Morty Express Challenge 🚀

Save 1000 Morties from the Citadel to Planet Jessica!

🎯 Key Findings - The Hot Hand Effect

After extensive data collection and analysis, we discovered the winning pattern:

ALL THREE PLANETS exhibit a strong "hot hand" effect - a Markov chain behavior where the probability of success depends heavily on the previous trip's outcome:

Planet	After WIN	After LOSS	Difference
"On a Cob" Planet	70.8%	29.7%	41.1%
Cronenberg World	73.6%	26.5%	47.1%
The Purge Planet	75.2%	26.8%	48.4%

The Pattern Intensifies with Streaks

Success probability increases dramatically with consecutive wins:

• After 1 win: ~75%
• After 2 wins: ~80%
• After 3 wins: ~88%
• After 4 wins: ~91%
• After 5+ wins: 93%

The Purge Planet after 5 consecutive wins: 92.8% success rate!

What About Temporal Patterns?

The Purge Planet DOES have a ~200-trip wave cycle, but:

• Each episode starts at a random phase in the cycle
• Phase detection is unreliable with limited data
• The hot-hand effect is more reliable and exploitable

The "Stable" Planets

"On a Cob" and Cronenberg World appear random (~50% overall), but they too follow the hot-hand pattern:

🏆 Ultimate Strategy - Variable Risk Management

The winning approach combines three insights:

1. Exploit Hot Hands: Stay with planets that just won
2. Avoid Cold Streaks: Switch away from planets that just lost
3. Variable Morty Count: Adjust risk based on confidence

npm run ultimate

Strategy Logic

High Confidence (85%+, 3+ win streak):
  → Send 3 Morties (maximize gains)

Medium Confidence (60-85%):
  → Send 2 Morties (balanced approach)

Low Confidence (<60%):
  → Send 1 Morty (probe/minimize losses)

This achieves 90%+ success rates by:

• Maximizing gains during hot streaks
• Minimizing losses during uncertainty
• Never blindly trusting predictions

📊 Data Collection & Analysis

Collect Comprehensive Data

# Collect data from all 3 planets (multiple iterations)
npm run collect-all-planets

# Analyze patterns
npm run analyze-all-planets

Specialized Analysis Scripts

# History-dependent analysis (Markov chains - THE KEY DISCOVERY!)
npm run history

# Modulo pattern analysis (even/odd, etc.)
npm run analyze-slow

# Frequency analysis (wave detection)
npm run frequency

# Granular trip-by-trip analysis
npm run granular

Generate Visualizations

# Create charts and heatmaps
npm run visualize

# Granular trip-by-trip visualization
npm run visualize-granular

🔬 Analysis Results

Planet Comparison

Overall success rates (deceptively close to 50%):

• "On a Cob" Planet: 50.5%
• Cronenberg World: 50.0%
• The Purge Planet: 51.7%

But the sequence matters! The hot-hand effect explains the 90%+ achievement.

Granular Trip-by-Trip Analysis

Cycle Analysis

The Purge Planet's wave pattern, overlaid across multiple iterations, shows the random phase offset problem.

🎮 Run Strategies

Basic Strategies

# Original multi-armed bandit approach
npm run dev

# Optimized with wave detection
npm run optimized

# Adaptive wave strategy
npm run adaptive

Advanced Strategies

# Hot-hand exploitation (simple)
npm run hot-hand

# Ultimate strategy (hot-hand + variable risk)
npm run ultimate

🧪 Other Patterns Investigated

We tested many hypotheses:

• ❌ Even/Odd trip numbers: No significant pattern
• ❌ Modulo patterns (3, 4, 5, 10): No exploitable cycles
• ❌ Cross-planet correlation: Planets are independent
• ❌ Group size effects: Insufficient data (always sent 3)
• ❌ Temporal patterns in Cob/Cronenberg: Too noisy
• ✅ Hot-hand effect: CONFIRMED ACROSS ALL PLANETS

📈 The Math Behind 90%+

With the hot-hand strategy:

1. Start by probing all 3 planets (1 Morty each)
2. One will likely win first (~67% chance someone wins)
3. That planet now has 75% success for next trip
4. If it wins again: 80% → 88% → 91% → 93%
5. Ride the streak with 3 Morties per trip
6. When it loses, probe other planets with 1 Morty
7. Find the next hot hand and repeat

Expected outcome:

• Long winning streaks with 3 Morties (maximized gains)
• Short losing probes with 1 Morty (minimized losses)
• Result: ~90%+ overall success rate

🔍 Understanding the Challenge

Rick's hint was key: "although the average survival rate is the same, the probabilities of the 3 planets are changing with time, some faster than others..."

This wasn't about temporal patterns in trip numbers - it was about state-dependent probabilities where each trip's outcome affects the next!

The Planets

• Planet 0: "On a Cob" Planet - Everything's on a cob (uniform chaos)
• Planet 1: Cronenberg World - Mutated randomness
• Planet 2: The Purge Planet - Annual purge cycle (plus hot-hand effect)

Good luck saving those Morties! 🎯

Notes

Built with TypeScript and Python for visualization. All analysis code is in src/ and visualization scripts are Python files in the root directory.