Chess

Piece values are approximate — context always matters. A bishop pair on an open board may outperform two rooks in certain endgames. The king, priceless in play, is the only piece that cannot be exchanged.

Modern engines (Stockfish, Leela) compute dynamic values that shift as position changes — a rook behind a passed pawn is worth far more than its nominal 5 points.

Nimzowitsch called pawns "the soul of chess." Pawn structure dictates strategy: isolated pawns are weak but create space; passed pawns are potential queens; doubled pawns lose flexibility.

The pawn is the only piece that cannot move backward — every advance is a permanent commitment.

"Winning the exchange" means trading a bishop or knight (~3 pts) for a rook (5 pts). Players constantly evaluate trades: equal material, winning material, or sacrificing for positional/tactical gains.

Grandmasters often sacrifice material for compensation: open files, active pieces, king safety, or a decisive attack that engines eventually validate.

Long-range pieces (queen, rook, bishop) grow stronger as the board opens up — more squares to cover, longer lines of attack.

Short-range pieces (king, knight) are less position-dependent. Knights thrive in closed positions where long-range pieces are blocked by pawns.

1. Control the center — e4, d4, e5, d5 are the key squares. Pieces radiate from center control.

2. Develop pieces — Get knights and bishops off the back rank quickly. Don't move the same piece twice in the opening without reason.

3. Castle early — King safety first. Castling connects the rooks and hides the king from central attacks.

4. Don't bring the queen out early — It can be chased by minor pieces, wasting tempi.

Hypermodernists challenged classical dogma: instead of occupying the center with pawns, provoke and attack it from the wings with bishops and pieces.

The Réti Opening (1.Nf3), Nimzo-Indian (1.d4 Nf6 2.c4 e6 3.Nc3 Bb4), and King's Indian Defense all embody this philosophy — let White build a big center, then undermine it.

After Deep Blue defeated Kasparov in 1997, engines reshaped opening theory. Moves once considered objectively bad were rehabilitated; long-accepted "best" lines were refuted overnight.

Modern players prepare 30–40 moves deep in critical lines, memorizing engine evaluations. The Berlin Defense, once considered passive and boring, became the dominant elite response to 1.e4 because engines showed it gives Black a rock-solid draw.

Published in the 1970s by Chess Informant, ECO codes classify every major opening: A00–A99 (flank/irregular), B00–B99 (semi-open), C00–C99 (open — 1.e4 e5), D00–D99 (closed), E00–E99 (Indian).

Over 1,327 named variations. New ones are added as theory evolves — the "anti-Berlin" systems generated dozens of new ECO entries in the 2010s alone.

Alexander Kotov's "Think Like a Grandmaster" introduced the concept of identifying candidate moves — a shortlist of plausible options — before calculating each line to its conclusion. This prevents blundering by overlooking a key move.

Top players calculate 5–10 moves ahead in critical positions, seeing the board in their mind without moving pieces.

German for "in-between move" — instead of making the expected recapture or reply, a player inserts an unexpected intermediate move that improves their position or creates a stronger threat.

Example: instead of recapturing a piece, deliver check first, forcing the king to move before recapturing. This often gains material or destroys the opponent's coordination.

The romantic era of chess (1800s) glorified sacrifices. Mikhail Tal — the "Magician from Riga" — built a World Championship career on speculative sacrifices that defied computer analysis for decades.

Modern theory distinguishes: sound sacrifices (engine-validated), speculative sacrifices (compensation unclear but practical), and positional sacrifices (long-term structural advantage).

Endgames are solved positions: with few pieces on the board, accuracy is everything. The opposition (two kings facing each other with an odd number of squares between), the Lucena position, and the Philidor position are essential knowledge.

Tablebase — exhaustive computer analysis — has solved all 7-piece endgames. Some positions require 500+ moves to force checkmate, far beyond any human's capacity to calculate.