https://fivethirtyeight.com/features/work-a-shift-in-the-riddler-gift-shop/ riddle express

pill_bottle_tumbler.py

# https://fivethirtyeight.com/features/work-a-shift-in-the-riddler-gift-shop/
# riddler express
# https://docs.google.com/spreadsheets/d/1n2WNPOeR2iOeWf5pUpHU6P92MDH7sk3rsUtvdFUsmHM/edit#gid=0

import random
random.seed(0)

# what if the half pills fall out of your hands back into the bottle?
# let p stand for probablity between 0 and 1.
def sample_pills_extra_credit(i, p):
	iteration_history = []
	for i in range(i):
		current_iteration = 0
		full_pills = 100
		half_pills = 0
		ate_half = False

		while ate_half == False:
			current_iteration += 1
			if random.randint(1,100) <= full_pills:
				full_pills += -1
				half_pills += 1
				# print(full_pills, half_pills)
			else:
				if random.uniform(0,1) < p:
					# print('you fumbled a pill back into the bottle, and you reach for another')
					current_iteration += -1
				else:
					# print('You just ate a half pill')
					# print('Current iteration =', current_iteration)
					iteration_history.append(current_iteration)
					break

	# print(iteration_history)
	average_iterations = sum(iteration_history) / len(iteration_history)
	print(p, 'fumble chance', 'average iterations (mean) for', len(iteration_history),'iterations =', average_iterations, '\n')


sample_pills_extra_credit(1000000, 0)
sample_pills_extra_credit(1000000, .1)
sample_pills_extra_credit(1000000, .2)
sample_pills_extra_credit(1000000, .3)
sample_pills_extra_credit(1000000, .4)
sample_pills_extra_credit(1000000, .5)
sample_pills_extra_credit(1000000, .6)
sample_pills_extra_credit(1000000, .7)
sample_pills_extra_credit(1000000, .8)
sample_pills_extra_credit(1000000, .9)

#   0 fumble chance average iterations (mean) for 1000000 iterations = 13.218755
# 0.1 fumble chance average iterations (mean) for 1000000 iterations = 13.81488
# 0.2 fumble chance average iterations (mean) for 1000000 iterations = 14.53912
# 0.3 fumble chance average iterations (mean) for 1000000 iterations = 15.367559
# 0.4 fumble chance average iterations (mean) for 1000000 iterations = 16.42008
# 0.5 fumble chance average iterations (mean) for 1000000 iterations = 17.747487
# 0.6 fumble chance average iterations (mean) for 1000000 iterations = 19.515661
# 0.7 fumble chance average iterations (mean) for 1000000 iterations = 22.02279
# 0.8 fumble chance average iterations (mean) for 1000000 iterations = 26.134048
# 0.9 fumble chance average iterations (mean) for 1000000 iterations = 34.646415