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winning_prob.py
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winning_prob.py
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def hold_serve_prob(rally_win_prob):
"""Calculates the probability of holding serve.
Args:
rally_win_prob (np.array): The probability of winning a rally on serve.
Returns:
np.array: The probability of holding serve.
"""
rally_lose_prob = 1 - rally_win_prob
term_1 = pow(rally_win_prob, 4)
term_2 = (1+4*rally_lose_prob+10*(pow(rally_lose_prob, 2)))
first_summand = term_1 * term_2
term_1 = 20 * pow(rally_win_prob * rally_lose_prob, 3)
term_2 = pow(rally_win_prob, 2)
term_3 = 1/(1 - 2*rally_win_prob*rally_lose_prob)
second_summand = term_1 * term_2 * term_3
result = first_summand + second_summand
return result
def prob_reach_tiebreak_score(i, j, win_serve_rally_prob_a,
win_serve_rally_prob_b):
"""The probability of reaching a given tiebreak score when player a serves
first.
Args:
i (int): Score for player a.
j (int): Score for player b.
win_serve_rally_prob_a (np.array): The probability that a wins a rally
on their serve.
win_serve_rally_prob_b (np.array): The probability that b wins a rally
on their serve.
Returns:
np.array: The probability of reaching tiebreak score [i, j].
"""
# Helpful renamings
lose_serve_rally_prob_a = 1 - win_serve_rally_prob_a
lose_serve_rally_prob_b = 1 - win_serve_rally_prob_b
a_served_last = (((i - 1 + j) % 4 == 0) or ((i - 1 + j) % 4 == 3))
# Initial conditions:
if (i == 0 and j == 0):
return 1
if (i < 0 or j < 0):
return 0
if a_served_last:
total = 0
if (not (i == 7 and j <= 6)):
total += prob_reach_tiebreak_score(
i, j-1, win_serve_rally_prob_a, win_serve_rally_prob_b) * (
lose_serve_rally_prob_a)
if (not (j == 7 and i <= 6)):
total += (prob_reach_tiebreak_score(
i-1, j, win_serve_rally_prob_a, win_serve_rally_prob_b) *
win_serve_rally_prob_a)
return total
else:
total = 0
if (not (i == 7 and j <= 6)):
total += (prob_reach_tiebreak_score(
i, j-1, win_serve_rally_prob_a, win_serve_rally_prob_b) *
win_serve_rally_prob_b)
if (not (j == 7 and i <= 6)):
total += (prob_reach_tiebreak_score(i-1, j, win_serve_rally_prob_a,
win_serve_rally_prob_b) *
lose_serve_rally_prob_b)
return total
def prob_win_tiebreak_a(win_serve_rally_prob_a, win_serve_rally_prob_b):
"""Calculates the probability that a wins a tiebreak.
Args:
win_serve_rally_prob_a (np.array): The probability that player a wins
a rally on their own serve.
win_serve_rally_prob_b (np.array): The probability that player b wins
a rally on their own serve.
Returns:
np.array: The probability a wins the tiebreak.
"""
total = 0
lose_serve_rally_prob_a = 1 - win_serve_rally_prob_a
lose_serve_rally_prob_b = 1 - win_serve_rally_prob_b
for j in range(6):
total += prob_reach_tiebreak_score(7, j, win_serve_rally_prob_a,
win_serve_rally_prob_b)
total += (prob_reach_tiebreak_score(6, 6, win_serve_rally_prob_a,
win_serve_rally_prob_b) *
win_serve_rally_prob_a * lose_serve_rally_prob_b *
1/(1 - win_serve_rally_prob_a * win_serve_rally_prob_b -
lose_serve_rally_prob_a * lose_serve_rally_prob_b))
return total
def prob_win_set_a(win_serve_rally_prob_a, win_serve_rally_prob_b):
"""Calculates the probability that player a wins a set.
Args:
win_serve_rally_prob_a (np.array): The probability that player a wins
a rally on their own serve.
win_serve_rally_prob_b (np.array): The probability that player b wins
a rally on their own serve.
Returns:
np.array: The probability that player a wins a set.
