The Shannon Number
Understand Claude Shannon's famous estimate of roughly 10^120 possible games and why game-tree complexity explodes so quickly.
Branching Factor and Game Trees
See how dozens of legal moves per position multiply across plies and why brute-force search needs pruning and evaluation.
Chess State-Space Complexity
Distinguish the number of possible legal positions from the number of possible games and understand why the figures are estimates.
Threefold and Fivefold Repetition
Learn when a draw can be claimed or automatically occurs under modern rules and why repeated positions depend on legal-move rights.
Fifty-Move and Seventy-Five-Move Rules
Understand the move-count draw rules, resets by pawn moves/captures, and the difference between claimable and automatic draws.
Castling Rules
Know every condition required for castling, including attacked transit squares, prior king/rook movement and pieces between them.
En Passant
Understand exactly when an en-passant capture is legal, why the opportunity lasts one move, and how it affects repetition identity.
Promotion and Underpromotion
Promote to the piece the position requires and recognize when rook, bishop or knight promotion avoids stalemate or creates tactics.
Elo Ratings
Understand expected score, rating differences, performance ratings and why ratings measure results within a pool rather than absolute chess knowledge.
From Classical to Hypermodern to Computer Chess
Trace how center occupation, flank control, dynamic counterplay and engine analysis changed opening and strategic thinking.