Simple Yahtzee simulation not giving proper result?

Question

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.

2. 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?
3. 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?

Answer 1

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):

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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!