Chess

White moves first, then the players alternate, one move each. Every move either moves one of your own pieces to an empty square or onto a square holding an enemy piece, which is then removed from the board. The single constraint that overrides everything else: you may never leave your own king under attack. That is where pins come from — a piece standing between your king and an enemy rook, bishop or queen simply has no legal move off that line. The goal is checkmate: attack the enemy king so that no legal move ends the attack.

The values in that table are the ones this engine's evaluation actually uses, in hundredths of a pawn. Note that the bishop is worth ten points more than the knight rather than exactly the same: a bishop's range grows as the board empties, and a knight's does not. The king has no value in the table because losing it is not a cost the search prices — it is the end of the game, scored separately.

Check is an attack on the king. You must answer it on your very next move, by moving the king, capturing the attacker, or putting something in the way — and if none of those is possible, the check is checkmate and the game ends immediately. Stalemate is the one that costs players whole games: you have no legal move at all and your king is not attacked. That is a draw, worth half a point to each side, no matter how far ahead the other player was.

The practical lesson is a defensive one. A lone king with no pawns, shuffled into a corner while the stronger side queens a pawn without checking first, is drawn far more often than beginners expect. When you are winning, count your opponent's legal moves before you take a square away from them; when you are losing, look for the move that leaves you with none.

• Castling through check. The king may not castle out of check, through an attacked square, or onto one. What is not forbidden: the rook passing over an attacked square, and — castling queen-side — the b-file square being attacked. The king never stands on b1, so only its own three squares are tested.
• Castling queen-side needs three empty squares, b1, c1 and d1, not two. A knight still on b1 blocks it.
• Losing the right by capture. Castling is lost when the rook is taken on its home square, not only when it moves. A version that forgets this lets you castle with a rook that is no longer on the board.
• En passant expires. The capture is available on the move immediately after the double push and never again. It is also the only capture where the captured piece is not on the square you land on.
• Under-promotion is legal. A pawn reaching the last rank must become a queen, rook, bishop or knight — your choice, and a knight is occasionally the right one because it is the only promotion that can give check on a square a queen cannot reach.
• Two knights is not insufficient material. King and two knights against a bare king cannot force mate, but mate is still reachable, so the game is not dead and it is not drawn here. King and one bishop, king and one knight, and bishops of the same colour on opposite sides all are.

It is a minimax search with alpha-beta pruning and piece-square tables — the same family of engine as this site's checkers and Four in a Row opponents, scaled up. It deepens one ply at a time and stops the moment it runs out of its budget in positions, throwing away the half-finished depth and playing the last one it completed — so a tangled middlegame costs the same ceiling of work as a quiet one instead of however long the position happens to take. Past the end of the main search it keeps looking at captures only, which is what stops it grabbing a defended pawn and calling the position winning one move before the recapture.

Casual is genuinely weak and genuinely honest about it: two plies with no capture search means it sees your threat and its own answer and nothing else, so it will take a defended pawn and walk into a fork that is two moves away. It never plays a random move, though — every move is the best its short search can see. Sharp plays the highest-rated move every time; Casual and Club pick from every move within 40 and 16 hundredths of a pawn of the best, which is what stops every game from being the same game.

From the opening position White has exactly 20 legal moves — sixteen pawn moves and four knight moves — and after one move each there are 400 positions. Three plies gives 8,902, four gives 197,281, and five gives 4,865,609. Those counts are the standard correctness probe for a chess move generator, because a rule implemented slightly wrong changes them: this site's generator reproduces every one, along with the published counts for five awkward test positions full of pins, en passant captures and promotions.

The growth does not stop. Claude Shannon's 1950 paper put the number of typical games at somewhere around 10^120 — far more than there are atoms in the observable universe — which is why no chess program searches the whole tree and why every one of them, including this one, has to decide what to look at and what to ignore.