[z_beeblebrox]

My simple Python Monte Carlo script gave me an average of 0.521408 (or 0.52141 rounded to 5 digits) in ~5e9 iterations (10 miles of hiking worth).

Code is below:

import numpy as np

iterations = 10000000

avg = 0

for i in range(100000):
    for i in range(iterations):
        pos = np.random.rand(4)
        length = np.sqrt((pos[0]-pos[1])**2+(pos[2]-pos[3])**2)
        avg = (avg*i + length)/(i+1)
    with open("test.txt", "a") as f:
        f.write(str(avg)+'\n')

import numpy as np

f = np.loadtxt('test.txt')
print(np.average(f))
print(len(f))

I split it into two scripts just so I could stop the computation whenever without altering the result.

Edit: Reps to whoever finds the bug in my code and explains what it does.