If a number of hens in a circle peck either left or right, what is the expected number of unpecked hens at the end?

unpecked_hens.py

import numpy as np
import random

number_of_hens = 100
repeats = 1000 # repeat many times so that we get some decent statistics

sums = []
for _ in range(repeats): 
    hens = np.zeros(number_of_hens, dtype=bool) # reset an array of False
    
    # for each hen, peck either left or right
    for i, hen in enumerate(hens):
        if random.random() < 0.5: # random() returns a number between 0 and 1
            index = (i-1) % number_of_hens # pecks left
        else:
            index = (i+1) % number_of_hens # pecks right
        hens[index] = True

    sums.append(number_of_hens - hens.sum()) # add "number of unpecked hens" to a list. (array_of_bools).sum() sums to ints
    
print(f"The mean is {np.mean(sums)}, with a standard error of {np.std(sums) / np.sqrt(number_of_hens):.2f}")