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"""
https://brilliant.org/community-problem/loser-keeps-bieber-we-stood-no-chance/
?group=4cgSapeNTVXO&ref_id=115277
"""
import random
def play_defensive(them):
if random.random() <= 0.04:
them += 1
return them
def play_offensive(us, them):
r1 = random.random()
r2 = random.random()
if r1 <= 0.05:
them += 1
if r2 >= 0.95:
us += 1
return us, them
def simulate(us=1, them=0, defensive=20, minutes_left=20):
"""
If leading with less than `defensive` minutes left,
play_defensive, else play_offensive.
"""
for minute in range(minutes_left, 0, -1):
if defensive >= minute and (us > them):
them = play_defensive(them)
else:
us, them = play_offensive(us, them)
if us > them:
return 1.0
if them > us:
return 0.0
return 0.5
A = 0
B = 0
C = 0
D = 0
tries = 100000
for i in range(tries):
A += simulate(defensive=10)
B += simulate(defensive=20)
C += simulate(defensive=15)
D += simulate(defensive=5)
print
print A
print B
print C
print D
import IPython; IPython.embed()
$ python optimal_strategy.py
76397.5
72070.0
74839.5
76561.0
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