"""
total = 0
for j in range(5):
total += prob_reach_set_score(6, j, win_serve_rally_prob_a,
win_serve_rally_prob_b)
total += prob_reach_set_score(7, 5, win_serve_rally_prob_a,
win_serve_rally_prob_b)
total += prob_reach_set_score(7, 6, win_serve_rally_prob_a,
win_serve_rally_prob_b)
return total
def prob_reach_set_score(i, j, win_serve_rally_prob_a, win_serve_rally_prob_b):
"""The probability of reaching a given set score when player A serves
first.
Args:
i (int): Score for player a.
j (int): Score for player b.
win_serve_rally_prob_a (np.array): The probability that a wins a rally
on their serve.
win_serve_rally_prob_b (np.array): The probability that b wins a rally
on their serve.
Returns:
np.array: The probability of reaching set score [i, j].
"""
assert (j <= 6 and i <= 6) or (i == 7 and j <= 6) or (i <= 6 and j == 7), \
'Please provide a valid set score!'
hold_serve_prob_a = hold_serve_prob(win_serve_rally_prob_a)
hold_serve_prob_b = hold_serve_prob(win_serve_rally_prob_b)
# Helpful renamings
lose_serve_prob_a = 1 - hold_serve_prob_a
lose_serve_prob_b = 1 - hold_serve_prob_b
a_served_last = ((i - 1 + j) % 2 == 0)
# Initial conditions
if (i == 0 and j == 0):
return 1
if (i < 0 or j < 0):
return 0
# We have the tiebreak case:
if i == 6 and j == 7:
return prob_reach_set_score(
i, j - 1, win_serve_rally_prob_a, win_serve_rally_prob_b) * (
1 - prob_win_tiebreak_a(win_serve_rally_prob_a,
win_serve_rally_prob_b))
elif i == 7 and j == 6:
return prob_reach_set_score(
i - 1, j, win_serve_rally_prob_a, win_serve_rally_prob_b) * (
prob_win_tiebreak_a(win_serve_rally_prob_a,
win_serve_rally_prob_b))
# We also have the 7-5 case:
if i == 7 and j == 5:
return prob_reach_set_score(i - 1, j, win_serve_rally_prob_a,
win_serve_rally_prob_b) * lose_serve_prob_b
elif i == 5 and j == 7:
return prob_reach_set_score(i, j - 1, win_serve_rally_prob_a,
win_serve_rally_prob_b) * hold_serve_prob_b
# Two possibilities
if a_served_last:
total = 0
if (not (j == 6 and i <= 5)):
total += (prob_reach_set_score(i-1, j, win_serve_rally_prob_a,
win_serve_rally_prob_b) *
hold_serve_prob_a)
if (not (i == 6 and j <= 5)):
total += (prob_reach_set_score(i, j-1, win_serve_rally_prob_a,
win_serve_rally_prob_b) *
lose_serve_prob_a)
return total
else:
total = 0
if (not (j == 6 and i <= 5)):
total += (prob_reach_set_score(i-1, j, win_serve_rally_prob_a,
win_serve_rally_prob_b) *
lose_serve_prob_b)
if (not (i == 6 and j <= 5)):
total += (prob_reach_set_score(i, j-1, win_serve_rally_prob_a,
win_serve_rally_prob_b) *
hold_serve_prob_b)
return total
def prob_win_match_a(win_serve_rally_prob_a, win_serve_rally_prob_b,
best_of_five=False):
"""Calculates the probability that player a wins the match.
Args:
win_serve_rally_prob_a (np.array): The probability that player a wins
a rally on their own serve.
win_serve_rally_prob_b (np.array): The probability that player b wins
a rally on their own serve.
best_of_five (Bool): Whether or not the match is in best-of-five
format. If False, it is assumed to be best-of-three.
Returns:
np.array: The probability that player a wins the match.
"""
prob_a_win_set = prob_win_set_a(win_serve_rally_prob_a,
win_serve_rally_prob_b)
prob_b_win_set = prob_win_set_a(win_serve_rally_prob_b,
win_serve_rally_prob_a)
total = 0
if (not best_of_five):
total += pow(prob_a_win_set, 2)
total += 2 * pow(prob_a_win_set, 2) * prob_b_win_set
else:
total += (pow(prob_a_win_set, 3) + 3 * pow(prob_a_win_set, 3) *
prob_b_win_set + 6 * pow(prob_a_win_set, 3) *
pow(prob_b_win_set, 2))
return total
if __name__ == '__main__':
print(prob_reach_set_score(6, 4, 0.8, 0.8))