def estimate_pi(n_trials):
"""Sample x,y ~ U(0,1) and test if x^2 + y^2 < 1."""
n_hits_in_circle = 0
for _ in range(n_trials):
x, y = unif_rand(), unif_rand()
f = circle_func(x, y)
if f < 1:
n_hits_in_circle += 1
estimate = 4 * n_hits_in_circle / n_trials
return estimate
def play_game():
player_amt = -5 # player initially pays 5 units
u = unif_rand()
success_counter = 0
payout = 1
while u > 0.5:
success_counter += 1
payout = 2 * payout
player_amt += payout
u = unif_rand()
return player_amt
def sample_die_from_unif(N=6):
"""Simulate an N-sided die."""
u = unif_rand()
x = u * N
for n in range(1, N + 1):
if x <= n:
return n
def simulate_game(max_iter):
"""Gambler wins with prob > 0 and the game stops when either:
i) the gambler runs out of money, or
ii) house runs out of money, or
iii) max_iter reached.
Params:
max_iter (int): upper bound on number of rounds in game.
Returns:
curr_iter (int): num iterations reached at end of game.
Notes:
"game" is synonymous with "trial".
"""
# hardcoded vals to make parallelization easier...
gambler_limit=100
house_limit=200
gambler_win_prob=0.5
curr_iter = 0
# simulate game
while gambler_limit and house_limit and curr_iter < max_iter:
curr_iter += 1
u = unif_rand()
payout = 1 if u > gambler_win_prob else -1
gambler_limit += payout
house_limit += -payout
return curr_iter
def simulate_gambler(max_iter=1e6,
gambler_limit=100,
house_limit=200,
gambler_win_prob=0.5):
"""Gambler wins with prob > 0 and the game stops when either:
i) the gambler runs out of money, or
ii) house runs out of money, or
iii) max_iter reached.
"""
curr_iter = 0
gambler_val_path = [gambler_limit] # cumulative win/loss each round
while gambler_limit and house_limit and curr_iter < max_iter:
curr_iter += 1
u = unif_rand()
payout = 1 if u > gambler_win_prob else -1
gambler_limit += payout
house_limit += payout
gambler_val_path += [gambler_limit]
return gambler_val_path, curr_iter
def est_sample(n_bernoulli):
bernoulli_sum = np.sum([unif_rand() for _ in range(n_bernoulli)])
s = (bernoulli_sum - (n_bernoulli / 2)) * (1 / (np.sqrt(n_bernoulli / 12)))
return s
def estimate():
x, y = unif_rand(), unif_rand()
z = x**2 + y**2
return z <= 1
def sample_pt(d=2):
"""Sample a d-dimensional point in the cube."""
pt = [unif_rand() for _ in range(d)]
return pt