Sums of Dice

Part of the Statistics for ML section of Coddy's Machine Learning journey. Lesson 15 of 64.

Roll two dice and add them: 7 comes up six times as often as 2. Count the pairs of faces:

A 6 by 6 grid of the totals of two dice, first die down the side and second die across the top. The six cells that make 7 run corner to corner and are shaded; only one cell makes 2

A simulation agrees. Add the dice roll by roll, then count each total; value_counts lists the most common first:

rng = np.random.default_rng(2)
first = rng.integers(1, 7, size=3600)
second = rng.integers(1, 7, size=3600)
counts = pd.Series(first + second).value_counts()
print(counts.head(3))

This prints:

7    605
6    522
8    443
Name: count, dtype: int64

ax.bar(counts.index, counts) draws the whole tent:

A bar chart of 3600 rolls of two dice: the bars rise from about 100 at a total of 2 to a peak of about 600 at 7, then fall back to about 100 at 12

A bar chart like this is your first look at any label: its rare values are the ones a model will barely learn.

Challenge

Medium

In a role-playing game, damage is the total of two four-sided dice, 1 to 4 each. The program reads how many attacks; the starter rolls into first and second and labels the chart.

Count each damage total.
Print the most likely damage and its share of the attacks, to 3 decimals.
Draw the counts as bars, one per total, and show them.

For 16 attacks, too few to trust:

Most likely damage: 6, share 0.312

A bar chart titled Damage Rolls for 16 attacks: bars at 3, 5, 6, 7 and 8, the tallest at 6 with 5 rolls

Then Coddy describes your chart. With more attacks, the peak settles.

Try it yourself

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

rolls = int(input())

# Don't change the lines below
rng = np.random.default_rng(4)
first = rng.integers(1, 5, size=rolls)
second = rng.integers(1, 5, size=rolls)

fig, ax = plt.subplots()
ax.set_title("Damage Rolls")
ax.set_xlabel("Damage")
ax.set_ylabel("Rolls")

# Write your code below

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Statistics for ML

3Probability by Simulation

Probability as Frequency The Law of Large NumbersSums of DiceExpected Value Conditional Probability Recap: Dice Stall Odds

6Relationships

Reading Scatter Plots Correlation Correlation Matrix Correlation Heatmaps Correlation Is Not Cause Recap: Ice Cream and Sun

9Feature Scaling

Why Scale Features Min-Max Scaling Standardization StandardScaler Recap: Climbing Partners

12Final Challenges

Train Delays Air Quality Wine Chemistry Clinic Survey

Practice on your own: Online Python compiler