Author: Joseph E. Armstrong
Dept. of Biological Sciences - 4120
Illinois State University
Normal IL 61790
Title & Keywords: ELUSIVE
Card game, logic, hypothesis, deductive, inductive, testing,
predictions.
Credit: This exercise is based upon the game New Eleusis (see
citations below). I thank a former colleague, Dr. Colin Barnett
for introducing his friends to this game.
Abstract:
ELUSIVE is an entertaining a card game that requires players
to formulate and test hypotheses regarding the nature of the
Universe, which consists of a linear sequence of cards. The game
teaches the skills of inductive and deductive logic, and allows
the players to make predictions and test their hypotheses. The
game is adapted to be a laboratory exercise.
Fair Usage:
BIOLAB is supported by NSF grant 9165094 to Joseph E.
Armstrong (ISU) and Marshall Sundberg (LSU). Although an
original laboratory exercise, this exercise is based upon the
published game Eleusis (references included). 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, this
source, and its NSF support.
ELUSIVE - A LAB EXERCISE TO TEACH LOGICAL THINKING
INSTRUCTOR'S GUIDE
BACKGROUND INFORMATION
Science teaching has two primary goals: conveying an
understanding of the subject matter of science, and training
students to think logically and use the scientific method to
solve problems. This is no small challenge. Often the subject
matter is taught bereft of logic and without mentioning the means
by which such knowledge was learned. Students with little or no
training or experience in problem-solving thinking find it
difficult to attempt scientific investigation, even when well
guided, because they fail to grasp central concepts. Thus we
seem to have a vicious cycle, students cannot think logically or
conceptually, so subject matter is learned by memorization, and
students still have not developed problem-solving skills.
The game ELUSIVE offers a more familiar environment in which
students may obtain considerable practice in thinking logically.
This exercise is based on the game Eleusis which was originally
designed to teach inductive logic. When confronted with
unfamiliar subject matter, many students will play it safe, and
merely memorize as much as they can and hope for the best. While
struggling with concepts, they find hypotheses, predictions and
testing too much to deal with. But in this game, the subjects
are familiar, playing cards. Most students have experience with
evaluating their many patterns and permutations. Hopefully this
exercise will provide practice with logical thinking where
students are not distracted by new terms and facts.
The complete game rules of Eleusis are provided. The
laboratory exercise only makes a few modifications. In the
original game, everyone takes a turn at being GOD, and your score
will depend upon formulating a good rule upon which to base the
Universe. Without experience it is very easy to make up a rule
which is too easy or too difficult. To keep things on an even
plane, I suggest the instructor will provide God with a rule; a
number are suggested below. After the first couple, students
will have a better idea of what will and will not work. In the
original game, since you are playing against everyone else,
players do not state their hypotheses or their reasoning, but if
you make and test sound hypotheses, you improve your chances of
winning. For classroom use, I think students benefit from
exercise in making explicit hypotheses. In this way, poorer
students will benefit from better students using the small group
situation.
This is an amusing and challenging game. At a departmental
picnic, faculty and graduate students participated in a large
version of the game, and I must report that the faculty really
cleaned up on the students. Many of my colleagues and their
spouses enjoy playing this game just for fun. Curiously both
students and colleagues often initially react negatively
displaying very bad attitudes ("This sounds dull!" "How
awful!"). Discovering a positive introduction might help.
OBJECTIVES:
To gain experience and develop logical skills by formulating
and testing hypotheses.
CONCEPTS:
To discover a rule that governs a linear sequence of cards
you must make and test explicit hypotheses. Initially hypotheses
are little more than guesses based upon our biases, experiences,
hunches, and intuition. But as cards are played, both correctly
and incorrectly, observations accumulate that allow the
formulation and testing of explicit hypotheses. Hypotheses are
plausible explanations accounting for the sequence of cards
played, just as scientific hypotheses must account for all
observed data. By being explicit students must observe and
think logically. Once a hypothesis has been developed, they then
must think about what play of cards would be consistent with the
hypothesis or falsify it. Thus this game mimics the scientific
process in an environment familiar to students, playing cards.
FACTUAL BACKGROUND:
The version of Eleusis published in Scientific American's
Mathematical Games feature written by Martin Gardiner provides a
brief history of the game's development, and the set of rules
provided.
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.
PROCEDURES:
Divide the class into groups of 6-8. Provide each with 3
decks of playing cards shuffled together, and several chess pawns
for markers.
A fairly quick review of the rules can get things started,
more details will surface as play progresses.
