Bunny problem: https://uli.rocks/p/bunny

bunny.py

N = 100

def guess(P, j):
  # after setting P[j] = 0 we have removed P[j] probability mass from
  # the distribution, so the new sum is 1-P[j]. Dividing everything by
  # 1-P[j] fixes this. (a minor detail, instead of 1 we use sum(P) for
  # numerical stability since sum(P) isn't exactly 1)
  s = sum(P) - P[j]
  return [
    0 if i == j else P[i] / s
    for i in range(N)
  ]


def jumps(P):
  Pn = P.copy()
  Pn[0] = P[1]*0.5
  Pn[N-1] = P[N-2]*0.5

  for j in range(1, N-1):
    Pn[j] = 0.5*P[j-1] + 0.5*P[j+1]

  return Pn


import random
def argmax(l):
  return max(range(len(l)), key=lambda i: l[i])

def play():
    P = [1/N] * N

    hole = random.randint(0, N-1)
    t = 0
    while True:
      t += 1
      j = argmax(P)
      # uncomment for random guessing strategy
      # j = random.randint(0, N-1)
      if j == hole:
        print(f'Found the bunny in hole {j} after {t} tries!')
        break
      else:
        #print(f'[{t}] Guessed {j} with P[{j}] = {P[j]:.4f} (true is {hole})')
        # wrong hole, update our beliefs
        P = guess(P, j)
        P = jumps(P)

        # the bunny moves!
        if    hole == 0:   hole += 1
        elif  hole == N-1: hole -= 1
        else:              hole += random.choice([-1, 1])

    return t


r = [play() for _ in range(10000)]

import statistics as stats
mean, median, stdev = stats.mean(r), stats.median(r), stats.stdev(r)
print(f'mean: {mean} median: {median} stddev {stdev}')