AI & Technology
Algorithms & Optimization
Understanding the Simplex Method
A comprehensive guide to understanding the Simplex Method in linear programming. Learn how this powerful algorithm solves optimization problems efficiently.
How to Build Objective Function for Simplex Method
Learn how to formulate and build objective functions for the Simplex Method. Step-by-step guide to translating real-world problems into linear programming objectives.
Simplex Arcade: Math for Kids & Beginners
Learn the Simplex Method with fun, interactive games! Lemonade stands, Lego factories, farms, fashion studios, space cargo, and hero training explain Linear Programming simply.
Chess & Strategy
Chess Tactics: Magic of Chess
Discover the magic of chess tactics — forks, pins, skewers, discovered attacks, and 10 essential techniques in this visual infographic guide to thinking like a chess master.
The Anatomy of a Simple Modern Chess Engine
Visual guide to bitboards, magic bitboards, alpha-beta search, transposition tables, and the UCI protocol — how engines turn a position into a best move.
Explain Chess Engine Move Generation
Pseudo-legal moves, castling, en passant, promotions, make/unmake, and perft — how engines list every legal move correctly.
Explain Chess Engine Magic Bitboards
O(1) sliding attacks for rooks and bishops — masks, magic numbers, multiply-shift-index tables, and PEXT.
Explain Chess Engine Search Algorithm
Negamax, alpha-beta, iterative deepening, quiescence, transposition tables, PVS, and move ordering — how engines search.
Explain Chess Engine Transposition Table
Zobrist hashing, TT entry layout, EXACT/ALPHA/BETA flags, depth replacement, and search cutoffs — the engine memory cache.
Explain Chess Engine UCI Protocol
How GUIs talk to engines — uci, position, go, stop, info lines, bestmove, setoption, and the threading model.
Explain Chess Engine Aspiration Windows
Narrow alpha-beta windows around the previous depth score — fail-high, fail-low, re-search, and node savings with iterative deepening.
Explain Chess Engine Endgame Tablebase
Syzygy WDL/DTZ probes, perfect endgame play, file types, score conversion, and integration with alpha-beta search.
Explain Chess Engine Quiescence Search
Horizon effect, capture extensions at depth 0, stand pat, SEE pruning, and leaf-node tactical resolution.
Explain Chess Engine Iterative Deepening
Why engines search depth 1, 2, 3...N instead of jumping straight to depth N — anytime results, PV-driven move ordering, and time management.
Explain Chess Engine Evaluation Function
Material, piece-square tables, tapered eval, pawn structure, mobility, and how NNUE replaced classical hand-tuned scoring.
Explain Chess Engine Delta Pruning
Skip hopeless captures in quiescence search — stand pat plus piece-value margin versus alpha.
Explain Chess Engine Futility Pruning
Skip quiet moves at low depth when static eval plus margin cannot raise alpha — forward pruning in main search.
Explain Chess Engine Killer Move Heuristic
Remember quiet moves that caused beta cutoffs at each ply — try them early for faster alpha-beta pruning.
Explain Chess Engine Late Move Reduction
Search late-ordered quiet moves at reduced depth — re-search full depth on fail-high with PVS.
Explain Chess Engine Null Move Pruning
Pass a turn at reduced depth — if still winning, cut off the subtree. Zugzwang guards and verification search.
Explain Chess Engine Razoring
When static eval is far below alpha, skip deep search and jump to quiescence — aggressive forward pruning.