Random Chess Player Panda
♟ Current board↓List legal moves
e4 · d4 · Nf3 · …↓🎲 Pick one
e4 · d4 · Nf3 · …↓🎲 Pick one
Every legal move is a possibility. Panda does not score boards or learn from its games.
Browser edition · no installation · one active workshop tab
15-MINUTE INSTRUCTOR-LED ROUTEHow does our opponent
become a better player?
Explain one layer. Try it. Inspect what changed. The engine’s name is a version, not a rating.
1 / A ladder of playable ideas · 3 minutes
Random Chess Player Panda 🐼
Choose a legal move. Following rules does not mean making a good decision.
Material Goblin
Count pieces after candidate moves. Greed can miss the opponent’s reply.
Positional Scout
Add hand-written preferences for center activity, pawn structure and king shelter. These are rules we supply, not learned knowledge.
Can adding one more half-move of search change a greedy capture?
Try the bot ladder →2 / Search is an experiment about the future · 3 minutes
Your move→Their best reply→Your best reply→Evaluate the leaf
Minimax chooses the best move against a strong reply. Alpha-beta stops branches that cannot change that answer. Move ordering tries promising branches first. Iterative deepening finishes depth 1, then 2, then 3 until the node budget is used.
Does pruning change the answer or only the amount of work?
Compare identical positions and fully completed depths. A budget can stop a deeper iteration. “Cutoffs” counts cutoff events; “moves skipped” counts immediate moves skipped there, not an invented count of entire unseen subtrees.
3 / What the neural model sees · 3 minutes
12 × 8 × 8 piece planes+Turn, castling, en passant, half-move clock→32 hidden neurons→Position score
Each input says where a piece is or describes game state. Connections have adjustable weights. Hidden neurons combine inputs nonlinearly, allowing the score to depend on patterns rather than five piece prices. The student network starts from seeded random weights.
Our targets come from saved Stockfish evaluations in the Lichess archive. We transform centipawns with tanh(cp / 400) into a bounded teaching scale. The output is not a calibrated win probability. Search converts it back to evaluation units.
Why does knowing the target during training not give the answer away during play?
4 / Make a challenger · 3 minutes
Predict training boards→Compare with teacher→Backpropagate errors→Adjust weights→Check new boards
One epoch is one full-batch gradient update in this small implementation. Compare training and validation error, then save a model version. During play, our search calls that saved network; it does not call Stockfish. A small dataset and network can still produce a poor player.
If the loss falls but the bot loses more games, did we improve the engine?
Train a network, then enter it in the arena →5 / Evidence, champion, rematch · 3 minutes
The arena freezes engine versions, uses paired openings and swaps colors. It records wins, draws, losses, unfinished games and PGNs. Games stopped at the move limit stay unfinished; they are not counted as draws or losses. Compare the named players’ results under the same search settings.
Promotion requires at least 40 completed games against the current champion, no caps, and a paired bootstrap score interval above 50%. This is a conservative development gate, not proof of broad strength. Use more varied, independent evaluation before making a human-strength claim.
Today: supervised neural training + our search + saved arena evidence.
Later: collect club-game labels → train another challenger → rematch.
Later: collect club-game labels → train another challenger → rematch.
Self-play game collection is possible by pairing networks in the arena. Training from their outcomes, live Stockfish re-labeling, transposition tables, quiescence, books, tablebases and policy/MCTS are future work. They are not silently active here.
END-OF-LECTURE VISUAL REFERENCEEngine illustrationsRandom Panda · Material · Positional · Neural Panda · Stockfish
Rules decide what is legal. An evaluator judges a position. Search looks ahead.
Material Goblin
Explore moves + replies↓Count material at leaf boards
♙ 1 · ♘ 3.2 · ♗ 3.3 · ♖ 5 · ♕ 9↓Search chooses a move
♙ 1 · ♘ 3.2 · ♗ 3.3 · ♖ 5 · ♕ 9↓Search chooses a move
Piece prices come from us. Search can reveal that a tempting capture loses a queen on the next turn.
Positional Scout
Explore moves + replies↓Material + positional features
Center activity · pawns · king shelter↓Search chooses a move
Center activity · pawns · king shelter↓Search chooses a move
The scoring recipe is written by people. Changing a coefficient is manual tuning; playing games alone does not change it.
Neural Panda
Explore moves + replies↓Saved neural network scores boards
Weights learned from teacher examples↓Search chooses a move
Weights learned from teacher examples↓Search chooses a move
We replace the scoring recipe with learned weights. The legal-move rules and our search stay in place.
Inside the model we train
Representative neurons shown, not every connection. 768 piece-square inputs + 14 game-state inputs = 782. This fully connected network has 25,089 adjustable parameters.
Why 768 inputs? One yes/no question for every piece and square.
6 piece types × 2 colors × 64 squares = 768. Imagine 12 transparent chessboards stacked together. Each layer tracks one kind of piece, such as White pawns. A 1 means that piece is on this square; a 0 means it is not.
White pawn
White knight
White bishop
White rook
White queen
White king
Black pawn
Black knight
Black bishop
Black rook
Black queen
Black king
Example: a White pawn on e4 turns on the e4 input in the White-pawn layer. The other 11 layers have 0 at e4. An empty square has 0 in all 12 layers. We flatten these layers into a list for the network; 768 describes the input slots, not the number of pieces.
