🎲 Multi-deck BlackJack Simulator (Monte Carlo)

This project simulates and analyzes the game of Blackjack (21) using Monte Carlo methods.
It evaluates different strategies by simulating large numbers of games, computing expected values (EV), win/draw/loss rates, and visualizing performance.

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Table of Contents

1. Overview
2. Features
3. Project Structure
4. Installation
5. Methodology
6. Compiling
7. Outputs & Analysis
8. Results & Discussion
9. Contact

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Overview

Blackjack is modeled as a finite-horizon stochastic control problem.
Each state includes:

• Player total
• Soft/hard flag
• Dealer upcard
• Split count
• Double availability

Actions = {Hit, Stand, Double, Split}.
We simulate many rounds to estimate EV with 95% confidence intervals, enabling fair comparisons of strategies and rules.

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Features

• Flexible house rules:
  • Decks: single or multi-deck
  • Dealer S17/H17
  • Payout: 3:2 vs 6:5
  • Double-after-split, re-splitting, etc.
• Two policies: Basic Strategy vs Naive.
• Supports dataset generation (EV lookups, action heatmaps) and finite-shoe simulation.
• Outputs EV curves, win/loss/push rates, quantile bands.
• All results export to CSV + plots for reproducibility.

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Project Structure

simulate-blackjack/
├── blackjack_pipeline.py # Main pipeline
├── data/
│ └── blackjack_games.csv 
├── outputs/ # Simulation results (CSVs + plots)
├── outputs_basic/
├── outputs_house_rules/ 
├── outputs_naive/ 
├── outputs_s17/ 
├── outputs_variant/ 
├── docs/images/ # Figures used in README & poster
├── requirements.txt
└── README.md

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Installation

Prerequisites

• Python 3.10+
• pip

Setup

git clone https://github.com/yourusername/blackjack_simulation_python.git

cd blackjack_simulation_python

pip install -r requirements.txt

Methodology

1. Game Modelling

   • Deck Model: Supports single or multiple decks with shuffling.
   • Ace Handling: Aces initially count as 11, adjusted to 1 if necessary to prevent busting.
   • Dealer Rules: Dealer hits until reaching at least 17 (soft 17 behavior configurable).

2. Strategies Tested

   • Simple Strategy: Always hit if hand value < 17, otherwise stand.
   • Basic Strategy (generated): Decision table derived from simulated outcomes (strategy.pkl), includes hit/stand/double/split logic.

3. Simulation Process

   • Deal two cards to player and dealer.
   • Apply chosen strategy to player until they stand, bust, or take a double/split action.
   • Dealer plays according to rules.
   • Compare outcomes to determine win/draw/loss and calculate payoff.
   • Repeat for thousands or millions of games to achieve stable statistics.

4. Performance Metrics

   • Win Rate – Percentage of units won.
   • Draw Rate – Percentage of units pushed.
   • Loss Rate – Percentage of units lost.
   • Average EV per Hand – Expected value in units over all hands.
   • Cumulative Earnings Graph – Visualizes performance over time with percentile bands.

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Compiling

Run the below commands in order(CMD):

Dataset generation (infinite deck)

• python blackjack_pipeline.py dataset --n-samples 50000 --outdir data

Aggregate / analyze results

• python blackjack_pipeline.py analyze --indir outputs --outdir summary

Simulation

• python blackjack_pipeline.py simulate --policy basic --decks 6 --n-games 200000 --replicates 5 --outdir outputs
• python blackjack_pipeline.py simulate --policy naive --decks 1 --n-games 100000 --replicates 5 --outdir outputs
• python blackjack_pipeline.py simulate --policy basic --decks 6 --s17 --outdir outputs
• python blackjack_pipeline.py simulate --policy basic --decks 6 --payout65 --outdir outputs
• python blackjack_pipeline.py simulate --policy basic --decks 6 --no-das --outdir outputs
• python blackjack_pipeline.py simulate --policy basic --decks 6 --double-911 --outdir outputs
• python blackjack_pipeline.py simulate --policy basic --decks 6 --hit-split-aces --outdir outputs
• python blackjack_pipeline.py simulate --policy basic --decks 6 --max-splits 2 --outdir outputs

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Outputs

The simulation produces CSV results (EV, win/draw/loss %, 95% CI) and visual plots that illustrate how strategy and rule variations impact outcomes.

EV vs Deck Count (Basic Strategy)

• Shows expected value (EV) per initial hand with 95% confidence intervals, using Basic Strategy.
• 1–2 decks: EV is close to break-even (CIs overlap zero).
• 4–6 decks: EV becomes negative, confirming that larger deck counts increase the house edge.
• Practical insight: Deck count matters, but less than payout and dealer rules.

