A multi-generational family card game that has captivated players for decades - now with computational analysis to discover just how special that "once in a lifetime" moment truly is!
This repository contains the computational analysis of a beloved family solitaire game passed down through generations. What started as a friendly family debate about the difficulty of achieving victory led to one of the most extensive card game probability studies ever conducted - with over 700 million simulated games!
The catalyst? A confident family member claimed to have won "several times" and found it "boring." With 40+ years of gameplay experience and a background in quantitative analysis, the challenge was set: prove just how extraordinary a win truly is.
Once In A Lifetime is a solitaire card game where the ultimate goal is to consolidate all 52 cards into a single stack. The name perfectly captures the rarity of this achievement - as our extensive computational analysis reveals!
- Start with a standard 52-card deck, shuffled
- Your goal: Get all cards into one stack
-
Initial Play: Draw and place the first card face-up
♠️ -
Draw and Compare: Draw the next card from the deck
-
Matching Logic: The new card is compared to existing stack tops using these rules:
- Cards match if they have the same rank OR same suit
- New cards can match with stacks in two specific positions only:
- Adjacent stack (immediately to the left)
- Stack exactly 3 positions back (3 positions to the left)
Position Rule Example (with stacks Z, C, Y, X from left to right):
Z C Y X ♠️K ♦️5 ♣️7 [New Card: ♠️A] ♠️A can match with: ✅ Y (adjacent): ♠️A vs ♣️7 = No match ✅ Z (3 back): ♠️A vs ♠️K = Same suit! Match! ❌ C (2 back): Not allowed by rules -
Player Choice: If both positions have matches, player chooses one (but not both)
-
Stack Consolidation: When cards match, place the new card on top:
Before: ♠️K ♦️5 ♣️7 After: ♠️A ♦️5 ♣️7 ♠️K -
Cascading Matches: After any match, check if stacks can now merge using the same position rules
-
No Match Rule: If no valid match exists (adjacent OR 3-back), create a new stack to the right
-
Scoring: Continue until all 52 cards are drawn. Count your final stacks - fewer is better!
| Stacks | Achievement Level | Rarity |
|---|---|---|
| 🏆 1 stack | ONCE IN A LIFETIME! | Extraordinarily Rare |
| 🥈 2 stacks | Legendary | 0.18% of games |
| 🥉 3 stacks | Exceptional | 13.3% of games |
| 📊 4-5 stacks | Good Game | 78% of games |
| 📈 6+ stacks | Keep Trying! | 8.3% of games |
# Run the latest, most complete version
python OiaLver0.0.5.py
# Try the clean, object-oriented version
python GoodOne2.py
# These will run 10,000 simulations by default# For serious statistical analysis
julia OnceInALifetime.jl 1000000 # 1 million games
julia OnceInALifetime.jl 1000000000 # 1 billion games!
# Standard version with plotting
julia OiaLver0.0.5.jl- Python:
matplotlibfor visualizations - Julia:
Random,Plotspackages
Using high-performance Julia code, we conducted one of the largest solitaire simulations ever:
- 700+ million games simulated
- Multiple implementations to verify accuracy
- Statistical analysis of score distributions
- Performance optimization achieving 240,000+ games/second
After 700 million simulations:
- 🏆 Wins achieved: 0
- 📊 Upper bound probability: Less than 1 in 700 million
- 🎯 Conclusion: "Once In A Lifetime" is perfectly named!
| Implementation | Games/Second | Matching Logic |
|---|---|---|
| Julia (OnceInALifetime.jl) | ~240,000 | Correct: adjacent + skip-two only |
| Python (GoodOne2.py) | ~35,000 | Correct: adjacent + skip-two only |
🎯 2 stacks: ████ 0.18% (1,830 games) - LEGENDARY!
📊 3 stacks: ████████████████ 13.28% - Exceptional
📈 4 stacks: ████████████████████████████████████████ 46.50% - Great!
📈 5 stacks: ████████████████████████████ 31.73% - Good!
📉 6+ stacks: ██████ 8.31% - Keep playing!
GoodOne2.py— Clean, object-oriented Python. Correctly checks only adjacent and skip-two positions.OnceInALifetime.jl— High-performance Julia simulation engine. Used for the 700M-game run.
All other implementations have been moved to deprecated/. They contain bugs in the matching logic — most commonly checking all positions within 3 instead of only adjacent and skip-two. See deprecated/README.md for details on each file's specific bug.
OnceInALifetime.qmd— Complete narrative and analysisCLAUDE.md— AI development guidance
from GoodOne2 import main
main(iterations=1) # Play one game and see your score!main(iterations=100000) # Analyze 100K gamesmain() # Run until first win (could take a VERY long time!)- Restrictive Position Rules: Cards can ONLY match adjacent OR exactly 3 positions back - no other positions allowed
- Limited Matching Options: Only rank OR suit matching
- Sequential Dependencies: Card order matters tremendously
- Cascade Complexity: Matches can trigger chain reactions, but still follow strict position rules
- Choice Constraints: When both positions have matches, choosing one eliminates the other opportunity
- Probabilistic Convergence: Getting close requires multiple rare events aligning perfectly
- 52! possible deck arrangements: 8.07 × 10⁶⁷ combinations
- Complex state space: Each card placement creates branching possibilities
- Convergence requirements: Multiple perfect matching sequences needed
- Statistical significance: 700M+ samples provide robust probability bounds
Our computational analysis definitively proves that achieving a "Once In A Lifetime" victory is:
✨ Extraordinarily rare - Less than 1 in 700 million chance
🎯 Perfectly named - The game title captures the true rarity
🧬 Statistically fascinating - A beautiful example of complex probability
👨👩👧👦 Family legend confirmed - 40+ years of gameplay experience validated!
While winning is incredibly rare, this makes the game:
- Endlessly replayable - Every game offers hope!
- Statistically fascinating - Each attempt contributes to understanding
- Family bonding material - Shared challenge across generations
- Computational showcase - Demonstrates the power of simulation
- Mathematical beauty - Probability theory in action
Feel free to:
- 🔧 Optimize the algorithms further
- 📊 Add new visualization features
- 🧪 Experiment with rule variations
- 📈 Extend the statistical analysis
- 🎮 Create interactive versions
This family card game simulation is shared freely - may it bring joy and statistical wonder to your household too!
"The best part about a 1-in-700-million chance? It's not zero!" 🎲✨