Hybrid extension · interactive demo

The Hybrid Systems on the Same Position

The secondary extension: how the existing hybrid systems (Stockfish, Maia-3 5M, sequence and statistical features combined in XGBoost) read one position, next to the Regan-inspired statistical view. For the direct comparison of the three predictive approaches, see Compare Models. Switch between the original human move and the substituted engine move, or between the three prepared studies.

Prepared study · same game, same player
Position15 / 36
Move 24, Black to move
31 legal moves
1
White king on g1
White rook on d1
2
White pawn on g2
White pawn on f2
White queen on c2
White pawn on a2
3
White pawn on h3
White pawn on b3
4
White pawn on c4
5
Black pawn on c5
6
Black pawn on b6
7
Black pawn on h7
Black pawn on g7
Black pawn on f7
Black queen on e7
Black pawn on a7
h8
g
Black king on g8
f
e
Black rook on e8
d
c
b
a
  • Substituted engine move24… Qe6
  • Original human move24… h6
  • Engine alternative24… Qf6
  • Engine alternative24… g6
Compare the two moves in this position

The substitute is evaluated in this original position; later positions are those of the original game, not a replayed game.

Stockfish
Excellent
#1 · +0.09
Maia-3
Low
#13 · 0.3%
Difficulty
High
0.82
Model contribution
0.99
per-move resemblance
Provenance: Regan — Verified public method. Concept documented in Professor Regan's public materials (cited, with page numbers). Not implemented by MoveLens unless stated.Provenance: MoveLens — Our approximation. Our simplified, empirical implementation inspired by a Regan concept. It does not reproduce his model or calibration.
Engine alternatives
  1. 1Qe6selected move+0.09
  2. 2Qf6+0.08
  3. 3g6+0.07
  4. 4h5+0.02
  5. 5Qc70.00
[IR user guide, p. 4]
Expected human behaviour
Qe6 · engine #117.0%
any other move83.0%
A 1956-rated player in a position of this difficulty is expected to match the engine's first choice about 17% of the time. Regan's model assigns a probability to every legal move; our approximation estimates only this top-1 probability.
[Regan, Apr 2026 talk, pp. 11–12]
Projected vs observed · this study's game
Engine top choice (T1)
expected 37% · observed 58%
Equal-value match (EV)
expected 41% · observed 75%
[Regan, Apr 2026 talk, p. 12; IR user guide, p. 13]
Statistical deviation
z = +2.60

Across 36 decisions, engine top-choice agreement was well above expectation. This move matched the engine's first choice (contribution +0.83 to observed − expected).

Technical details
Regan's framework
Provenance: Regan — Verified public method. Concept documented in Professor Regan's public materials (cited, with page numbers). Not implemented by MoveLens unless stated.
  • Input is Multi-PV engine analysis in AIF files; ordinary Single-PV data is deliberately refused. [IR user guide, p. 4]
  • Player parameters trained against Elo: s (sensitivity), c (consistency), h (heave/nudge) per the April 2026 talk; the user guide describes s, c and an equal-value parameter ev as the active player parameters. [Regan, Apr 2026 talk, p. 10; IR user guide, p. 3]
  • Generates a probability pᵢ for each legal move mᵢ (loglog-linear model) and derives confidence intervals from them. [Regan, Apr 2026 talk, pp. 11–12]
  • z-scores for actual-versus-projected quantities, with an after-the-fact correction because chess decisions are not independent. [Regan, Apr 2026 talk, p. 12; IR user guide, p. 13]
  • T1-match (move listed first), EV-match (includes equal-optimal moves), ASD (average scaled difference) and an Intrinsic Performance Rating (IPR). [Regan, Apr 2026 talk, p. 12]
  • Regan's EWN (“expectation weights normalized”) can give greater influence to complex positions. It is an optional alternative to unit weighting, which the user guide says is used over 99% of the time. Difficulty awareness is part of Regan's framework, not a MoveLens contribution. [IR user guide, pp. 1, 10–11]
Our approximation, this move
Provenance: MoveLens — Our approximation. Our simplified, empirical implementation inspired by a Regan concept. It does not reproduce his model or calibration.
Expected top-1
0.1702
Observed
1 (top-1 match)
Difficulty
0.818 (hard ≥ 0.732)
Top-1 engine match
proj. 0.372 · obs. 0.583 · z +2.60
Equal-value engine match
proj. 0.412 · obs. 0.750 · z +3.75
Top-3 engine match
proj. 0.634 · obs. 0.806 · z +1.97
Mean move loss
proj. 38.966 · obs. 5.889 · z +2.04
Top-1 match, hard positions
proj. 0.228 · obs. 0.800 · z +5.10
Top-1 match, ordinary positions
proj. 0.749 · obs. 0.750 · z +0.01
Human surprisal (Maia-3)
proj. 1.067 · obs. 1.374 · z +1.46
Not implemented
s, c, h · value scaling · ASD · IPR · EWN · Proj1…Proj7+
Provenance: MoveLens — Our augmentation. Added by MoveLens. Not part of Regan's documented framework.

Controlled Assistance Experiment

The same game, scored at every target level and strategy. The prepared studies above are three of these variants.

Loading the controlled experiment…
Download this study as AIFProvenance: MoveLens — Our augmentation. Added by MoveLens. Not part of Regan's documented framework.Experimental AIF-compatible export. Compatibility with Professor Regan's current IR analyzer has not been tested.

AIF stores the chess game together with detailed engine analysis for each position.

About the AIF export
Format
Analysis Interchange Format (AIF), the input format of Regan's IR analyzer
Contents
PGN-compatible game · engine ID/settings · per move: FEN, legal moves, engine evaluations, depth, MultiPV lines, principal variation
Our data
MultiPV 5 at one fixed depth (12); shallower depth columns are “n.a.”; node counts not recorded (“n.a.”)
Specification
K. W. Regan & T. Biswas, AIF v0.5, described in “A Computer Chess Analysis Interchange Format”, Gödel’s Lost Letter and P=NP, 20 Jan 2015.
Compatibility
Not tested with Regan's current analyzer. Internal storage is JSON/Parquet, not AIF.
Full move-by-move report · live PGN analysis