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farkle.py
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farkle.py
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import collections
import random
from functools import reduce
def getScore(dice):
'''Return a Farkle score and the indicies of the scoring dice'''
dice.sort()
if dice == [1, 2, 3, 4, 5, 6]:
return 1500, range(6)
elif any([dice == [x, x, x, y, y, y] for x in range(1, 4)
for y in range(4, 7)]):
return 2500, range(6)
elif any([dice.count(x) == 4 and dice.count(y) == 2
for x in range(1, 7) for y in range(1, 7)]):
return 1500, range(6)
elif any([dice == [x, x, y, y, z, z] for x in range(1, 3)
for y in range(3, 5) for z in range(5, 7)]):
return 1500, range(6)
elif any([dice.count(x) == 6 for x in range(1, 7)]):
return 3000, range(6)
cumScore = 0
counter = collections.Counter(dice)
for i in range(1, 7):
if counter[i] == 5:
cumScore += 2000
cumScore += addOnesFives(i, counter)
return cumScore, getIndexScoring(dice, i)
if counter[i] == 4:
cumScore += 1000
cumScore += addOnesFives(i, counter)
return cumScore, getIndexScoring(dice, i)
if counter[i] == 3:
if i != 1:
cumScore += i*100
else:
cumScore += 300
cumScore += addOnesFives(i, counter)
return cumScore, getIndexScoring(dice, i)
cumScore += counter[1]*100
cumScore += counter[5]*50
return cumScore, getIndexScoring(dice, 0)
def getIndexScoring(dice, i):
return [ix for ix in range(len(dice))
if dice[ix] == i or dice[ix] == 5 or dice[ix] == 1]
def addOnesFives(i, counter):
score = 0
if i != 1:
score += counter[1]*100
if i != 5:
score += counter[5]*50
return score
def testScore():
assert getScore([5, 4, 3, 2, 1, 6])[0] == 1500
assert getScore([6, 6, 6, 2, 2, 2])[0] == 2500
assert getScore([4, 4, 4, 1, 1, 1])[0] == 2500
assert getScore([6, 6, 6, 6, 1, 1])[0] == 1500
assert getScore([6, 6, 2, 2, 4, 4])[0] == 1500
assert getScore([1, 1, 1, 1, 1, 1])[0] == 3000
assert getScore([5, 5, 5, 5, 2, 3])[0] == 1000
assert getScore([5, 5, 5, 5, 5, 2])[0] == 2000
assert getScore([2, 2, 2, 2, 2, 1])[0] == 2100
assert getScore([2, 2, 2, 2, 1, 5])[0] == 1150
assert getScore([6, 6, 6, 2, 3, 3])[0] == 600
assert getScore([6, 6, 6, 1, 1, 5])[0] == 850
assert getScore([2, 2, 2, 1, 3, 3])[0] == 300
assert getScore([1, 1, 1, 5, 5, 2])[0] == 400
assert getScore([1, 1, 2, 3, 4, 4])[0] == 200
assert getScore([1, 5, 2, 3, 4, 4])[0] == 150
assert getScore([2, 3, 4, 6, 6, 2])[0] == 0
assert list(getScore([1, 2, 3, 4, 5, 6])[1]) == [0, 1, 2, 3, 4, 5]
assert getScore([1, 1, 2, 3, 4, 5])[1] == [0, 1, 5]
assert getScore([1, 1, 1, 2, 5, 6])[1] == [0, 1, 2, 4]
print("Scoring test passed!")
testScore()
def rollDice(numDice):
return [random.randint(1, 6) for x in range(numDice)]
def getFarklePercentages(numRolls):
'''Monte Carlo simulation of rolling 1, 2, 3, ... dice for numRolls and
counting the number of times the score is zero'''
farkleCount = []
for x in range(1, 7):
scores = [getScore(dice)[0]
for dice in [rollDice(x) for y in range(numRolls)]]
farkleCount.append(scores.count(0))
farklePcts = [x*100.0/numRolls for x in farkleCount]
str2print = "Farkle percent for {} {}: {:5.2f}"
for i, farklePct in enumerate(farklePcts):
diceTxt = "dice" if i != 0 else "die "
print(str2print.format(i+1, diceTxt, farklePct))
print("")
getFarklePercentages(100000)
def summation(vals):
return reduce(lambda x, y: x + y, vals)
def average(vals):
return summation(vals)/float(len(vals))
def stdDev(vals):
mean = average(vals)
return (summation([(x - mean)**2 for x in vals])/float(len(vals)-1))**0.5
def getExpectedValues(numRolls):
'''Get the expected value or average score for each roll of a number of
dice based on Monte Carlo simulation'''
expectedValues = []
for x in range(1, 7):
scores = [getScore(dice)[0]
for dice in [rollDice(x) for y in range(numRolls)]]
expectedValues.append(average(scores))
str2print = "Expected value for {} {}: {:6.2f}"
for i, expectedValue in enumerate(expectedValues):
diceTxt = "dice" if i != 0 else "die "
print(str2print.format(i+1, diceTxt, expectedValue))
print("")
getExpectedValues(100000)
def simulateStrategy(func, numSims):
'''Pass a function (func) and the number of simulations to run (numSims) and
this function will print the average number of plays to reach 10,000 points
, a winning score.
