Eleusis

a game of inductive reasoning for 4-8 Players

this version of the rules created by Dave Howell

Materials

• Three standard decks of playing cards, shuffled together
• God and Prophet tokens in two colors, about five of each (chess pawns, pennies and nickels, etc.)
• One Prophet marker (chess bishop, quarter, etc.)
• Paper and pencil

Objective

To figure out the Rule governing the ordering of the Universe, which consists of a linear sequence of cards.

God (the Dealer)

One player at a time plays God. God's first task is to devise a secret card sequence rule ("defining the order of the Universe"), which God then writes down and conceals. For example, "each card played must differ in color from the preceeding card" (This would result in an alternating pattern of red and black cards, and a low score for God; God's score benefits from choosing a rule which is neither too hard or too easy.)

Each player is God once during a game, the role passing to the left between hands.

The Play

God starts play by dealing 14 cards to the other players. God does not get a hand and plays the remaining deck. God takes cards from the top of the deck until he has a legal play, and places the card(s) upon the playing surface, which ideally will be large and flat. Normally, a single card is sufficient, unless the rule depends on more than one starter card. Any illegal cards drawn are returned to the bottom of the deck without revealing them to the players.

Face cards values are Jack = 11, Queen = 12, King = 13; Aces are one.

To determine which player starts, God starts counting with the player to the immediate left and continues around the circle until reaching the count on the starter card. If there are multiple starter cards, the last one played is used.

A play consists of placing one or more cards upon the playing surface in a line from the last legally played card. God will then indicate whether the card or cards are in accord with their rule of the Universe.

If correctly played, the cards become part of the Main Sequence, and the play passes to the next player.

If incorrect, the card or cards are placed in a vertical column perpendicular to the last correctly played card in the main line, forming a side line.

Thus consecutive correct plays constitute the main line, and consecutive incorrect plays constitute the side lines. A God token is placed upon every tenth card played.

For each card incorrectly played, God gives the player a 2 card penalty. Since in the scoring it is advantageous to get rid of your cards first, playing strings of cards is advantageous, but only if you are quite certain of the "rule". Strings are initially played by displaying them in a slightly overlapping spread. If one card in a string is incorrect, the entire string is invalidated and God does not indicate what in particular is wrong. The string is placed on the sideline overlapping so other players can see they were played as a string.

If a player thinks they have no cards which may be legally played, they may declare "No Play". The hand is placed upon the table and examined by God. All other players get to look as well. If the player is correct and has 4 or fewer cards, the cards are returned to the deck, and since this player has no cards left, the round ends. If the player is correct and has 5 or more cards, the hand is returned to the deck and God deals the player a new hand less 4 cards, and the play continues. So a valid No Play hand of 8 cards results in a new hand of 3. If God declares that there is a play (i.e., the player is wrong), God selects one correct card and places it upon the main sequence. The player receives a 5 card penalty and play continues. Note: If you do not know the rule, it is much better to play a single card at random than declaring "No Play".

After 30 cards have been played (in both the main sequence and sidelines combined), if there is no Prophet (see below), players are expelled from the round when they make an incorrect play and receive their penalty cards. The round ends when a player plays their last card, or the last player is expelled.

See the Cause and Effect Table at end of these rules for complete grid of possible outcomes.

The Prophet

When a player decides they know and understand the Rule of the Universe, they can greatly increase their score by declaring themselves a Prophet and proving their understanding to all. The Prophet stops playing their hand and immediately takes over the role of God judging the correct order of cards played by the remaining players. A player may declare themselves a Prophet only if

1. the player has just played (correctly or incorrectly), and the next player has not played;
2. there is no other Prophet;
3. at least 2 other players in addition to God and the Prophet remain in the round;
4. they have not been a Prophet before in this round.

If a Prophet is declared, the main sequence is marked with the Prophet marker, and every 10 cards played subsequently with a Prophet token. Expulsions are delayed until after 20 cards have been played following the Prophet's marker. Thus if on the 15th card a Prophet is declared, no expulsions take place until after the 35th card is played. If expulsions have begun when a Prophet is declared, they are suspended for 20 more cards, but previously expelled players remain out.

