A chessboard floating in a night sky splits into four quadrants, light towers rise for the quadrant score and columns of light rank the candidates. Switch to a standard 2D board at any moment: the same run, every variable computed on a formula desk. Five real positions, three levels of intuition.
The brief it was built from
Train a visitor in the Viveka method (version 3) for choosing a chess move: identify the quadrants, propose candidate moves, score them. Two formulas and five variables, found visually and run step by step, ending with Stockfish's move, Viveka's move and the centipawn loss. Suitable for beginners through grandmasters.
What is real, and what is a scenario
Real data
- The two equations and constants are Viveka v3 as published: Φ = U + 1.5·ln(1 + N) for each quadrant, S = M + 1.25·K + 0.25·C for each move (α and β fitted at 1.13 and 0.21, rounded to quarters)
- Every U, N, Φ, M, K, C and S on screen was computed by the method's own TypeScript (src/lib/chess/viveka3.ts in the Viveka repository) when this page was built (build/bake.mts); the page runs no chess logic of its own
- The 2D view draws the same baked numbers with lesson2d.js, the module the 2D experience viveka-board-2d uses; the method rail above both views shows the three steps and two equations, lighting the variable each chapter computes
- The five positions are worked examples from the method's lessons, chosen by fixed rules from 21 openings held out of fitting; each has Stockfish 19's evaluation of every legal move (hybrid depth-22 and depth-15 labels) and its stored depth-22 top lines
- The engine line that plays out in the verdict is Stockfish's stored principal variation for its best move
- Study figures are from the held-out test of 5,587 positions: the top two quadrants held Stockfish's best move 78% of the time; with three candidates in them, the method lost 36.4, 47.1 or 102.7 centipawns a move on average for the strong, good and club models of intuition
- A random legal move loses 361 centipawns on average, and the site's automatic shortlist rule 24.9, on 5,494 held-out positions with every move evaluated
- Where Stockfish's best move landed by quadrant (35%, 36%, 16%, 13%) and the temperature scan (any T from 0.25 to 3 gives a top-two loss of 14.1 to 15.1 cp) are from the training openings
Scenario & assumptions
- The level input maps each visitor level to one of the study's three models of intuition: new to chess uses the club model (three of the eight best moves in the top two quadrants, drawn at random), club player the good model (the best move plus two of the next seven), master the strong model (the three best). That mapping is this experience's assumption, not a measured rating band
- The random draws for the good and club models were made once with a fixed seed, so each position always shows the same three candidates; another draw would show different ones
- The Clarity meter is illustrative and rises step by step; it is not a measurement
- The free-energy reading of the quadrant equation is an analogy the research uses to motivate its form, not a claim about chess
- The method's study covers positions with 8 or more pieces from engine games; it says nothing about positions outside that scope
- Five minutes is the autoplay pace at the club level; the hands-on panels take longer
What you leave with
- Where to look: Φ = U + 1.5·ln(1 + N), material at stake plus options, for each quadrant seen from your side; search the top two
- What to play: S = M + 1.25·K + 0.25·C, material after the exchange, a check worth about a pawn, a quarter per ring towards the centre
- The formula only chooses among the candidates you propose: candidate quality moves the average loss from 36 to 103 centipawns
- It looks one move deep, so it can take a poisoned pawn that Stockfish takes a move later
Sources
3D with three.js (MIT) · Narration voice: Kokoro-82M v1.0, voice af_heart (kokoro-onnx 0.4.7). Apache-2.0 (Kokoro-82M weights). · Classic chess pieces by Colin M.L. Burnett (GPLv2+; also BSD and GFDL), as bundled with react-chessboard · Merida pieces by Armando Hernandez Marroquin (GPLv2+) · Chessnut pieces by Alexis Luengas (Apache-2.0) · Fantasy and Spatial pieces by Maurizio Monge (MIT) · RhosGFX pieces (CC0 1.0)
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