Project 2: Is This Game Rigged? A Loot Box Simulator

Build a simulator that estimates rare drop probabilities.

Project Overview

Attribute Value
Difficulty Level 1: Beginner
Time Estimate Weekend
Main Language Python
Alternative Languages R, JavaScript
Knowledge Area Probability
Tools Random generator
Main Book “Introduction to Probability” by Blitzstein & Hwang

What you’ll build: A simulator that opens loot boxes thousands of times and estimates drop rates.

Why it teaches stats: Monte Carlo shows how probabilities emerge from repeated trials.

Core challenges you’ll face:

  • Modeling random outcomes
  • Running large trials efficiently
  • Interpreting convergence

Real World Outcome

You will estimate drop rates and show confidence intervals.

Example Output:

$ python lootbox.py --trials 100000
Estimated legendary drop: 0.98%
95% CI: [0.92%, 1.04%]

Verification steps:

  • Compare estimates at different trial counts
  • Check convergence behavior

The Core Question You’re Answering

“How many trials do I need to trust a probability estimate?”

This is applied probability in action.

Concepts You Must Understand First

Stop and research these before coding:

  1. Law of large numbers
    • Why do estimates stabilize with more trials?
    • Book Reference: “Introduction to Probability” Ch. 5
  2. Confidence intervals
    • How do you compute uncertainty around an estimate?
    • Book Reference: “OpenIntro Statistics” Ch. 4
  3. Random variables
    • How does a Bernoulli trial model a drop?
    • Book Reference: “Introduction to Probability” Ch. 2

Questions to Guide Your Design

  1. Drop model
    • Will you use a single probability or multiple tiers?
    • How will you store outcomes?
  2. Visualization
    • Will you plot convergence over trials?
    • How will you show distribution of outcomes?

Thinking Exercise

Rare Drops

If the true drop rate is 1%, how many trials would you need to expect about 100 drops?

Questions while working:

  • Why are rare events noisy?
  • How does variance scale with trials?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What is the law of large numbers?”
  2. “Why do rare events require many trials?”
  3. “What is a confidence interval?”
  4. “How do you simulate Bernoulli trials?”
  5. “Why might early estimates be misleading?”

Hints in Layers

Hint 1: Starting Point Start with a simple Bernoulli model.

Hint 2: Next Level Track running estimates over time.

Hint 3: Technical Details Compute confidence intervals using normal approximation.

Hint 4: Tools/Debugging Plot estimate vs trial count to see convergence.

Books That Will Help

Topic Book Chapter
LLN “Introduction to Probability” Ch. 5
Confidence intervals “OpenIntro Statistics” Ch. 4
Bernoulli trials “Introduction to Probability” Ch. 2

Implementation Hints

  • Use vectorized random generation for speed.
  • Keep results reproducible with a seed.
  • Report both estimate and uncertainty.

Learning Milestones

  1. First milestone: You can simulate random drops.
  2. Second milestone: You can estimate probabilities reliably.
  3. Final milestone: You can explain confidence in estimates.