SWADE: odds of rolling target number for wild cards, based on trait die

swade_target_number_odds.py

#!/usr/bin/env python3
MAX = 16
TRAIT_DICE = (4, 6, 8, 10, 12)
WILD_DIE = 6


def main():
    # CSV header
    print(','.join([''] + [f'{i}' for i in range(1, MAX+1)]))

    for trait_die in TRAIT_DICE:
        probs = [0 for _ in range(MAX)]

        # recursive
        def _handle_rolls(roll_trait, prev_trait, roll_wild, prev_wild, prev_prob):
            nonlocal trait_die, probs

            current_prob = prev_prob
            trait_rolls = [0]
            wild_rolls = [0]
            if roll_trait:
                current_prob /= trait_die
                trait_rolls = range(1, trait_die+1)
            if roll_wild:
                current_prob /= WILD_DIE
                wild_rolls = range(1, WILD_DIE+1)

            for trait_roll in trait_rolls:
                for wild_roll in wild_rolls:
                    trait_value = trait_roll + prev_trait
                    wild_value = wild_roll + prev_wild

                    if trait_value >= MAX or wild_value >= MAX:
                        # end case: we hit the max with one die or the other
                        for i in range(MAX):
                            probs[i] += current_prob

                    elif trait_roll < trait_die and wild_roll < WILD_DIE:
                        # simple case: take the max and update the array
                        value = max(trait_value, wild_value)
                        for i in range(value):
                            probs[i] += current_prob

                    elif trait_roll == trait_die and wild_roll < WILD_DIE:
                        # trait explodes
                        _handle_rolls(True, trait_value, False, wild_value, current_prob)

                    elif trait_roll < trait_die and wild_roll == WILD_DIE:
                        # wild explodes
                        _handle_rolls(False, trait_value, True, wild_value, current_prob)

                    elif trait_roll == trait_die and wild_roll == WILD_DIE:
                        # both explode
                        _handle_rolls(True, trait_value, True, wild_value, current_prob)

        _handle_rolls(True, 0, True, 0, 1.0)

        # CSV row
        print(','.join([f'd{trait_die}'] + [f'{100*p:.1f}' for p in probs]))


if __name__ == '__main__':
    main()