Monte Carlo dart simulator

Question

I've been trying to make a dart simulator using the Monte Carlo simulation in Python 3. So far, I have written the following code:

import random
import math

n = (input("Enter the number of darts you have. "))
count = 1
circleval = 0
squareval = 0
while count <= n:
    y = 2*random.random()*2-1
    x = 2*random.random()*2-1
    if math.sqrt((x-1)**2+(y-1)**2)<=1:
        circleval+=1
        squareval+=1
    else:
        squareval+=1
    count+=1

print("Pi is " + 4*(1.*circleval/squareval))

However, when I run this I reccive the following error message:

TypeError: '<=' not supported between instances of 'int' and 'str'

Answer 1

The main reason why this does not work is because:

n = (input("Enter the number of darts you have. "))

will put a string into n, we can solve this with:

n = int(input("Enter the number of darts you have. "))

and:

print("Pi is " + 4*(1.*circleval/squareval))

expects a string, but you do not provide one, we can solve this with:

print("Pi is " + str(4*(1.*circleval/squareval)))

But that being said, the program is still incorrect: it gives 0.773 as output for Pi, which is clearly wrong.

The main problem is your sampling: you want to generate numbers between -1 and 1, but you generate numbers between -1 and 3. In your distance computations, you then use x-1 and y-1 shifting it to the -2 to 2 domain, but that is still too large. Furthermore the code not very elegant.

from random import random

n = int(input("Enter the number of darts you have. "))
c = 0
for i in range(n):
    x = 2*random()-1
    y = 2*random()-1
    if x*x + y*y <= 1:
        c += 1
print("Pi is %s" % (4.0*c/n))

for n=100000, this has given me 3.14368 (although it might vary of course between several simulations).