CODEWITHSUNDEEP
pythonpython-2.7simulationmontecarlo
lmurdock12
lmurdock12

Reputation: 1021

Simple Yahtzee simulation not giving proper result?

I am working through the MIT OpenCourseWare intro to computer programming course and I am not sure if I am solving a simple simulation the right way.

  1. What is the probability of rolling a Yahtzee! on the first roll? That is, what is the probability of rolling five 6-sided dice, and having them all display the same number?
  2. Write a Monte Carlo simulation to solve the above problem (the Yahtzee problem), and submit your code as

So the probability of rolling a Yahtzee is 1/1296 or about .077%

Here is my code to run the simulation:

import random

def runYahtzee(numTrials):
    """Runs the classes version of the yahtzee simulation"""

    success = 0
    for i in range(numTrials):

        dices = []
        for i in range(6):
            dices.append(random.randrange(1,7))
        #print dices

        state = True
        for dice in dices:
            if dice != dices[0]:
                state = False
        if state == True:
            print "You got a Yahtzee"
            print dices
            success += 1

    print "numTrials is: " + str(numTrials)
    print "Success is: " + str(success)
    rate = float(success)/numTrials
    return rate

runYahtzee(10000000)

Running the program multiple times, I get around .0001258 each time. This is .012%, but the actual probability is around .077%. Is there something that I am doing wrong here?

Upvotes: 1

Views: 856

Answers (2)

Hugh Bothwell
Hugh Bothwell

Reputation: 56684

Here's how I'd write it (Python 3):

from collections import Counter
from random import randint

def roll():
    return randint(1, 6)

def is_yahtzee(num_dice = 5):
    first = roll()
    return all(roll() == first for _ in range(1, num_dice))

def montecarlo(fn, num_trials):
    return Counter(fn() for _ in range(num_trials))

def main():
    num_trials = 10000000
    result = montecarlo(is_yahtzee, num_trials)
    prob = result[True] / num_trials
    print(
        "After {} trials, probability of Yahtzee is {:0.5f}%"
        .format(num_trials, 100. * prob)
    )

if __name__ == "__main__":
    main()

which runs like

After 10000000 trials, probability of Yahtzee is 0.07605%

Note that keeping your functions short generally makes them easier to understand and test.

Upvotes: 0

Prune
Prune

Reputation: 77860

What you're doing wrong is rolling 6 dice instead of 5.

0.001258 * 6 = 0.0007548

... which is close to your 0.077%

Change your loop:

    for i in range(5):

BTW, the plural is dice; the singular is die. dices is wrong, unless you're trying to be amusing. In that case, you can use the singular "douse" ... never say die!

Upvotes: 5

Related Questions