Rolling two dice and tabulating outcomes

Question 1

There are 4 changes required to make your code work (other than the minor typos already mentioned in the comments):

Firstly, you only add 1 to results[sum] if first == second. So, results[sum] = results[sum] + 1 should not be under the if statement:

if(first == second):
    number_of_double_dice = number_of_double_dice + 1

results[sum] = results[sum] + 1

Secondly, for some reason that I don't yet know what, "{0:d} - {1:d}{2:0.4f}%" should be changed to "{0:d} - {1:d} {2:0.4f}%" (notice the added space between the second } and the third {).

Thirdly, when calculating the percentage of total for the number of doubles, you have forgotten to divide by count. So, it should be:

print("Doubles- {0:d}-{1:0.6f}%".format(number_of_double_dice,       number_of_double_dice/count*100))

Fourthly, the line where you print the number of doubles needs to be put outside the for statement because you only want to print it once; not on every iteration of the for statement:

for x in range (2,13):
    print "{0:d} - {1:d} {2:0.4f}%".format(x, results[x], results[x] / count * 100)

print("Doubles- {0:d}-{1:0.6f}%".format(number_of_double_dice, number_of_double_dice / count *100))

So your code should look like this: https://gist.github.com/s16h/b4c2bc791880b61418b2.

I have quickly re-written your program; I have tried to keep your logic and way of doing things:

from __future__ import division
import random
import sys

def dice_roll():
    return random.randint(1, 6)

def number_of_rolls():
    return int(raw_input('Enter the number of rolls: '))

def simulate(number_of_times):
    counter = {n : 0 for n in range(2, 13)}
    doubles = 0

    for i in range(number_of_times):
        first_dice = dice_roll()
        second_dice = dice_roll()
        total = first_dice + second_dice

        doubles += 0 if first_dice != second_dice else 1
        counter[total] += 1

    return counter, doubles

def main():
    rolls = number_of_rolls()
    counter, doubles = simulate(rolls)  
    total = sum(counter.values())

    for total, count in counter.items():
        print("{} - {} {:0.4f}%".format(total, count, count / rolls * 100))

    print("Doubles - {} - {:0.6f}%".format(doubles, doubles / rolls * 100))

if __name__ == '__main__':
    sys.exit(main())

I hope this helps.

Question 2

Here is a better version of your code:

import random

num = int(input('How many rolls do you want to simulate? '))

rolls = {}
for k in range(2, 13):
        rolls[k] = 0

doubles = 0

for k in range(num):
        first = random.randint(1, 6)
        second = random.randint(1, 6)
        if first == second:
                doubles+=1
        rolls[first+second]+=1

for k in rolls:
        print('%d - %d %f%%' %(k, rolls[k], float(rolls[k])/float(num)*100))

print('Doubles - %d - %f%%' %(doubles, float(doubles)/float(num)))

This runs as:

How many rolls do you want to simulate? 10000
2 - 286 2.860000%
3 - 571 5.710000%
4 - 788 7.880000%
5 - 1066 10.660000%
6 - 1393 13.930000%
7 - 1731 17.310000%
8 - 1470 14.700000%
9 - 1034 10.340000%
10 - 840 8.400000%
11 - 541 5.410000%
12 - 280 2.800000%
Doubles - 1669 - 0.166900%

Your problem was that you were only adding one to the sum if there were doubles, which was why you only had results for even rolls. You also had {{1:0.6f}% which should've been {1:0.6f}%.

Question 3

import random
def roll_two_dice():   
    return random.randint(1, 6)*2

Question 4

import random
def problem2_6(): 
random.seed(82)
    for i in range(100):
        k=random.randint(1,6)
        for j in range(100):
            a=random.randint(1,6)
            s=a+k
            print(s)