The other 14 inputs are: 1 for whose turn it is, 4 for castling rights, 8 for the en-passant file, and 1 for the half-move clock. Total: 768 + 14 = 782. This is our simple encoding choice; other chess networks use different features.
What is tanh? A smooth squashing curve.
“Tanh” is short for hyperbolic tangent. It converts any real number into a value between −1 and +1. Values near zero stay near zero; large positive or negative values flatten toward the ends.
tanh(−1) ≈ −0.76tanh(0) = 0tanh(1) ≈ +0.76
Two jobs in our model: hidden neurons use tanh to make the network nonlinear, so stacked layers can represent patterns beyond a single weighted sum. The output uses tanh to match the bounded teacher targets.
For training we first divide a teacher score by 400 centipawns: +400 cp becomes tanh(1) ≈ +0.76, 0 cp becomes 0, and −400 cp becomes about −0.76. This scale keeps very large scores from dominating the target range. It does not turn +0.76 into a 76% chance of winning.
Limit: near −1 or +1 the curve is flat, so gradients become small and learning can slow. Tanh is a design choice for this small model; Stockfish’s NNUE uses different activation functions.
During training · weights change
Example board → network prediction↓Compare with saved teacher target
target = tanh(Stockfish centipawns / 400)↓Squared error → backpropagation → adjust weights↺Repeat; check validation boards
target = tanh(Stockfish centipawns / 400)↓Squared error → backpropagation → adjust weights↺Repeat; check validation boards
During a game · weights stay fixed
Search generates future boards↓Network scores the leaf boards↓Search compares replies → chooses a move
No teacher answer is supplied during play. The output describes White’s advantage on a bounded scale; it is not a measured chance of winning.
Why have a prepared Neural Panda too?
It has the same 782 → 32 → 1 architecture as your student model, with weights prepared ahead of time using more training and validation-based checkpoint selection. It is a reference for this small learning approach, not a guarantee of strong human-level chess. Lower teacher error must still be checked through games.
Stockfish: learned evaluation + highly optimized search
Prepared before our session
Large-scale chess training data↓Train NNUE evaluation weights↓Compatible network ships with the engine
When we request a move
Stockfish’s own optimized search↕NNUE evaluates positions efficiently
Reuse calculations when only a few pieces change↓Best move + search continuation
Reuse calculations when only a few pieces change↓Best move + search continuation
Inside Stockfish 18’s NNUE evaluator
A neuron-and-connection view of the Stockfish 18 release. Each circle represents a value in a layer; only a few circles are drawn, and labels give the actual sizes.
● Learned layers● Squared clipped activation● Direct scoring path
Read left to right. The first layer has 16 outputs: 15 each pass through two activation functions, creating 30 values; the remaining output follows the gold bypass. The teal path adds a learned piece-square contribution. The resulting evaluation helps search choose a move.
Feature processing and layer details
Chess position
Piece-square features relative to kings; big network also uses threat features↓Incrementally updated accumulators
Keep running feature sums; add/remove changed features instead of rebuilding everything↓Clip + multiply paired features; combine both perspectives
Transformed input: 1,024 values (big) or 128 (small)↓First dense layer: 16 outputs
15 feed the next layers; 1 takes a direct path toward the score↓Clipped + squared clipped activations → 30 values↓Dense layer: 32 → clipped activation → 1 output↓Combine network output + direct path + learned piece-square contribution
Then apply evaluation scaling and game-state adjustments↓Position evaluation → search compares moves → best move
Piece-square features relative to kings; big network also uses threat features↓Incrementally updated accumulators
Keep running feature sums; add/remove changed features instead of rebuilding everything↓Clip + multiply paired features; combine both perspectives
Transformed input: 1,024 values (big) or 128 (small)↓First dense layer: 16 outputs
15 feed the next layers; 1 takes a direct path toward the score↓Clipped + squared clipped activations → 30 values↓Dense layer: 32 → clipped activation → 1 output↓Combine network output + direct path + learned piece-square contribution
Then apply evaluation scaling and game-state adjustments↓Position evaluation → search compares moves → best move
There are big and small networks; Stockfish selects between them and can re-evaluate with the big one. It also selects one of 8 output-layer stacks by piece count. These details are simplified here. This is an evaluator inside search, not a network that directly outputs a move.
Release-specific sources: layer dimensions & activations · feature transformation · network selection & score adjustments · piece-count layer selection
NNUE means “Efficiently Updatable Neural Network.” This diagram is conceptual: Stockfish does not use our small 782 → 32 → 1 network. Its strength comes from both its trained evaluator and years of search engineering.
Our demo runs the installed Stockfish engine with 1 CPU thread, 32 MiB hash memory and 0.3 seconds per analysis. Its compute limits differ from Panda’s node budget, so this is a reference comparison rather than an equal-compute experiment. We do not train Stockfish in this lab.
Sources: Stockfish evaluation & search · How NNUE reuses calculations · Stockfish overview
What changes as we improve?
Random → add evaluation → add better hand-written features → learn the evaluation from examples → test whether the new player actually wins more games.
Random → add evaluation → add better hand-written features → learn the evaluation from examples → test whether the new player actually wins more games.
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