To start out, it will be necessary to provide inexperienced
players with reasonable rules; several suggestions follow. If
they are too easy or too hard, the game does not play well. The
rule can exclude certain cards from play, but any more than 1 in
5 is usually too many for good play. Type rules upon cards to be
distributed to the Gods once chosen. You may want to include a
sequence of cards as an example.
The groups can keep score as described below, and at the end of
play, I reward players with the highest scores with some type of
prize. A worksheet should be supplied upon which students keep
track of the sequence of cards, hypotheses being tested, and
whether they remain possibly true, or were falsified.
SOME SUGGESTED 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. 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 below.)
3. On black cards, play a card of equal or higher value; on
a red card play a card of equal or lower value.
4. 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.
5. 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.
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.
MATERIALS AND SUPPLIES
3 decks of playing cards per group. Casinos and bridge
clubs often give away old decks if your budget can't stand this
expense.
Several white and black markers. One cheap chess set should
provide more than enough pawns.
EXPECTED OUTCOMES
1. Value of Specific Hypotheses - By formulating specific
hypotheses regarding a somewhat familiar subject, a sequence of
playing cards, students will understand how sometimes limited
observations of both successful and unsuccessful tests are used
to generate more possible explanations.
2. Role of Prediction and Testing - Depending upon their
hand and the cards previously played, each specific hypothesis
will allow a number of potential tests, either plays expected to
be correct, or plays expected to falsify the hypothesis.
3. Truth versus Falsification - This simulation of science
clearly will demonstrate that hypotheses can be falsified with
certainty, but that they cannot be proven absolutely true. The
play of the game generates many opportunities where the value of
certainty found in falsification will be obvious.
4. Practice in making explicit statements - While scientists
are quite comfortable with this language, students are not. This
game offers an opportunity to practice in a non-threatening, non-
critical environment.
TIME FRAME
A 3 hour laboratory section should provide sufficient time.
Subsequent rounds of play proceed much faster after learning the
rules and scoring. It also is not necessary to play a complete
round, wherein every student has the opportunity to play God.
STUDENT PROTOCOL
ELUSIVE
A Game to Teach Inductive and Deductive Logic
Introduction
Normal problem-solving thinking involves an unconscious
cylcing between inductive and deductive reasoning, generating
and testing explanations, and accepting them as tentatively true
or rejecting them as absolutely false accordingly. Science is no
different than regular problem-solving thinking except that the
inductive and deductive reasoning is explicit rather than
unconscious.
When confronted with a problem, you have already made an
observation about which you generate a plausible, that is, a
testable explanation. For example, if your car's engine quits
while you are driving, you might think, "I've got another
carburator demon", an untestable explanation. However, rather
than seek an auto exorcism, "I've run out of fuel", represents a
testable and more useful explanation of the observation. You use
INDUCTIVE logic to construct aa tentative explanation, a
hypothesis, based upon the observation that the engine had
stopped running. This hypothesis allows you to make a simple
testable prediction using DEDUCTIVE logic. IF the car is out of
gas, THEN adding fuel to the tank will allow the engine to
restart. If it starts, you are reasonably confident your
hypothesis was true, but if it does not start, you are absolutely
certain that your hypothesis was false. In the first case (the
engine starts), the results are consistent with your hypothesis,
but they do not prove it is true. Perhaps your car overheated
and stalled, but while waiting for fuel the engine cooled down
and would restart. Note that all observations are consistent
with the over-heated hypothesis also. However, in the second
case the falsification of the "out-of-gas" hypothesis is
absolute. There must be something else wrong with your car, and
you must formulate another plausible explanation to solve the
problem.
In problem-solving and in science our thinking cycles from
observation to hypothesis formation to prediction and testing to
the test observation, and then if the problem remains unsolved,
back to hypothesis formation. This in its simplest and most
idealized form is the scientific method, something that active
scientists do routinely.
The following game was invented to teach inductive and
deductive logic. This adaptation is based upon rules published
in Scientific American in Mathematical Games feature by Martin
Gardiner. The rules of the game are included so that you may
play with other people. The name ELUSIVE refers to the search
for truth in science. The original name of the game is Eleusis
referring to classical mysteries.
Science is a process that attempts to discover how nature,
the Universe, operates. In this game, the Universe is
simplified; you must attempt to discover the one rule governing a
linear sequence of playing cards. You will discover this rule by
applying inductive and deductive reasoning, and testing your
hypothesis by playing certain cards.
