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import random
import collections
import itertools
Game of Set (Peter Norvig 2010-2015)
How often do sets appear when we deal an array of cards?
How often in the course of playing out the game?
Here are the data types we will use:
card: A string, such as '3R=0', meaning "three red striped ovals".
deck: A list of cards, initially of length 81.
layout: A list of cards, initially of length 12.
set: A tuple of 3 cards.
Tallies: A dict: {12: {True: 33, False: 1}}} means a layout of size 12
tallied 33 sets and 1 non-set.
#### Cards, dealing cards, and defining the notion of sets.
CARDS = [number + color + shade + symbol
for number in '123'
for color in 'RGP'
for shade in '@O='
for symbol in '0SD']
def deal(n, deck):
"Deal n cards from the deck."
return [deck.pop() for _ in range(n)]
def is_set(cards):
"Are these 3 cards a set? No if any feature has 2 values."
for f in range(4):
values = {card[f] for card in cards}
if len(values) == 2:
return False
return True
def find_set(layout):
"Return a set found from this layout, if there is one."
for cards in itertools.combinations(layout, 3):
if is_set(cards):
return cards
return ()
#### Tallying set:no-set ratio
def Tallies():
"A data structure to keep track, for each size, the number of sets and no-sets."
return collections.defaultdict(lambda: {True: 0, False: 0})
def tally(tallies, layout):
"Record that a set was found or not found in a layout of given size; return the set."
s = find_set(layout)
tallies[len(layout)][bool(s)] += 1
return s
#### Three experiments
def tally_initial_layout(N, sizes=(12, 15)):
"Record tallies for N initial deals."
tallies = Tallies()
deck = list(CARDS)
for deal in range(N):
for size in sizes:
tally(tallies, deck[:size])
return tallies
def tally_initial_layout_no_prior_sets(N, sizes=(12, 15)):
"""Simulate N initial deals for each size, keeping tallies for Sets and NoSets,
but only when there was no set with 3 fewer cards."""
tallies = Tallies()
deck = list(CARDS)
for deal in range(N):
for size in sizes:
if not find_set(deck[:size-3]):
tally(tallies, deck[:size])
return tallies
def tally_game_play(N):
"Record tallies for the play of N complete games."
tallies = Tallies()
for game in range(N):
deck = list(CARDS)
layout = deal(12, deck)
while deck:
s = tally(tallies, layout)
# Pick up the cards in the set, if any
for card in s: layout.remove(card)
# Deal new cards
if len(layout) < 12 or not s:
layout += deal(3, deck)
return tallies
def experiments(N):
show({12: [1, 33], 15: [1, 2500]},
'the instruction booklet')
'initial layout')
show(tally_game_play(N // 25),
'game play')
'initial layout, but no sets before dealing last 3 cards')
def show(tallies, label):
"Print out the counts."
print('Size | Sets | NoSets | Set:NoSet ratio for', label)
for size in sorted(tallies):
y, n = tallies[size][True], tallies[size][False]
ratio = ('inft' if n==0 else int(round(float(y)/n)))
print('{:4d} |{:7,d} |{:7,d} | {:4}:1'
.format(size, y, n, ratio))
def test():
assert len(CARDS) == 81 == len(set(CARDS))
assert is_set(('3R=O', '2R=S', '1R=D'))
assert not is_set(('3R=0', '2R=S', '1R@D'))
assert find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R=D']) == ('3R=0', '2R=S', '1R=D')
assert not find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R@D'])
photo = '2P=0 3P=D 2R=0 3GO0 2POD 3R@D 2RO0 2ROS 1P@S 2P@0 3ROS 2GOD 2P@D 1GOD 3GOS'.split()
assert not find_set(photo)
assert set(itertools.combinations([1, 2, 3, 4], 3)) == {(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)}
print('All tests pass.')