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Eleusis

Eleusis is a game with a simple premise—only the dealer knows which cards are acceptable to play and which are not, and the players have to determine what the rule of play is! But getting there is the fun of the game; players only have the history of previous cards played to go off of, and must deduce the rule of play from that knowledge.

Robert Abbott invented the game in 1956, and was the subject of a column by Martin Gardner in Scientific American in June 1959. Abbott began revising the game in 1973, adding the role of the prophet, and Gardner wrote about the game again in Scientific American‘s October 1977 issue. After the latter column, Eleusis started to be added to the game books. The game’s uniquely deductive game play has been noted as being a practical application of the scientific method in everyday life, and scientific papers have been written analyzing the thought processes of Eleusis players for this reason. A variant of the game, Eleusis Express, was even created to help provide educators a hands-on tool to illustrate the scientific method to students.

“[Eleusis] should be of special interest to mathematicians and other scientists because of its striking analogy with scientific method and its exercise of precisely those psychological abilities in concept formation that seem to underlie the ‘hunches’ of creative thinkers.” —Martin Gardner, Scientific American, June 1959

Object of Eleusis

The object of Eleusis is different for the dealer than it is the players. The dealer’s goal is to create a rule of play that is difficult enough that the players cannot easily deduce it but easy enough that it is eventually solved. The players’ goal is to correctly deduce the rule of play.

Setup

Eleusis requires quite a few cards to be played right. Use two decks of Denexa 100% Plastic Playing Cards, shuffled together (not including jokers), to form the initial stock. You should also have a third and possibly fourth deck handy if necessary to replenish the stock.

Eleusis has quite a large layout, so a suitably large table will be necessary in order to play the game. If nothing else, you may be required to play on the floor (although this leaves the game vulnerable to roving toddlers and dogs if any are present).

Before dealing, the dealer comes up with a rule of play that will be followed throughout the hand and records it on a scrap of paper, keeping it concealed from the players. The rule must prescribe which cards are acceptable to play, determining this in terms of the previous cards played and cannot reference anything outside of the layout, such as the time or date, details about the players or the number of cards they hold, et cetera. Rules often, but not always, use something about the last card played as their basis, such as its color, suit, or number (if number is used, aces are normally treated as having a value of one, jacks equalling eleven, queens equalling twelve, and kings equalling thirteen). Some example rules are:

If the last card played was red, play a black card, and vice-versa.
Each card played must have a value of two less or two more than the last card played.
Two consecutive cards of the same color must be played, then three consecutive cards of the other color, and so on.
The cards must cycle through the suits in the order ♠♣♦♥.

Shuffle the deck and deal fourteen cards to each player, except for the dealer, who receives no cards and takes no active part in game play. Turn the top card of the deck face-up and place it at one edge of the play area; this card is the starter. The remainder of the deck becomes the stock.

Game play

The player on the dealer’s left plays first. They lay a card down, face-up, as a potential play. The dealer calls this card “Right” if it fits with the rule of play or “Wrong” if it does not. If the card is right, it is placed beside the starter, forming a horizontal line called the mainline. Otherwise, it is placed above or below the starter, forming a line of incorrect plays called a sideline, and the player who attempted the incorrect play is dealt two cards to add to their hand.

As players become more confident in their knowledge of the rule, they may set down multiple cards as their play, specifying the order they are to be played in. The dealer then declares this string to be “Right” or “Wrong” in its entirety. In the event of a wrong play, the dealer does not specify which or how many of the played cards caused the string to be incorrect. The cards are moved to the sideline as a unit, fanned together to show that they were played as a string and not as singleton plays, and the player is dealt twice the number of cards in the string as a penalty (e.g. for an incorrect five-card string, the player is dealt ten cards).

If a player believes they have no legal play, they may expose their hand and call “No play”. The dealer then examines their hand. If the player truly has no moves, the player’s hand is discarded to the bottom of the stock and they are dealt a new hand with four fewer cards than they had previously, unless the player only has four or fewer cards, in which case the hand ends immediately. If the dealer spots one or more cards that can be legally played, they move one of these cards to the mainline and receive a penalty of five cards from the stock.

