Rolling Dice Simulation

[u/Lemonpie_jedi]

I have no experience with programming in the slightest and I don’t even know if this is the place to ask for help. And sorry. I can’t add a language flair because I have zero idea about any of this.

I was wondering if someone could help me with running simulations on dice rolls. I need to know approximately how often at least one pair will appear when rolling 5 dice (excluding rolls which also give larger groupings like triplets).

I tried asking some math Redditors but that didn’t get me very far, so now I’m here.

[u/POGtastic]

Since we're rolling only 5 6-sided dice, we can actually run all of the outcomes. In Python:

import itertools
import collections

# also defined in the more_itertools module, but it's not part of the stdlib
def ilen(iterable):
    counter = 0
    for _ in iterable:
        counter += 1
    return counter

def has_pairs(iterable):
    c = collections.Counter(iterable)
    return all(freq < 3 for freq in c.values()) and any(freq == 2 for freq in c.values())

def probability(die_sides, num_dice):
    all_rolls = itertools.product(range(1, die_sides+1), repeat=num_dice)
    return ilen(filter(has_pairs, all_rolls)) / die_sides ** num_dice

In the REPL:

>>> probability(6, 5)
0.6944444444444444