# Delphi

Delphi is a simplified version of Eleusis for three to seven players. As in Eleusis, the central premise of the game is discovering a secret rule created by the dealer. Accomplishing this goal is done by looking over the line of previously-played cards and attempting to spot a pattern. The main difference between Delphi and Eleusis is that in Delphi, each card played to the table is one randomly drawn from the deck, rather than intentionally placed by the players. Players are rewarded for correctly declaring which cards correctly fit the pattern and which do not.

Delphi is the creation of the American scientist and mathematician Martin David Kruskal. Dr. Kruskal published the game in 1962 while a professor of astronomy at Princeton University. Noted for his playfulness, Dr. Kruskal also devised the “Kruskal count”, a magic trick that could even stump other magicians because it was based on deep mathematical principles, rather than the usual sleight of hand.

## Object of Delphi

The object of Delphi depends on whether you’re the dealer or just a player. For the players, the object is to figure out the dealer’s secret rule as quickly as possible. For the dealer, the object is to create a secret rule that’s neither too hard nor too easy to figure out (ideally, about half the players should be able to guess it).

## Setup

For a game of Delphi, you’ll need one standard 52-card deck of playing cards. Of course, we very much recommend using a deck of Denexa 100% Plastic Playing Cards. You also need pencil and paper (or something similar like a smartphone app) to keep score with, as well as some form of marker or token (like poker chips, beans or other counters) to keep track of the number of correct guesses a player has made on that hand. You should have around 25 tokens for each player (other than the dealer) in the game. If desired, you may also give a decision marker to each player, something that clearly indicates a yes or no response, such as a coin (heads being yes and tails being no) or simply an index card marked “YES” and “NO” on opposite sides.

Determine the first dealer, who is also referred to as the oracle. The oracle devises a secret rule and writes it down on a scrap of paper, keeping it concealed from the players. The rule dictates which cards will be considered “correct” throughout the play of the following hand. The rule must determine this based solely on the cards previously played, and not anything outside the game. (Further explanation and some example rules can be found in the Eleusis setup section.)

Give each player one token, keeping the rest as the oracle’s bank. Shuffle the deck and turn one card, face up, to serve as a starter. The rest of the deck becomes the stock.

## Game play

The oracle turns one card face up from the stock, placing the card where it can be easily seen by all of the players and announcing its rank and suit. The players then decide whether this is a “correct” play according to the dealer’s secret rule. Obviously, on the first turn of play, this is likely little more than a 50/50 guess, but as the game goes on players will become more confident in their knowledge of the rule and thus be able to decide more accurately.

Once players have reached a decision, they set their decision counter, if playing with one, to reflect this, keeping it concealed with their hand from the other players. If not playing with a decision counter, each player just takes a token or other small object in their hand, shuffles it from hand to hand under the table, and places their closed fist above the table. If they have something concealed in their hand, it indicates a “yes”, and if their hand is empty, it indicates a “no”.

Once all players have reached a decision on the card, on a signal from the oracle, they all reveal their decision. The oracle then declares whether the card was “correct”. If so, the card is placed to the right of the last card played, forming a continuous line of correct cards across the table. If the card is incorrect, it is placed below the last correct card played. The oracle then pays out one token to each player who guessed correctly and collects one token from those who did not. (If a player does not have a token to collect, no penalty is assessed.)

The next card is then drawn, and the process repeats until all 52 cards have been placed on the table.

### Scoring

After the hand ends, each player counts the number of tokens they have. Their hand score is the difference between their own token count and that of each player who collected fewer tokens, added together, minus the total count the difference between their count and that of each player who collected more tokens.

For example, consider a game where Player A collected 29 tokens, B collected 26, C collected 19, D collected 11, E collected 9, and F collected 6. Player C’s hand score would be the difference between their count of 19 and that of D, E, and F, minus the difference between their count and that of A and B. Thus, their score would be (8 + 10 + 13) – (10 + 7) = 31 – 17 = 14. Note that it is possible to get a negative hand score, as F’s score would be 0 – (23 + 20 + 13 + 5 + 3) = –64.

The oracle’s score for the hand is the total of each player’s difference between their count and that of each player who collected more tokens. (That is, everything that is subtracted when each player calculates their score.) In the example above, Player A’s total difference is 0, B’s is 3, C’s is 17, D’s is 25, E’s is 27, and D’s is 64, so the oracle would score 136 points.

All of the tokens are then returned to the bank, and the next player to the oracle’s left becomes the new oracle. Game play continues until each player has been the oracle once.