MATERIALS
3 Standard Card Decks - Shuffled together
White and Black Markers (Chess Pawns, 3 or 4 each)
1 Prophet Marker (Another Chess piece)
6-8 Players
OBJECTIVE
To determine the "RULE" governing the ordering of the Universe,
which consists of a linear sequence of cards. The rule will be a
statement that unambiguously determines the order of cards.
HOW TO PLAY GOD
In ordinary play, one player at a time plays God (or they may
select an alternative name, e.g., Oracle, Delphi, Seer, Almighty,
Umpire, Dean, Mom, etc.). God's first task is to devise a rule
defining the ordering of their Universe (defining what sequence
of cards may be legally played).
In this case the first player to be God will be determined by a
draw of cards; the lowest card (a humble beginning) will play
God. Because you lack experience in creating, God will receive a
rule written upon a card handed down from an even higher diety,
your Laboratory Instructor, who in turn got the rule from the
most, high and mighty Faculty.
RULES ABOUT THE RULE
The rule must concern the physical characterisitics of the cards
themselves, the order of their numbers 1-13 (A=1, J=11, Q=12,
K=13), their colors, their suits, or their status (e.g. face
cards vs. number cards). Circumstances beyond the cards, e.g.,
the time, the sex of the player, which hand of God is touching
their nose, are not allowed. If God deems it necessary, a
truthful hint may be given, e.g., "Suits are irrelevant in this
Universe", or "The rule depends on the 2 previously played
cards". The scoring is such that God's score is optimized by
choosing a rule which is neither too hard or too easy.
In real play, a game would consist of one round wherein each
player would play God once. Scoring (described below) is
adjusted in a partial round to compensate players not having the
opportunity to be God.
The rule must be written down on a card or piece of paper in
unambiguous language.
PLAY OF THE GAME
God starts play by dealing 14 cards to every player. God
does not get a hand and uses the remaining deck. A single
starter card is taken from the top of the deck (or selected if
necessary) and placed upon the playing surface, which ideally
will be large and flat. If the rule depends on more than one
starter card, e.g., 2 or 3, the correct number of starting cards
would be placed on the playing surface (with an explanation,
i.e., a hint from God, as mentioned above).
Face cards have the numerical values of Aces = one, Jack = 11,
Queen = 12, King = 13. Here and below, C = clubs, D = diamonds, H
= hearts, and S = spades. Although more difficult to keep track
of in print, remember that Clubs and Spades are black, and Hearts
and Diamonds red.
To determine which player starts, God starts counting with the
player to their immediate left and continues CW around the circle
until reaching the count on the starter card. Play then
continues CW player to player.
THE PLAY
The first player will basically have to guess about the rule and
state a hypothesis accordingly. This will be recorded in
everyone's notes as well as the starting card. For each
hypothesis, the player will decide how to test the hypothesis
with the play of what they think will be a correct or an
incorrect card. NOTE: since there is only certainty in
falsification, and the object is to determine truth, deliberately
trying to falsify a hypothesis can be a very profitable play.
For example if the starter card is 3H, the 1st player may guess
the rule is "Black and red cards must alternate." The prediction
is simple, if true, then a black card will be correct and a red
card wrong." The player then selects one or more cards and plays
it. In early stages of the game, a single card play is the best
strategy.
God will then indicate whether the card or cards played are in
accord with their Universe (the rule) or not. If correctly
played, the cards become part of the Main Sequence and remain
arranged in a linear sequence, and the play rotates CW to the
next player. Players will record that the hypothesis remains
tentatively true (TT). 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 Sequence, and
consecutive incorrect plays constitute the Side Lines. A white
Pawn or other marker is placed upon every tenth card played
counting both the Main Sequence and Side Line cards.
For the "black and red cards must alternate" hypothesis, playing
a black card after the red 3H is predicted to be correct, while a
red card is predicted to be incorrect. If the player chooses to
play the black 4S, and God says correct, the Main Line appears as
follows.
3H - 4S
If the 4S was ruled incorrect the "black alternating with red
hypothesis" would be falsified, and players will record this (F)
as well. However, a true prediction does not prove the
hypothesis is true. Even though the 4S played was a correct
card, many alternative hypotheses still exist that can account
for the sequence so far. The rule could also be "alternate even
and odd cards," "play cards of greater and lesser values in
alternation," "play cards in consecutive value to 13 and then
back down to one," and so on. So, in falsification there was
certainty, but correct cards, while conforming to the hypothesis
do not prove it was true.
