Why Using Our Simulators to Build Your Blackjack Strategy Suites
Developing a powerful and profitable blackjack strategy requires more than just intuition—it demands rigorous testing, data analysis, and optimization. Our simulators are specifically designed to empower players and teams to refine their strategies with precision, maximizing their long-term edge in real-world casino environments. Here's why our simulators stand out:
100% Flexibility in Strategy Definition
Our simulators allow users to fully define their own strategy suites, offering unmatched flexibility. Players can customize every aspect, including:
- Basic Strategy: tailor decisions for hard hands, soft hands, and pairs.
- Counting Systems: implement any card counting strategy, whether popular or unique.
- Betting Strategies: configure advanced betting models, including dynamic adjustments based on count and bankroll.
Users can also emulate diverse real-world casino conditions, adjusting for specific rules (e.g., number of decks, penetration, side bets) and combining different rulesets for comprehensive simulations.
Powerful Data Representation and Analysis
Our simulators are equipped with robust data visualization tools, providing:
- Pre-Defined Reports: analyze outcome statistics, penetration dependency, and card counting score impacts.
- Custom Data Access: access complete simulation data for users who want to perform their own post-processing, enabling tailored insights and optimizations.
These tools help players turn raw data into actionable strategies, ensuring informed decisions based on empirical evidence.
Kelly Criterion-Based Betting Strategies
Our simulator includes integrated support for the Kelly Criterion, optimized for popular card counting systems. This approach is backed by rigorous mathematical derivations, ensuring:
- Optimal Compound Gains: maximize your long-term returns while minimizing the risk of ruin.
- Prevention of 100% loss: it is garanteed theoretically. Even if the minimal bet limit exists, It largely increases the chance that you ride through consecutive bad hands.
- Stable Edge: maintain a consistent positive edge even if you're unable to exponentially increase your bets.
Multi-Threaded Simulation Technology for Speed and Efficiency
We leverage multi-threading to dramatically speed up simulations, with performance scaling directly with your system's CPU cores and memory.
By combining cutting-edge flexibility, powerful analytics, and optimized betting strategies, our simulators empower users to achieve a stable positive edge in blackjack, turning a complex game into a data-driven pursuit of consistent profits. Whether you're a professional player or a dedicated enthusiast, our tools are designed to elevate your game and maximize your returns.
Ask for a demo program (BJ-SIM-DEMO)?
Please contact [email protected] for a download link and specify the OS in your email. Currently, our programs support windows and macOs.
Example of Basic Strategy Only
This example demonstrates a player employing only the basic strategy with a flat betting approach (same base bet for every round). The simulation runs under the following conditions:
Table Rules:
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6 decks
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0.25 deck penetration
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"777" is not considered blackjack
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Blackjack payout ratio: 1.5
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Surrender payout ratio: 0.5
Simulation Parameters:
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Total games: 50,000
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Total rounds: 2,177,310
The simulation tracks counts for various outcomes, including: losses, surrenders, wins, double wins, double losses, blackjack occurrences. The BJ payout ratiod, surrender rule, and correct double down are essential to benefit players' edge.
The player's edge is the division of total gain by total bet across all rounds. In this simulation, the player achieved a -0.18% edge, reflecting a slight disadvantage to the house over the long term.
Example of A Card Counting System
In this example, a player applies a basic strategy and basic Omega II to the same tabler rules and simulation parameters.
The Omega II system calculates the card count of a game by:
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+2 for cards 2–6
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+1 for 7, 8, and Ace (no change in the count)
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−1 for 9
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−2 for 10, J, Q, and K
The true count (TC) is the card count divided by penetration, aka remaining card percentage. A scatter plot of TCs versus penetration was generated, along with a distribution of TCs for each penetration range. Because Omega II is a balanced system, the average TC at each penetration level remains close to zero. However, the spread of TCs increases as penetration progresses (fewer cards remaining in the shoe).
