Simulate human blunders

Deep Dive into "Simulate Human Blunders"

1. Introduction to the Feature

Introduced in Alexander 4.1, the "Simulate Human Blunders" feature (which replaces the previous "Handicap Avatar Player") represents a groundbreaking innovation in chess training tools.

Instead of simply acting as a weakened, predictable machine, Alexander now plays like a real human opponent by simulating the natural, unpredictable mistakes that humans make over the board. It achieves this by dynamically adjusting the frequency and severity of its errors based on two main pillars: your specific Elo rating and the current complexity of the position.

2. The Engine Architecture: How a Human Error is Born

Based on the engine's source code (evaluate_handicap.cpp), human-like blunders are not generated purely at random. They are governed by a rigorous logical flow orchestrated by the get_perturbated_value() function. The process is divided into three fundamental phases:

A. Evaluating Positional Complexity (isComplex)

Humans are far more likely to make mistakes when the board is chaotic. Alexander calculates a complexity factor by evaluating specific concrete elements of the position. A position is deemed "complex" if it meets specific conditions:

• Advanced Pawns: The presence of pawns pushing close to promotion (e.g., on the 5th to 7th ranks for White).
• King Safety: If the King is currently under check or facing severe attacking pressure.
• Material Tension & Legal Moves: A combination of a high amount of material on the board alongside a high number of legal moves (e.g., $\ge 25$ moves), which stretches the limits of human calculation.

B. The Probability of Blundering (should_apply_perturbation)

The engine does not blunder on every move. The algorithm decides whether to apply a mistake by calculating a probability percentage based on:

• Elo Ranges: The engine uses mathematical curves (sigmoids) to ensure a smooth, gradual transition in error rates as the simulated Elo increases.
• Game Phase (Opening Factor): Errors are mathematically mitigated during the earliest moves of the game. This simulates the reality that human players often memorize opening theory and rarely commit severe blunders in the first few moves.
• Adaptive Complexity: The more complex the position is, the higher the likelihood that the engine will introduce a human-like error.

C. The Magnitude of the Mistake (get_handicap_value)

If the engine decides it is time to "blunder," it must determine how severe the mistake will be (the magnitude).

• Error Ranges: Specific minimum and maximum error thresholds are defined for each Elo bracket (e.g., massive evaluation swings for beginners, but microscopic positional inaccuracies for experts).
• Complexity Multiplier: If the position is verified as complex, the magnitude of the error is artificially amplified (by a multiplier of $1.2x$ in the code).
• Error Direction: Once the severity is calculated, the engine temporarily alters the mathematical evaluation of the board (either adding or subtracting the error margin), effectively tricking its own search algorithm into approving a sub-optimal, human-like move.

3. Adaptive Elo-Based Evaluation

The severity and type of blunders are strictly modeled around the user's skill level. Alexander 4.1 categorizes its playstyle into four distinct tiers:

• Beginner (Elo up to 1999): The engine produces frequent and simple blunders, perfectly mimicking a novice player who might overlook basic tactics or hang pieces.
• Intermediate (Elo 2000 to 2199): The engine stops making obvious single-move blunders. Inaccuracies become less obvious but are still noticeable, simulating miscalculations in medium-depth variations.
• Advanced (Elo 2200 to 2399): Simulating a National Master or Candidate Master, the engine makes only occasional mistakes while maintaining strategically sound play. Blunders here are often subtle positional inaccuracies rather than tactical oversights.
• Expert (Elo 2400 and beyond): Simulating International Masters and Grandmasters, errors become exceptionally rare. When they do occur, they are strictly positionally relevant errors reflecting high-level, complex decision-making.

4. Conclusion: Psychological Realism

The ultimate goal of the "Simulate Human Blunders" feature is to enhance psychological realism. Because the probability and magnitude of an error dynamically scale with the complexity of the position, you will experience the genuine sensation of "putting pressure" on your opponent. By creating tense, complicated positions on the board, you will force the engine to crack and make mistakes-exactly as you would against a real human player in a tournament setting.