Playing Eleusis Nina Gierasimczuk & Jakub Szymanik (slides by - - PowerPoint PPT Presentation

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Playing Eleusis Nina Gierasimczuk & Jakub Szymanik (slides by - - PowerPoint PPT Presentation

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Playing Eleusis Nina Gierasimczuk & Jakub Szymanik (slides by Lena Kurzen) August 17th, 2012 ESSLLI Student Session Sunday, August 26, 12 ELEUSIS Inductive inference game for four and more players, invented by Robert Abbott in 1956.

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SLIDE 1

Playing Eleusis

Nina Gierasimczuk & Jakub Szymanik

(slides by Lena Kurzen)

August 17th, 2012 ESSLLI Student Session

Sunday, August 26, 12

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SLIDE 2

ELEUSIS

  • Inductive inference game for four and more players, invented

by Robert Abbott in 1956.

  • M. Gardner. On playing New Eleusis, the game that simulates the search for truth. Scientific

American, 237:18–25, 1977.

  • J. Golden. Eleusis Express. http://www.logicmazes.com/games/eleusis/express.html.

Sunday, August 26, 12

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SLIDE 3

ELEUSIS: A CARD GAME

1 2 3 4 5 6 7 8 9 10 11 12 13 C l u b s Diamonds Hearts Spades

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SLIDE 4

ELEUSIS: THE RULES 1

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SLIDE 5

ELEUSIS: THE RULES 1

  • Player 1 gets the role of “God” or “Nature” and has to come

up with a secret rule about which sequences of cards are accepted.

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SLIDE 6

ELEUSIS: THE RULES 1

  • Player 1 gets the role of “God” or “Nature” and has to come

up with a secret rule about which sequences of cards are accepted.

  • Rules about the rule: It can only take into account previously

accepted cards (i.e. “Every black card has to be followed by a card with a face.” is OK, but “accept all and only the cards played by male players” isn’t).

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SLIDE 7

ELEUSIS: THE RULES 1

  • Player 1 gets the role of “God” or “Nature” and has to come

up with a secret rule about which sequences of cards are accepted.

  • Rules about the rule: It can only take into account previously

accepted cards (i.e. “Every black card has to be followed by a card with a face.” is OK, but “accept all and only the cards played by male players” isn’t).

  • The other players each get 14 cards and take turns in playing a

card in the sequence and Player 1 says whether it is accepted/ rejected.

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SLIDE 8

ELEUSIS: THE RULES 2

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SLIDE 9

ELEUSIS: THE RULES 2

  • If a card is rejected, it is placed below the position at which it

was played and the player has to draw two cards from the deck.

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SLIDE 10

ELEUSIS: THE RULES 2

  • If a card is rejected, it is placed below the position at which it

was played and the player has to draw two cards from the deck.

  • If a player thinks any of his cards would be rejected, he can

declare “no play”, and show his cards to everyone. If he was right, he gets a new hand of cards, 4 cards less than before. If he was wrong, Player 1 plays a correct card from his hand; and the player gets 5 additional cards.

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SLIDE 11

ELEUSIS: THE RULES 2

  • If a card is rejected, it is placed below the position at which it

was played and the player has to draw two cards from the deck.

  • If a player thinks any of his cards would be rejected, he can

declare “no play”, and show his cards to everyone. If he was right, he gets a new hand of cards, 4 cards less than before. If he was wrong, Player 1 plays a correct card from his hand; and the player gets 5 additional cards.

  • If a player thinks he knows the rule, he can declare himself a

Prophet, and he will take the role of Player 1.

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SLIDE 12

ELEUSIS: THE RULES 3

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SLIDE 13

ELEUSIS: THE RULES 3

  • If there is a prophet, Player 1 has to approve/disprove what

the prophet does in each round. If the prophet makes a mistake he gets five cards as penalty, and returns back to normal play with his former hand of cards.

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SLIDE 14

ELEUSIS: THE RULES 3

  • If there is a prophet, Player 1 has to approve/disprove what

the prophet does in each round. If the prophet makes a mistake he gets five cards as penalty, and returns back to normal play with his former hand of cards.

  • If a prophet correctly predicts the acceptance/rejection of 40

cards, a sudden death period is entered in which players are

  • ut of the game as soon as they play a card that is rejected.

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SLIDE 15

ELEUSIS: THE RULES 3

  • If there is a prophet, Player 1 has to approve/disprove what

the prophet does in each round. If the prophet makes a mistake he gets five cards as penalty, and returns back to normal play with his former hand of cards.