The function needs to return only the number of plays that it took to get
to 10,000 points'''
counts = []
for _ in range(numSims):
counts.append(func())
avg = average(counts)
std = stdDev(counts)
str2print = "Average number of plays to {} points for {}: {}"
print(str2print.format(numSims, func.__name__, avg))
str2print = "Std. deviation for number of plays for {}: {}"
print(str2print.format(func.__name__, std))
def keepGreaterThanX(X):
'''A farkle strategy where one keeps any amount of points obtained greater
than X and also naively keeping all points on a roll'''
score, currentTurnScore, numDice, numTurns = 0, 0, 6, 0
while score < 10000:
currentRollScore, scoringIdx = getScore(rollDice(numDice))
currentTurnScore += currentRollScore
if currentRollScore == 0:
numDice, currentTurnScore = 6, 0
numTurns += 1
continue
if currentTurnScore > X:
score += currentTurnScore
currentTurnScore = 0
numDice = 6
numTurns += 1
else:
numDice -= len(scoringIdx)
return numTurns
def strategy1(verbose=False):
'''A slightly better strategy, maybe the best?'''
takeScoreLimit = {1: 50,
2: 50,
3: 100,
4: 150,
5: 250,
6: 350}
score, currentTurnScore, numDice, numTurns = 0, 0, 6, 0
while score < 10000:
dice = rollDice(numDice)
currentRollScore, scoringIdx = getScore(dice)
#takeScoreLimit = 13.55*numDice**2-34.19*numDice+54.1
if currentRollScore == 0:
numDice, currentTurnScore = 6, 0
numTurns += 1
continue
if len(scoringIdx) == numDice:
currentTurnScore += currentRollScore
numDice = 6
continue
if currentRollScore+currentTurnScore >= takeScoreLimit[numDice]:
score += currentTurnScore+currentRollScore
numDice, currentTurnScore = 6, 0
numTurns += 1
else:
numOnes = dice.count(1)
numFives = dice.count(5)
if numOnes > 0:
currentTurnScore += 100
numDice -= 1
elif numFives > 0 and len(scoringIdx) < 3:
currentTurnScore += 50
numDice -= 1
else:
currentTurnScore += currentRollScore
numDice -= len(scoringIdx)
return numTurns
def strategy2(verbose=False):
'''A slightly worse strategy.'''
takeScoreLimit = {1: 50,
2: 50,
3: 100,
4: 150,
5: 250,
6: 350}
score, currentTurnScore, numDice, numTurns = 0, 0, 6, 0
while score < 10000:
dice = rollDice(numDice)
currentRollScore, scoringIdx = getScore(dice)
#takeScoreLimit = 13.55*numDice**2-34.19*numDice+54.1
if currentRollScore == 0:
numDice, currentTurnScore = 6, 0
numTurns += 1
continue
if len(scoringIdx) == numDice:
currentTurnScore += currentRollScore
numDice = 6
continue
if currentTurnScore >= takeScoreLimit[numDice]:
score += currentTurnScore+currentRollScore
numDice, currentTurnScore = 6, 0
numTurns += 1
else:
numOnes = dice.count(1)
numFives = dice.count(5)
if numOnes > 0:
currentTurnScore += 100
numDice -= 1
elif numFives > 0 and len(scoringIdx) < 3:
currentTurnScore += 50
numDice -= 1
else:
currentTurnScore += currentRollScore
numDice -= len(scoringIdx)
return numTurns
def printStrat1():
print('Dice | Score Limit')
takeScoreLimit = {1: 50,
2: 50,
3: 100,
4: 150,
5: 250,
6: 350}
for numDice in range(1, 7):
#takeScoreLimit = 13.55*numDice**2-34.19*numDice+54.1
print(f'{numDice} | {round(takeScoreLimit[numDice])}')
simulateStrategy(lambda: keepGreaterThanX(220), 10000)
simulateStrategy(strategy1, 10000)
print('')
printStrat1()