two-blue-stones-puzzle

import os, sys
import random

random.seed(12345)


stone_combinations = [('W', 'Y'), ('W', 'B1'), ('W', 'B2'), ('Y', 'B1'), ('Y', 'B2'), ('B1', 'B2')]

stone_permutations = [('W', 'Y'), ('W', 'B1'), ('W', 'B2'), ('Y', 'B1'), ('Y', 'B2'), ('B1', 'B2'),
                      ('Y', 'W'), ('B1', 'W'), ('B2', 'W'), ('B1', 'Y'), ('B2', 'Y'), ('B2', 'B1')
                     ]

def stoneColor(stone):
    """Pick stone color from entry -- needed because we represent two different blues as 'B1' and 'B2'"""
    return stone[0:1]


def simIfAtLeastOneBlueCombo(trials):
    """Simulation: Pick combination of two, check both stones, proceed only if at least one of the stones is blue."""
    numTrialsAdmitted = 0
    numTrialsPassed = 0
    for i in xrange(trials):
        choice = random.choice(stone_combinations)
        if stoneColor(choice[0]) == 'B' or stoneColor(choice[1]) == 'B':
            numTrialsAdmitted += 1
        if choice == ('B1', 'B2'):
            numTrialsPassed += 1
    print "Simulation: Pick combination of two, check both stones, proceed only if at least one of the stones is blue."
    print "-"*80
    print "Total Sims: %d, Trials Admitted = %d, Trials Passed = %d, Percent of Passing over Admitted: %6.2f%%" % (trials, numTrialsAdmitted, numTrialsPassed, numTrialsPassed / float(numTrialsAdmitted) * 100 )
    print





def simIfRandomStoneIsBlueCombo(trials):
    """Simulation: Pick combination of two, randomly pick a stone, proceed only if that stone is blue."""
    numTrialsAdmitted = 0
    numTrialsPassed = 0
    for i in xrange(trials):
        choice = random.choice(stone_combinations)
        random_stone_from_choice = random.choice(choice)
        if stoneColor(random_stone_from_choice) == 'B':
            numTrialsAdmitted += 1
        if choice == ('B1', 'B2'):
            numTrialsPassed += 1
    print "Simulation: Pick combination of two, randomly pick a stone, proceed only if that stone is blue."
    print "-"*80
    print "Total Sims: %d, Trials Admitted = %d, Trials Passed = %d, Percent of Passing over Admitted: %6.2f%%" % (trials, numTrialsAdmitted, numTrialsPassed, numTrialsPassed / float(numTrialsAdmitted) * 100 )
    print



def simIfFirstBluePerm(trials):
    """Simulation: Pick permutation of two, check first stone, proceed only if first stone is blue."""
    numTrialsAdmitted = 0
    numTrialsPassed = 0
    for i in xrange(trials):
        choice = random.choice(stone_permutations)
        if stoneColor(choice[0]) == 'B':
            numTrialsAdmitted += 1
        if choice == ('B1', 'B2') or choice == ('B2', 'B1'):
            numTrialsPassed += 1
    print "Simulation: Pick permutation of two, check first stone, proceed only if first stone is blue."
    print "-"*80
    print "Total Sims: %d, Trials Admitted = %d, Trials Passed = %d, Percent of Passing over Admitted: %6.2f%%" % (trials, numTrialsAdmitted, numTrialsPassed, numTrialsPassed / float(numTrialsAdmitted) * 100 )
    print





    # The simulations
simIfAtLeastOneBlueCombo(10000)
simIfRandomStoneIsBlueCombo(10000)
simIfFirstBluePerm(10000)


# ================================================================================
# Output
# ================================================================================
# Simulation: Pick combination of two, check both stones, proceed only if at least one of the stones is blue.
# --------------------------------------------------------------------------------
# Total Sims: 10000, Trials Admitted = 8306, Trials Passed = 1651, Percent of Passing over Admitted:  19.88%
#
# Simulation: Pick combination of two, randomly pick a stone, proceed only if that stone is blue.
# --------------------------------------------------------------------------------
# Total Sims: 10000, Trials Admitted = 4967, Trials Passed = 1674, Percent of Passing over Admitted:  33.70%
#
# Simulation: Pick permutation of two, check first stone, proceed only if first stone is blue.
# --------------------------------------------------------------------------------
# Total Sims: 10000, Trials Admitted = 4892, Trials Passed = 1715, Percent of Passing over Admitted:  35.06%