EV vs Deck Count (Naive Strategy)

• Shows expected value (EV) per initial hand with 95% confidence intervals, using Naive Strategy.
• 1–6 decks: EV stays around −0.059, with overlapping CIs indicating no significant deck effect.
• Practical insight: Deck count has little influence compared to the large inherent disadvantage of the Naive policy.

Hit-Threshold Strategy Returns

• Simulated a naive policy: “Hit until hand total ≤ T, else Stand.”
• EV peaks around T ≈ 15–16 (soft hands ≈ 17–18).
• Increasing T initially reduces premature stands, but after ~16 busts increase and EV declines.
• Even at its peak, EV remains negative, showing that ignoring dealer upcard and softness leads to poor outcomes.

Comparative EV across Strategies

• Table shows the effect of rule variations on expected value (EV) per initial hand under Basic Strategy, with results averaged over 5 replicates.
• The Base game (6-deck, H17, DAS allowed, 3:2 payout) has an EV of −0.0058 (≈−0.6% house edge), with Win% ≈43.3%, Draw% ≈8.7%, and Lose% ≈48.1%.
• Rule changes shift EV as expected: 6:5 payout strongly worsens EV (−1.36 pp), restrictions on doubles or DAS reduce player edge (−0.15 to −0.17 pp), while S17 (+0.25 pp) and hitting split Aces (+0.11 pp) improve EV.
• Overall, payout rules and dealer standing rules have the largest impact, while max splits have little effect.

Soft Hands Heatmap

• A2–A6: Always hit (low risk of bust, potential to improve).
• A7 (soft 18): Flexible:- stand vs weak dealer (2–7), but hit vs strong dealer (8–Ace).
• A8–A10: Always stand (already strong hands).

Hard Hands Heatmap

• Totals 4–11: Always hit (no risk of bust).
• Totals 12–16: Critical zone:- hit against strong dealer cards (7–Ace), but stand against weak dealer cards (2–6) to let the dealer bust.
• Totals 17+: Always stand (bust risk is too high).

Full-Policy Outcomes: Basic vs Naive

• Basic Strategy (6-deck):

  • Win / Push / Lose ≈ 43.28% / 8.68% / 48.04%
  • EV ≈ −0.55%

• Naive Strategy (6-deck):

  • Win / Push / Lose ≈ 41.03% / 9.66% / 49.32%
  • EV ≈ −6.03%

Key Insights:

Results & Discussion

Our simulations quantify the performance gap between Basic Strategy and a Naive hit-threshold strategy, as well as the influence of deck count and rule variations.

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Deck Count Effect

• Under Basic Strategy, EV is near break-even for 1–2 decks (confidence intervals overlap 0).
• With 4–6 decks, EV turns clearly negative (≈ −0.5% per hand at 6 decks).
• Interpretation: More decks slightly worsen the house edge, but the impact is modest compared to rules like payout ratios.

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Hit-Threshold Policy

• Naive “Hit ≤ T, else Stand” rule peaks around T ≈ 15–16 (soft ≈ 17–18).
• EV improves initially but never crosses into positive territory.
• Bust rates rise quickly beyond T ≈ 16, reducing overall EV.
• Conclusion: Ignoring dealer upcard and hand softness leads to unavoidable long-term losses.

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Full-Policy Outcomes: Basic vs Naive

• Policy impact: Switching from Naive to Basic improves EV by ~+5.5pp, reducing losses from ~6 units to ~0.5 units per 100 hands.
• Rule sensitivity:
  • S17 (dealer stands on soft 17) improves EV by ~+0.2pp.
  • 6:5 payout worsens EV by ~−1.3 to −1.5pp.
  • Deck count effect is minor compared to these.
• Practical takeaway:
  • Always play Basic Strategy.
  • Prefer 3:2 payout, S17, DAS tables.
  • Avoid 6:5 tables, where the house edge becomes significantly higher.

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Overall Conclusion:

• Basic Strategy is nearly break-even under favorable rules, while Naive play incurs severe losses.
• Casino rule variations (payouts, dealer behavior) have far stronger influence on EV than the number of decks.
• Correct strategy choice and table selection are critical for minimizing expected losses.

Contact

In case of any clarifications or queries, do reach out to the author :-

Krishna Ramachandra krishna.ramachandra@ucdconnect.ie

zhixuan zhou zhixuan.zhou@ucdconnect.ie

DISCLAIMER : This project is intended purely for educational and academic purpose and does not endorse betting or gambling in any form.