THE PENALTY
For each card incorrectly played, God deals 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 any 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. The player gets a
2 card penalty for each card of the string, so 4 wrong cards
results in an 8 card penalty.
The play rotates CW to the next player who states another
hypothesis, or a more explict statement of the first hypothesis.
If the next player uses the same hypothesis as the previous
player, this player must deliberately predict and make a play
that will potentially falsify the hypothesis. After recording
the hypothesis and explaining their play, play proceeds as above.
This is a small penalty for not being original.
OBJECTIVE
To determine the "RULE" governing the ordering of the Universe,
which consists of a linear sequence of cards. The rule will be a
statement that unambiguously determines the order of cards.
HOW TO PLAY GOD
Eventually you may get to the point where you think, none of
your cards can be played correctly based upon a particular
hypothesis. After stating their hypotheis, if a player thinks they
have no cards in their hand which may be legally played, they may
declare "No Play". The hand is placed upon the table and
examined by God and all other players. If the player is correct
and has 4 or fewer cards, the cards are returned to the deck, and
since this player is out of cards, 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 four.
If God declares that there is a play (i.e., the player is wrong),
God selects one correct card from the hand and places it upon the
main sequence. The player receives a 5 card penalty and play
continues. Note: In the actual game, 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 (3 markers), unless there is a 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.
THE PROPHET
If a player thinks 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 a
Prophet marker, and every 10 cards played subsequently with a
black marker. 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 over 30 cards had been played prior
to a Prophet, expulsions are suspended until 20 more cards are
played, although 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 (also probably having lost one or more opportunities to get
rid of cards). The Prophet's marker and black pawns are removed
from the cards, and the white markers are brought up to date. If
more than 30 cards have been played, then expulsions begin with
the very next incorrect play. 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.
Any 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, the player gets 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 falsify the operating hypothesis of the Prophet,
which will demonstrate they are in reality a False Prophet.
PROPHESY AND THE NO PLAY
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
(New hand = Old hand - 4). 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's 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.
THE LOGIC
Just like discovering the rules governing our own Universe, the
rules of this Universe are discovered by a combination of
deductive and inductive logic. Initially, with no information to
go on, discovery must be by random guessing. However, both
correct and incorrect plays are informative, and like real
science, hypotheses cannot be proven true, but they can be
falsified with certainty. So as more cards are played, a pattern
emerges that allows you to correctly hypothesize the Rule of the
Universe.
You make observations of correct and incorrect cards, those that
conform to the Universe and those that do not, then you use
inductive logic or reasoning to construct a possible explanation,
a hypothesis. Next, deductive logic is used to predict which
card or cards from your hand will be correct or incorrect based
upon your hypothesis. Thus false hypotheses may be discarded,
and simple hypotheses may become more complex, more correct.
This can best be illustrated with an example. Suppose the play
starts with the 3H, and the next player's guess is the 9S, the
play is correct. But several rules might give this result, for
example, if the number is higher, change color or suit, and if
lower, keep it the same. If you decided this was a possible
hypothesis you could test it by selecting the JD (an increase,
therefore change color or suit). But God says this is incorrect,
and your hypothesis is falsified, it cannot possibly be true.
The next player decides the rule says to simply alternate colors
and values, so they select the 5D, and it also is incorrect, thus
falsifying this hypothesis also. 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, but this does not prove the hypothesis is true. In
fact, this hypothesis is immediately falsified when the next
player selects the JD. After the play of 22 cards, the mainline
and sideline sequences look like this (*s mark the 10th (2C) and
20th (2S) cards):
*
3H - 9S - 4C - JD - 2C - 10D - 8H - 7H - 2C - 5H - ?
JH AS AS 10H *
5D 8H 10S 10S,9H,4S,2S
QD
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.
If told any black card would be correct, and any red card
incorrect can you explain the Rule?
RECORD KEEPING
You should keep a record of the cards played, the hypotheses
stated, and whether they were falsified or remain tentatively
true. Make your notes explicit enough that you can reconstruct
the logic and the testing of the sequence. The best way to do
this is to keep a master sequence showing the mainline and
sideline sequences. Then below, keep more specific notes. For
each player's turn, indicate (1) the card being played upon, (2)
the hypothesis, (3) the prediction and card(s) played, and (4)
the result (allowed by the Rule or not allowed).
REPORT
To demonstrate your understanding to the higher dieties, write a
report completely describing the logic, the hypotheses, the
predictions, and the results of one round of the game. Then
construct a diagram showing the cycling between inductive and
deductive logic, hypotheses, predictions, and testing.
