which side is which doesn't make any difference for Knight cards--both sides are identical. The Frontside of a Knave card is identified by the small image depicting the Back of the card. The Backs are identified as Backs because there is no insert. Remember, the Frontside is the one that the player holding the hand is seeing, the Three of Hearts in this case.

 

 

Preparation

 

For most games to be played with a fifty-two card deck the following preparation should be done.

  1. Remove the Jokers.
  2. Take the Knight deck and the Knave deck and shuffle them together. Be sure that all of the Knave cards are Back-side-up.
  3. Imagine a four by thirteen table in front of you. The four rows are for suites. The thirteen columns are for the card values, A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K.
  4. Go through the shuffled deck of 104 cards viewing the value of each card in turn. For Knave cards, look at the Front, the side with the small inserted card. The value of the Knave card is that of the large card that surrounds it.
  5. Put the card in the cell it belongs in, in the table, unless the cell is already occupied. If the cell is already occupied, put the card aside and continue with the next card.
  6. When all fifty-two positions of the table are full, assemble a deck and thoroughly shuffle it.
  7. Note that the cards that were set aside because the table position was already occupied are a second, complementary deck also suitable for play.

This deck can be used over and over again. The preparation is for a session not a single game.

 

Pictures

 

The following pictures capture the Back and Front of a card with the aid of a mirror. The Knight card, a 4 of Clubs is on the left. The Back and the Front are the same. On the right is a Knave card whose Back is a King of Diamonds, which is a lie. The true value of the card is the Ace of Diamonds. Note how a small King of Diamonds image is embedded in the Ace of Diamonds so the player holding the hand can see what other players see.

 

The following pictures show the two decks, Knights and Knaves, as packaged in a clear, plastic box.

 

 

Here is another view of the decks in the box.

 

 

 

Observations

 

A player may appear to have two of the same card; they may have the Knight version and the Knave version. Another player might see, for example, your king of spades and a knave version, that has a king of spades on the card back, but its face value is actually an ace of spades. A player's hand may show that they have a king of spades and another player may also appear to have a king of spades. 

 

 

 

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