The Heart of MQ-Chess

Understanding the Original MQ-Chess (Loss Index) Engine

Developed in 2024 by Ivan (IvanKulkin / @vansGAMee), Loss Index (MQ-Chess) replaces flawed Average Centipawn Loss (ACPL) by combining Win Chance Sigmoids with Decision Complexity Weighting.

Official MQ-Chess Engine GitHub Repository

Interactive MQ-Chess Simulator

Live Sigmoid Math

Eval Before Move:0.50 pawns

Eval After Move:-2.50 pawns

Legal Candidate Moves (N):28 options

Win Chance Before / After

77.3% → 64.4%

Sigmoid ΔW = 25.7%

Decision Complexity Weight

3.367

ln(28 + 1)

MQ Move Loss Index

25.7%

Raw ACPL would be 300 cp

Why Average Centipawn Loss (ACPL) Fails

Traditional chess analyzers compute raw average centipawn loss across all moves. MQ-Chess measures true Win Chance Delta (ΔW) weighted by Decision Complexity ln(N_legal + 1).

Traditional ACPL Metric

Flawed

Centipawn Loss:

-100 Centipawns

Penalizes player -100 cp for dropping from +8.00 to +7.00.

The Problem: ACPL treats both scenarios identically! It penalizes a player who is up a queen for making a harmless move just as harshly as a player who blunders their queen in an equal game.

MQ-Chess Loss Index

Mathematically Exact

MQ Win-Chance Loss (ΔW):

0.0% Loss

Win chance remains 100%. MQ Loss Index is 0.0%.

The MQ Solution: Converts evaluation to Win Chance via sigmoid σ(cp) = 2/(1 + e^(-0.003624 * cp)) - 1 and weights moves by legal options ln(N_legal + 1).

The Mathematical Equations

The exact mathematical formulation implemented in C++, Python, and TypeScript inside the original MQ-Chess.

1. Centipawn to Win Chance Sigmoid Mapping:

σ(cp) = 2.0 / (1.0 + e^(-0.003624 * cp)) - 1.0

Maps raw evaluation cp into win probability σ(cp) in [-1.0, +1.0].

2. Decision Complexity Weighting:

w_i = ln(N_legal,i + 1.0)

Weights each move by the natural logarithm of available legal candidate moves N_legal in that board state.

3. Aggregate MQ-Chess Loss Index (%):

Loss Index % = (∑ |σ(cp_best,i) - σ(cp_played,i)| * ln(N_legal,i + 1)) / (∑ ln(N_legal,i + 1)) * 100%

The weighted average percentage win-chance loss across all non-trivial decisions.