  • If a prophet correctly predicts the acceptance/rejection of 40

cards, a sudden death period is entered in which players are

  • ut of the game as soon as they play a card that is rejected.
  • The game ends if all non-prophet players got rid of all their

cards or ‘died’ during the sudden death period.

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SLIDE 16

ELEUSIS: THE RULES 4

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SLIDE 17

ELEUSIS: THE RULES 4

Scoring:

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SLIDE 18

ELEUSIS: THE RULES 4

Scoring:

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SLIDE 19

ELEUSIS: THE RULES 4

Scoring:

  • 1. Everyone except Player 1 gets as many points as the largest

number of cards held by any player minus the number of cards in his/her hand.

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SLIDE 20

ELEUSIS: THE RULES 4

Scoring:

  • 1. Everyone except Player 1 gets as many points as the largest

number of cards held by any player minus the number of cards in his/her hand.

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SLIDE 21

ELEUSIS: THE RULES 4

Scoring:

  • 1. Everyone except Player 1 gets as many points as the largest

number of cards held by any player minus the number of cards in his/her hand.

  • 2. Anyone (except Player 1) with no cards at all gets a 4 point

bonus.

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SLIDE 22

ELEUSIS: THE RULES 4

Scoring:

  • 1. Everyone except Player 1 gets as many points as the largest

number of cards held by any player minus the number of cards in his/her hand.

  • 2. Anyone (except Player 1) with no cards at all gets a 4 point

bonus.

Sunday, August 26, 12

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SLIDE 23

ELEUSIS: THE RULES 4

Scoring:

  • 1. Everyone except Player 1 gets as many points as the largest

number of cards held by any player minus the number of cards in his/her hand.

  • 2. Anyone (except Player 1) with no cards at all gets a 4 point

bonus.

  • 3. A prophet who survives until the end gets 1 point for each card

he correctly accepted and 2 points for each correctly rejected card.

Sunday, August 26, 12

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SLIDE 24

ELEUSIS: THE RULES 4

Scoring:

  • 1. Everyone except Player 1 gets as many points as the largest

number of cards held by any player minus the number of cards in his/her hand.

  • 2. Anyone (except Player 1) with no cards at all gets a 4 point

bonus.

  • 3. A prophet who survives until the end gets 1 point for each card

he correctly accepted and 2 points for each correctly rejected card. Player 1's score is the minimum of (a) the highest score of the

  • ther players and (b) twice the number of cards played before the

successful prophet started being a prophet.

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EXAMPLE

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SLIDE 26

EXAMPLE

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SLIDE 27

EXAMPLE

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SLIDE 28

EXAMPLE

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SLIDE 29

EXAMPLE

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SLIDE 30

EXAMPLE

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SLIDE 31

EXAMPLE OK

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SLIDE 32

EXAMPLE

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SLIDE 33

EXAMPLE

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SLIDE 34

EXAMPLE

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SLIDE 35

EXAMPLE

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SLIDE 36

EXAMPLE

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SLIDE 37

EXAMPLE

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SLIDE 38

EXAMPLE

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SLIDE 39

EXAMPLE OK

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SLIDE 40

EXAMPLE

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SLIDE 41

EXAMPLE OK

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SLIDE 42

EXAMPLE

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SLIDE 43

EXAMPLE OK

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SLIDE 44

EXAMPLE OK

b l a c k r e d b l a c k r e d e t c .

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SLIDE 45

EXAMPLE OK

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SLIDE 46

EXAMPLE OK

the value of a card has to be either lower than that of the previous one, or larger with a difference of at least 5 and at most 10

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SLIDE 47

AN INTERESTING GAME!!

  • offers various levels of difficulty
  • simulation of scientific inquiry
  • illustrates active learning frameworks
  • M. J. Berry. APL and the search for truth: A set of functions to play New Eleusis. In APL ’81:

Proceedings of the international conference on APL, pages 47–53, New York, NY, USA, 1981. ACM.

  • T. G. Diettrich and R. S. Michalski. Learning to predict sequences. In Machine Learning: An

Artificial Intelligence Approach, volume II. Morgan Kaufmann, 1989.

  • R. S. Michalski, H. Ko, and K. Chen. SPARC/E(V.2): An Eleusis rule generator and player. Report

ISG85-11, UIUCDC-F-85941, Department of Computer Science, University of Illinois, 1985.

Sunday, August 26, 12

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SLIDE 48

ACKNOWLEDGEMENTS

  • Thanks to Lena Kurzen for the slides!
  • L. Kurzen, Complexity in Interaction. PhD Thesis (Chapter 6), University of Amsterdam 2011.
  • F. Sangati, eleusisgame.org, 2011.

Sunday, August 26, 12

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SLIDE 49

LET’S PLAY!

Sunday, August 26, 12