Dice Rolling Probability

dice.py

import matplotlib.pyplot as plt
import numpy as np

def rolld20():
    return np.random.randint(1, 21)

def rolld20adv():
    return max(np.random.randint(1, 21),np.random.randint(1, 21))

def rolld20dis():
    return min(np.random.randint(1, 21),np.random.randint(1, 21))

def rollfate():
    return np.sum(np.random.randint(-1, 2, size=4))

def rollnd6(n):
    return np.max(np.random.randint(1, 7, size=n))

def rollmax10(n):
    return max(np.random.randint(1, 11, size=n))

def sum_two_largest_nd10(n):
    if n < 2:
        raise ValueError("n must be at least 2 to sum the two largest numbers")

    rolls = np.random.randint(1, 11, size=n)  # Roll n 10-sided dice
    rolls.sort()  # Sort the rolls
    return rolls[-1] + rolls[-2]  # Sum the two largest values

def roll_target(sides, num_die, target, explode=False):
    results = np.random.randint(1, sides + 1, size=num_die)  # Roll num_die dice with sides
    
    def adjust_result(result):
        if result == 1:
            return -1
        elif result >= target:
            return 1
        else:
            return 0

    total = np.sum([adjust_result(result) for result in results])
    if explode:
        num_explode_die = np.count_nonzero(results == sides)  # Count the number of results equal to sides
        if num_explode_die > 0:
            exploded_total = roll_target(sides, num_explode_die, target, explode=True)
            total += exploded_total

    return total

def propCurve(dice_func, num_rolls):
    results = [dice_func() for _ in range(num_rolls)]
    unique_results, counts = np.unique(results, return_counts=True)
    return unique_results, counts

def propCurveVar(dice_func, num_rolls, dice_var):
    results = [dice_func(dice_var) for _ in range(num_rolls)]
    unique_results, counts = np.unique(results, return_counts=True)
    return unique_results, counts

def propCurveTarget(num_rolls, sides, num_die, target, explode=False):
    results = [roll_target(sides, num_die, target, explode) for _ in range(num_rolls)]
    unique_results, counts = np.unique(results, return_counts=True)
    return unique_results, counts

def plot_save(desc, filename):
    plt.xlabel('Result')
    plt.ylabel('Frequency')
    plt.title(desc)
    plt.legend()
    plt.savefig(filename)
    plt.show()

    plt.figure()

def main():
    num_rolls = 100000

    plt.figure()
    
    if False: # D20
        unique_results, counts = propCurve(rolld20, num_rolls)
        plt.plot(unique_results, counts, color='red', label='Rolld20')

        unique_results, counts = propCurve(rolld20adv, num_rolls)
        plt.plot(unique_results, counts, color='green', label='Rolld20Adv')

        unique_results, counts = propCurve(rolld20dis, num_rolls)
        plt.plot(unique_results, counts, color='blue', label='Rolld20Dis')
        
        plot_save("d20", "dice_d20.png")
    
    if False: # Fate
        unique_results, counts = propCurve(rollfate, num_rolls)
        plt.plot(unique_results, counts, color='black', label='RollFate')

        plot_save("Fate Dice", "dice_fate.png")

    if False: # nd6
        unique_results, counts = propCurveVar(rollnd6, num_rolls, 2)
        plt.plot(unique_results, counts, color='red', label='Roll2d6')

        unique_results, counts = propCurveVar(rollnd6, num_rolls, 4)
        plt.plot(unique_results, counts, color='green', label='Roll4d6')

        unique_results, counts = propCurveVar(rollnd6, num_rolls, 10)
        plt.plot(unique_results, counts, color='blue', label='Roll10d6')

        plot_save("Sum D6", "dice_sum_d6.png")

    if True: # Roll max 10
        
        colors = ["#FF0000","#FF7F00","#FFFF00","#00FF00","#0000FF"]

        for i, col in enumerate(colors):
            num_die = (i*2)+1
            unique_results, counts = propCurveVar(rollmax10, num_rolls, num_die)
            plt.plot(unique_results, counts, color=col, label=f'Roll {num_die}d10')

        plot_save("Max D10", "dice_max_d10.png")

    if True: # Roll max 10 sum2
        
        colors = ["#FF0000","#FF7F00","#FFFF00","#00FF00","#0000FF"]

        for i, col in enumerate(colors):
            num_die = (i*2)+2
            unique_results, counts = propCurveVar(sum_two_largest_nd10, num_rolls, num_die)
            plt.plot(unique_results, counts, color=col, label=f'Roll {num_die}d10')

        plot_save("Sum Max 2D10", "dice_summax_2d10.png")
    
    if False: # D10 Target Explode vs Not
        # First, plot with explode=False and slightly darker colors
        sides = 10
        target = 6
        rolls = [1, 3, 5, 7, 10]

        explode = False        
        colors = ['darkred', 'darkorange', 'darkgoldenrod', 'darkgreen', 'darkblue']
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides}')

        # Then, plot with explode=True and slightly brighter colors
        explode = True
        colors = ['red', 'orange', 'gold', 'limegreen', 'dodgerblue']
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides} (Explode)')
        
        plot_save("D10 Target Explode vs Not", "dice_target_d10.png")
    
    if False: # D6 Target Explode vs Not
        # First, plot with explode=False and slightly darker colors
        sides = 6
        target = 4
        rolls = [1, 3, 5, 7, 10]

        explode = False        
        colors = ['darkred', 'darkorange', 'darkgoldenrod', 'darkgreen', 'darkblue']
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides}')

        # Then, plot with explode=True and slightly brighter colors
        explode = True
        colors = ['red', 'orange', 'gold', 'limegreen', 'dodgerblue']
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides} (Explode)')

        plot_save("D6 Target Explode vs Not", "dice_target_d6.png")

    if False: # D6 Target with vary Target number (always explode)        
        sides = 6
        explode = True
        rolls = [1, 3, 5, 7, 10]

        target = 3
        colors = ['darkred', 'darkorange', 'darkgoldenrod', 'darkgreen', 'darkblue']
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides}  (Explode)')

        colors = ['red', 'orange', 'gold', 'limegreen', 'dodgerblue']
        target = 4
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides} (Explode)')

        colors = ['#FF6666', '#FFB266', '#FFD700', '#CCFF99', '#ADD8E6']
        target = 5
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides} (Explode)')            
        
        plot_save("D6 Target with vary Target number (always explode)", "dice_target_d6_shift.png")

    if False: # D10 Target with vary Target number (always explode)        
        sides = 10
        explode = True
        rolls = [1, 3, 5, 7, 10]

        target = 5
        colors = ['darkred', 'darkorange', 'darkgoldenrod', 'darkgreen', 'darkblue']
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides}  (Explode)')

        colors = ['red', 'orange', 'gold', 'limegreen', 'dodgerblue']
        target = 6
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides} (Explode)')

        colors = ['#FF6666', '#FFB266', '#FFD700', '#CCFF99', '#ADD8E6']
        target = 7
        for i, num_die in enumerate(rolls):
            unique_results, counts = propCurveTarget(num_rolls, 10, num_die, target, explode)
            plt.plot(unique_results, counts, color=colors[i], label=f'Target {target} {num_die}d{sides} (Explode)')            
        
        plot_save("D10 Target with vary Target number (always explode)", "dice_target_d10_shift.png")

if __name__ == "__main__":
    main()