The prophet

Once a player is certain they have discovered the rule of play, they may, after their turn but before the next player’s, declare themselves to be the prophet (or in some rules, the forecaster). There can only be one prophet at a time, and a player may not serve as prophet twice in one hand. There must also be two or more active players other than the prophet and the dealer in order to become the prophet. A marker of some kind (such as a chip, a coin, or a roulette dolly) is placed on the last card played whenever a player becomes a prophet. The prophet sets their hand aside (but does not discard it).

The prophet then takes over all functions as dealer, declaring the other players’ actions to be “Right” or “Wrong”, and the dealer merely calls out “Correct” so long as the prophet continues to accurately follow the rule of play. If the prophet makes an incorrect declaration, they are deposed as a “false prophet” and are dealt five penalty cards from the stock. They then pick up their hand, remove their marker from the mainline, and resume normal game play again. If the prophet was overthrown as a result of a player’s incorrect play, the player does not receive any penalty cards for that play (as an incentive to try to deliberately trip up the prophet).

Expelling players from the game

Beyond a certain point in the game, players who make an incorrect play (i.e. a card or string of cards declared “Wrong” or an incorrect “no play” declaration) are expelled from the game. If there is a prophet, this is when 30 or more cards have been played after the prophet’s marker on the layout. If not, then it occurs when there are 40 or more cards on the mainline. Note that it is possible for expulsion periods to stop and start again, as a new prophet essentially resets the clock for the start of the expulsion period, and overthrowing a prophet means that an expulsion period begins on the next turn if 40 or more cards have been played to the mainline.

There is one exception to expulsion, and that is when a player’s incorrect play overthrows the prophet. A player who successfully causes a prophet to be deposed is immune to both penalty cards and expulsion for their incorrect play.

When a player is expelled, they still retain their hand and receive their penalty cards, as normal. They simply do not take any part in active game play for the rest of the hand (which includes becoming the prophet).

Ending the hand

A hand of Eleusis ends when:

A player correctly declares “no play” while holding four or fewer cards.
A player depletes their hand.
All players (other than the prophet, if any) have been expelled.

At this point the hand is scored. Each of the players counts the number of cards in their hand, then scores the difference between the number of cards they hold and the number held by whoever had the most cards (who scores zero). For example, if a player holding thirteen cards had the most cards, then a player holding nine cards would score four points.

If there is a prophet, they score their hand as usual, but receive a bonus of one point for each correct card after their marker and two points for each incorrect card after their marker.

The dealer’s score is typically equal to whatever the highest hand score of all the players was. However, if there was a prophet, the number of cards between the starter and the prophet’s marker is counted and multiplied by two. If this value is less than the high score for the hand, this is the dealer’s score instead. (This is to provide a deterrent to making easy rules.)

Game play continues until all players have had a chance to deal. Whoever has the highest total score at this point is the winner.

Eleusis Express

Eleusis Express is a pared-down version of Eleusis that was developed by mathematics professor John Golden in 2006. It was intended as a teaching tool to illustrate the scientific method to elementary-school-aged children, although it makes for a quicker, simpler game. Eleusis Express is identical to base Eleusis except:

Players start with twelve cards rather than fourteen.
Only one card may be played at a time—no strings.
If a player correctly declares a no play, they are dealt a new hand with one card fewer than the number they had (if they were down to one card the hand ends). If they declared no play in error, the dealer plays a correct card from their hand to the mainline, and the player receives only two cards as a penalty.
There is no prophet and no expulsion.
If a player believes they know the rule of play, they may simply guess it out loud after any correct play. The dealer confirms if they are right or wrong (note that the exact wording on the sheet is, of course, not necessary, only an accurate and complete description of the rule). If they are right, the hand ends.

Scoring for Eleusis Express is as follows:

Each player scores twelve points minus one point for each of the cards in their hand.
A player who depleted their hand scores a three-point bonus (scoring fifteen in all).
A player who successfully guessed the rule scores a six-point bonus.
The dealer’s score is equal to whatever the highest hand score of all the players was.