CONCLUSIONS
Based upon your experiences with this game, what would be
important features for a scientific hypothesis? Why is potential
falsification so important?
* * * * * * * * * * * * * * * * * *
NEW ELEUSIS
A game that simulates the scientific search for truth.
GAME RULES - (4-8 Players)
Materials
3 Standard Card Decks - Shuffled together
White and Black Markers (Chess Pawns)
1 Prophet Marker (Another Chess piece)
Objective
To figure out the "RULE" governing the ordering of the Universe,
which consists of a linear sequence of cards.
God
In ordinary play, one player at a time plays God (or they may
select an alternative name, e.g., Oracle, Delphi, Seer, Almighty,
etc.). God's first task is to devise a rule that will define
the ordering of their Universe (defining what sequence of cards
may be legally played). Example: Each card played must differ in
color from the preceeding card (a too simplistic rule resulting
in an alternating pattern of red and black cards). The rule must
concern intrinsic features of the cards themselves. The scoring
is such that God's score is optimized by choosing a rule which is
neither too hard or too easy.
Circumstances beyond the cards, e.g., the time, the sex of the
player, which hand of God is touching their nose, are not
allowed. If God deems it necessary, a truthful hint may be
given, e.g., "Suits are irrelevant in this Universe", or "The
rule depends on the 2 previously played cards".
In real play, a game would consist of one round wherein each
player would play God once. Scoring (described below) can be
adjusted in a partial round to compensate players not having the
opportunity to be God.
The rule must be written down on a card or piece of paper in
unambiguous language.
The Play
God starts play by dealing 14 cards to every other player. God
does not get a hand and plays the remaining deck. A single
starter card is taken from the top of the deck (or selected if
necessary) and placed upon the playing surface, which ideally
will be large and flat. If the rule depends on more than one
starter card, e.g., 2 or 3, the correct number would be placed on
the playing surface (with an explanation, i.e., a hint from God,
as mentioned above).
Face cards have the numerical values of 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 CW around the circle
until reaching the count on the starter card.
A play consists of placing one or more cards upon the playing
surface in a linear sequence from the starter card(s) or 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 rotates CW 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 white
Pawn (or other marker) 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 in their hand 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, 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 three. 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.
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 a
Prophet marker, and every 10 cards played subsequently with a
black marker. 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 black pawns are removed from the cards, and
the white markers 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.
The Logic
Just like discovering the rules governing our own Universe, the
rules of this Universe are discovered by a combination of
inductive reasoning to form tentative hypotheses based upon
whatever evidence is available. Initially, with no information
to go on, hypotheses are little more than guesses. But, whatever
hypothesis is chosen tentatively, a correct play is predicted and
the appropriate card selected. Both correct and incorrect plays
are informative, and like real science, hypotheses cannot be
proven true, but they can be falsified with certainty. So as
more cards are played, a pattern emerges that allows you to
correctly hypothesize the Rule of the Universe based upon both
correct and incorrect cards. Many possible hypotheses can be
rejected upon the basis of previously played cards.
This can best be illustrated with an example. Suppose the play
starts with the 3H, and the next player's guess is the 9S, the
play is correct. But several rules might give this result, for
example, if the number is higher, change color or suit, and if
lower, keep it the same. If you decided this was a possible
hypothesis you could test it by selecting the JD (an increase,
therefore change color or suit). But God says this is incorrect,
so your hypothesis is falsified, it cannot possibly be true. The
next player decides the rule says to simply alternate colors, so
they select the 5D, and it also is incorrect, thus falsifying
this hypothesis also. 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, but this
does not prove the hypothesis is true. In fact, this hypothesis
is immediately falsified when the next player selects the JD.
After several more plays, the mainline and sideline sequences
look like the card layout that follows.
*(10)
3H - 9S - 4C - JD - 2C - 10D - 8H - 7H - 2C - 5H - ?
| | | |
JD AH AS 10H
| | | | *(20)
5D 8H 10S 10S-9H-4S-2S
|
QD
There is an incorrect four card side line sequence under the
7H, but remember, only one wrong card makes the entire string
wrong. 22 cards have been played; asteriks mark the 10th and
20th cards played. 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?
The rule is "If the last legally played card is odd, play a black
card; if the card is even, play a red card".
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.
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 in their hand which may be
legally played, they may declare "No Play". The hand is placed
upon
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
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