Following declaration, play continues with the Prophet deciding which cards are correct and incorrect. If the Prophet is successful the play continues until a player is out of cards or all other players are expelled. However, God verifies the Prophet's every decision, and if judged incorrect by God, the Prophet is instantly cast down as a False Prophet, and God resumes their original role. The False Prophet gets 5 penalty cards and resumes play of their hand in correct turn. The Prophet's marker and tokens are removed from the cards, and the God tokens are brought up to date. If more than 30 cards have been played, with their next wrong play, the player is expelled.

After a Prophet is cast down, any remaining player satisfying the necessary conditions may declare themselves a Prophet. The Prophet marker is placed on the last legally played card, and expulsions are suspended for another 20 cards.

The play that results in the downfall of a Prophet is completed by God. If correct cards were ruled incorrect by the Prophet, they are moved to the main sequence, there is no penalty, and play resumes. If incorrect cards were ruled correct by the Prophet, they are moved to the sideline, but the player is not penalized because their play resulted in the discovery of a False Prophet. Thus players are encouraged to make plays that may potentially cast down the Prophet.

If a player declares No Play, and the Prophet correctly agrees, play continues as described above. But if the Prophet says correct, and God disagrees, the Prophet is cast down, God takes over and handles everything as above, except the player receives no penalty. If the Prophet says No Play is incorrect (thinking there is a legal play), and God disagrees (there isn't a legal play, so the player was correct), the Prophet is cast down and God deals the player the appropriate number of new cards. If the Prophet declares the No Play incorrect, and God agrees, the Prophet must now select a correct card and play it. If the Prophet does this correctly, the player receives their penalty cards and play continues. If the Prophet makes a mistake and selects an incorrect card to play, they are cast down, the card goes back into the player's hand, God selects a correct card, and play continues. The player is not penalized because their play resulted in the downfall of the Prophet.

Scoring

1. At the end of a round, the largest hand remaining including the Prophet is the high count. Each player receives a score which is the number of cards in their hand subtracted from the high count. So if the largest hand is 11, and you hold 8, your score is 3. If one player has played all their cards, the score is the high count plus a bonus of 4. In the example above they would get 11 (11 - 0) + 4 = 15.
2. If there is a successful Prophet, they score a bonus also, which is calculated at 1 point for every main sequence card that follows the Prophet marker until the end of the game, and 2 points for every sideline card played after the Prophet marker (1 pt for every correct and 2 pts for every incorrect card played while they were Prophet).
3. God's score equals the highest score of any player, unless there was a Prophet. If there is a Prophet, count the cards (right and wrong) played up to and including the card with the Prophet marker and double this number. If this number is smaller than the highest score (including the Prophet), God's score is the smaller number. This is designed to place a premium on being a Prophet, and helps optimize God's score when the rule is neither too hard or too easy.
4. If the game ends before everyone gets to be God, the winner is determined by the total of all rounds, and every player who has not been God get 10 more pts in compensation.

Scoring Strategies

The high Player score is based on the difference between the size of the biggest and smallest hands. A Rule which one or two people quickly discover but remains unknown to the other players results in higher Player scores. If there is no (successful) Prophet, this is also God's score.

If there is a Prophet, then God either gets the high Player score or one point for each card on the table before the Prophet appeared, whichever is lower. If the Prophet appeared early, their hand when they stopped playing was probably relatively large, and might be the 'biggest hand' used to calculate the high Player score.

If the Prophet does have the biggest hand, then they'll get zero points for their hand. But they get to double the value of incorrect cards played during their reign. A Prophet scores big if they're the only one to discover the Rule for an extended period of time.

Example of Play

The round starts with the 3H. The next player's guess is the 9S, which is correct. Several rules might give this result, for example, "if the number is higher, change color or suit, and if lower, keep it the same." You test it by selecting the JD (an increase, therefore change color or suit). God says this is incorrect. The next player decides the rule says to simply alternate colors, so they select the 5D This is also ruled incorrect.

