import random
import statistics
 
def reflected_walk_hits(num_steps=100_000, trials=40):
    counts = []
    for _ in range(trials):
        x = 0
        hits = 1  # start at 0
        for _ in range(num_steps):
            step = random.choice([-1, 1])
            if x == 0 and step == -1:
                x = 0
            else:
                x += step
            if x == 0:
                hits += 1
        counts.append(hits)
    return statistics.mean(counts), statistics.stdev(counts)
 
mean_hits, stdev_hits = reflected_walk_hits()
print(f"Average hits to 0: {mean_hits:.2f} ± {stdev_hits:.2f}")

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