For a player aiming to bet only when the true count exceeds certain thresholds:
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To bet on TCs above +6, the player should avoid betting during the first 20% of the shoe.
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To bet on TCs above +10, the player should avoid betting during the first 30% of the shoe.
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To bet on TCs above +13, the player should avoid betting during the first 40% of the shoe.
In summary, a player should conserve bankroll during the early stages of the game and focus betting efforts on the later stages, where higher TCs are more likely to occur.
Example of Kelly Criterion Based Bet
In this example, a player applies basic strategy and the Omega II counting system across 30,000 games and 1,306,121 rounds, using the same table rules as in the first example. The graph on the left shows the bankroll trajectory as games progress, plotted on a log10 scale to highlight the exponential growth of the bankroll with Kelly Criterion based betting strategy, with an initial bankroll of 100 and a base bet of 1 (1% of bankroll).
The orange line represents the outcome when the player using our GKC based betting strategy. On a log scale, this appears as a straight line, indicating exponential growth in the bankroll. After 3,162 flawless games, the bankroll increases from 100 to 31,622, and to 10^17.6 after 30,000 games, showcasing the powerful effect of compound growth.
In comparison, the red line represents an overbet strategy, where the player bets per KC based betting strategy+1% bankroll. This results in greater variability and leads to a lower final bankroll due to large withdraws. The overbet strategy produces increased risk, and ultimately less growth.
The green line represents an underbet strategy, where the player bets per KC based betting strategy-1% bankroll. The bankroll increases in a more consistent manner, but at a lower speed. The ending bankroll is 7 orders of magnitude smaller than that achieved with the Kelly Criterion.
In contrast, with flat bet (as shown in the first example), the player consistently loses money over time and to 0 after ~600 games due to a negative edge, even though it seems to be as small as -0.2%.
Key Takeaways:
The Kelly Criterion maximizes long-term compound growth by optimizing bet size relative to the bankroll and game odds.
Overbetting introduces more risk, leading to greater fluctuations and a lower final bankroll.
Underbetting provides more consistent growth but is still suboptimal compared to the Kelly Criterion.
Flat betting will lead to consistent losses due to the negative edge, regardless of how small the disadvantage is.
In conclusion, the Kelly Criterion strikes the optimal balance between growth and risk management, making it the most effective strategy for long-term profitability in games with a known edge.
Example of GKC-Based Betting
The above simulation is impressive but ignoring the reality that casino has bet limits, or no one can continuously play with 30000 games.
This example is simulated with the same casino rule, the same KC based strategy suite, but every game, its base bet is constant 1 and dosen't scale with bankroll. The simulator raises the bets when TC is high per KC. It mimics the min/max bet rules in casinos. Also a player can stop or continue a game with the same base bet.
Each game's ending bankroll is sorted. Each game wins 0.43x base bet on average, and the average edge of 1.9% for 30,000 games.
Importantly, Kelly Criterion can achieve a decent edge considering a game can be discontiued and/or in presence of bet limits.
Example of Kelly Criterion on Blackjack - Edge
Following the above exmaple, the accumulative edge of the strategy suite is calcualted. The accumulative edge is defined as the total gain divided by the total bet up to a certain time. The KC strategy gives +2.2% edge on the player side, which is significantly improved from the basic strategy only edge (-0.2%).
The underbet bets on higher true counts and produces additional 1.5% edge, but it results in fewer bets hurting the overall bankroll growth. The overbet can makes edge drop, but the large drawback is the killer to the compound growth.
Extensive Tests of The Simulator
Our simulator has been rigorously tested through over one thousand of millions of games, encompassing a variety of table rules and algorithms. Additionally, our KC-based betting strategies have been evaluated with over 10 different counting systems. The results consistently demonstrate optimal compound growth and well-balanced withdrawals when using the KC betting strategy.
Unlock our simulator and KC-based betting strategies to begin developing your own strategy suite, powered by advanced mathematical theories, data science, and cutting-edge computer technologies. This is your key to mastering and dominating every blackjack table.