def optimal(self, epsilon=10**-9):
"""Compute optimal play for pig game
"""
goal = self.values['goal']
def pwin(probabilities, i, j, k):
"""Probability of winning for a given situation
"""
if i + k >= goal:
return 1.0
elif j >= goal:
return 0.0
else:
return probabilities[i][j][k]
def action_probs(indexes, probabilities):
"""Compute the probability of winning for the different
possibles actions
"""
roll = 0.0
i, j, k = indexes
wrong = self.data.get(['dice', 'wrong'])
for value in range(1, self.values['dice'] + 1):
if value in wrong:
roll += (1.0 - pwin(probabilities, j, i, 0))
else:
roll += pwin(probabilities, i, j, k + value)
roll /= self.values['dice']
return [
(True, roll),
(False, 1 - pwin(probabilities, j, i + k, 0)),
]
values = markov.value_iteration([
lambda : goal,
lambda i : goal,
lambda i, j : goal - i,
], epsilon, action_probs, True)
result = list()
for i in range(goal):
result.append(list())
for j in range(goal):
try:
todo = min(k for k in range(goal) if not values[i][j][k])
result[i].append(todo)
except ValueError:
result[i].append(goal)
return result
def optimal(self, epsilon=10**-5, max_dice=50):
"""Determine optimal play using markov process
"""
def pwin(probabilities, i, j):
"""Compute probability to win for a given situation
"""
if i >= self.goal:
return 1.0
elif j >= self.goal:
return 0.0
else:
return probabilities[i][j]
dice_probs = dices.dice_probability(self.dice, max_dice, self.wrong)
def action_probs(indexes, probabilities):
"""Compute the probability of winning for the different
possibles actions
"""
probs = list()
i, j = indexes
for k in range(1, max_dice + 1):
total_prob = self.dice - len(self.wrong)
total_prob = 1 - (total_prob / self.dice) ** k
roll = total_prob * (1 - pwin(probabilities, j, i))
for result, prob in dice_probs[k]:
roll += prob * (1 - pwin(probabilities, j, i + result))
probs.append((k, roll))
return probs
result = markov.value_iteration([
lambda : self.goal,
lambda i : self.goal,
], epsilon, action_probs, True)
return result