The next player decides the rule is play a pattern of odd, odd, even, even, and so on without regard for color or suit. So they select the 4C, which is correct. Their hypothesis is not; the next player selects the JD. After several more plays, the mainline and sideline sequences look like the card layout that follows. (* denotes a God token.)

There is an incorrect four card side line sequence under the 7H, but remember, only one wrong card makes the entire string wrong. Consider the pattern carefully and try and figure out the Rule before you read on. Pick a card (any card) to play.

If told any black card would be correct, and any red card incorrect can you explain the Rule? Hint: it's one of the rules listed below.

The Rule

The rule must concern intrinsic features of the cards themselves. Circumstances beyond the cards, e.g., the time, the gender of the player, which hand of God is touching their nose, are not allowed. God may give hints if it seems necessary ("Suits are irrelevant in this Universe", or "The rule depends on the 2 previously played cards"). God, of course, will never lie.*

Example Rules

1. Each card should match the previously played card in either suit or number. (So after play of QS, any Q or any S would be legal. Play of another Q changes the suit, and play of another S changes the number, and so on.)
2. On black cards, play a card of equal or higher value; on a red card play a card of equal or lower value.
3. Play a consecutive sequence of three cards, increasing or decreasing in value by 1, then play a face card. Any card may start the next sequence after a face card is played.
4. Cards are played consecutively upward or downward by 1, except skipping all the prime numbers (3,5,7,11,13). When 1 or 12 is reached the pattern reverses with the next card up or down. This Universe may start on any card except a prime number.
5. If the last legally played card is odd, play a black card; if the card is even, play a red card. (This rule was used in the example above.)
6. Play a progressive pattern of alternating red and black cards, such that first one black and one red card alternate, then two black and 2 red, then 3 black and 3 red, then repeat the pattern.
7. Play a sequence of suits from clubs to spades and back repeating the suit with clubs and spades, thusly, C, D, H, S, S, H, D, C, C, etc.
8. Play a sequence of cards by 2's either up or down. At 2 the correct play is either 4 or 13, at 12 the correct play is either 10 or 1; at 13 the correct play is either 2 or 11, and at 1 the correct play is either 12 or 3.
9. Each card played must be lower in value than the previous card, unless the card is 3 or less (3, 2, or 1), then the next card is that card's value plus 10 (3+10=13, 2+10=12, 1+10=11).
10. The sum of the card played plus the last card played must total a number that can be divided by 3 evenly. Thus totals of 3, 6, 9, 12, 15, 18, 21, & 24 are allowed. (For example, if the first card turned is an 8, correct cards are 1, 4, 7, 10, 13). The starting card may be anything but a 3, 6, 9, or 12, and that means these 4 values will never be played.

Bibliography

Abbott, Robert. 1963. Abbott's New Card Games. Stein &;Day, New York.

Gardiner, Martin. 197?. Mathematical Games. Scientific American

Gardiner, Martin. 1961. The 2nd Scientific American Book of Mathematical Puzzles. Simon &;Schuster, N.Y.

Kruskal, Martin D. 1962. Delphi: A game of Inductive Reasoning.

Credits

This version of the rules for Elusis is based on a more verbose version prepared by Joseph E. Armstrong, a professor of Botany at Illinois State University. He got it from Scientific American's "Mathematical Games" column.

"The teaching materials placed on BIOLAB BBS may be freely copied, modified, and disseminated for all non-commercial educational activities provided that appropriate credit is given to the author [Joseph Armstrong], this source [BIOLAB, A Repository for Innovative, Investigative Laboratory Exercises in Biology], and its NSF support [The National Science Foundation]."

"God does not lie" is a redundant rule. It's already covered by the same rule that implicitly says that a player may not introduce new cards into the game, "palm" or conceal cards, or alter the scorepad. It's called "cheating." As a professional game designer and tester, I have been astonished at how often clever but inexperienced game players will assume that lying isn't cheating. When a game, any game, has a rule about revealing concealed information, it means just what it says. Misrepresenting hidden information is cheating unless the game explicitly allows it.

—Dave Howell

The Master Table of Cause and Effect

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