dnd_dice.py

#!/usr/bin/env python
# Answer to the Fiddler On the Proof newsletter for Jan 12, 2024

from fractions import Fraction
from itertools import combinations

dice_values = [4, 6, 8, 10, 12, 20]

# Part 1
probs = []
for pair in combinations(dice_values, 2):
    # The probability of both getting the same value is 1/<larger of the two dice>
    probs.append(Fraction(1, max(pair)))
    
result = sum(probs)/len(probs) 
print("Part 1", result, float(result))

# Part 2
probs = []
for triple in combinations(dice_values, 3):
    # The probability is the 1/<product of the two largest dice sizes>
    in_order = list(sorted(triple))
    probs.append(Fraction(1, in_order[1]*in_order[2]))
    
result = sum(probs)/len(probs) 
print("Part 2", result, float(result))