Heuristics

✨ If you ask a chess pro why a chess move is good, they'll probably give you a bunch of reasons, many of them intuitive, about why they made that decision.

It is important to develop your pieces in the opening while trying to control the center of the board at the same time. Castling is an excellent move as long as the king gets safe. Then, in the middlegame space becomes an advantage. And if a complex position can be simplified when you have an advantage, then so much the better. The pawn structure could determine the endgame.

The list of reasons goes on and on.

The mathematician Claude Shannon came to the conclusion that there are more chess moves than atoms in the universe. The game is complex and you need to learn how to make decisions to play chess like a pro. Since no human can calculate more than, let's say 30 moves ahead, it's all about thinking in terms of heuristics.

Heuristics are quick, mental shortcuts that we humans use to make decisions and solve problems in our daily lives. While far from being perfect, heuristics are approximations that help manage cognitive load.

Listed below are the chess heuristics implemented in PHP Chess.

Heuristic	Description	Evaluation
Absolute fork	A tactic in which a piece attacks multiple pieces at the same time. It is a double attack. A fork involving the enemy king is an absolute fork.	Chess\Eval\AbsoluteForkEval
Absolute pin	A tactic that occurs when a piece is shielding the king, so it cannot move out of the line of attack because the king would be put in check.	Chess\Eval\AbsolutePinEval
Absolute skewer	A tactic in which the enemy king is involved. The king is in check, and it has to move out of danger exposing a more valuable piece to capture. Only line pieces (bishops, rooks and queens) can skewer.	Chess\Eval\AbsoluteSkewerEval
Advanced pawn	A pawn that is on the fifth rank or higher.	Chess\Eval\AdvancedPawnEval
Attack	If a piece is under threat of being attacked, it means it could be taken after a sequence of captures resulting in a material gain. This indicates a forcing move in that a player is to reply in a certain way. On the next turn, it should be defended by a piece or moved to a safe square. The player with the greater number of material points under attack has an advantage.	Chess\Eval\AttackEval
Backward pawn	The last pawn protecting other pawns in its chain. It is considered a weakness because it cannot advance safely.	Chess\Eval\BackwardPawnEval
Bad bishop	A bishop that is on the same color as most of own pawns.	Chess\Eval\BadBishopEval
Bishop outpost	A bishop on an outpost square is considered a positional advantage because it cannot be attacked by enemy pawns, and as a result, it is often exchanged for another piece.	Chess\Eval\BishopOutpostEval
Bishop pair	The player with both bishops may definitely have an advantage, especially in the endgame. Furthermore, two bishops can deliver checkmate.	Chess\Eval\BishopPairEval
Center	It is advantageous to control the central squares as well as to place a piece in the center.	Chess\Eval\CenterEval
Checkability	Having a king that can be checked is usually considered a disadvantage, and vice versa, it is considered advantageous to have a king that cannot be checked. A checkable king is vulnerable to forcing moves.	Chess\Eval\CheckabilityEval
Connectivity	The connectivity of the pieces measures how loosely the pieces are.	Chess\Eval\ConnectivityEval
Defense	This heuristic evaluates the defensive strength of each side by analyzing how the removal of attacking pieces would affect the opponent's protection. A higher score indicates a stronger defensive position.	Chess\Eval\DefenseEval
Diagonal opposition	The same as direct opposition, but the two kings are apart from each other diagonally.	Chess\Eval\DiagonalOppositionEval
Direct opposition	A position in which the kings are facing each other being two squares apart on the same rank or file. In this situation, the player not having to move is said to have the opposition.	Chess\Eval\DirectOppositionEval
Discovered check	A discovered check occurs when the opponent's king can be checked by moving a piece out of the way of another.	Chess\Eval\DiscoveredCheckEval
Doubled pawn	A pawn is doubled if there are two pawns of the same color on the same file.	Chess\Eval\DoubledPawnEval
Far-advanced pawn	A pawn that is threatening to promote.	Chess\Eval\FarAdvancedPawnEval
Flight square	The safe squares to which the king can move if it is threatened.	Chess\Eval\FlightSquareEval
Isolated pawn	A pawn without friendly pawns on the adjacent files. Since it cannot be defended by other pawns it is considered a weakness.	Chess\Eval\IsolatedPawnEval
King safety	An unsafe king leads to uncertainty. The probability of unexpected, forced moves will increase as the opponent's pieces get closer to it.	Chess\Eval\KingSafetyEval
Knight outpost	A knight on an outpost square is considered a positional advantage because it cannot be attacked by enemy pawns, and as a result, it is often exchanged for a bishop.	Chess\Eval\KnightOutpostEval
Material	The player with the most material points has an advantage. The relative values of the pieces are assigned this way: 1 point to a pawn, 3.2 points to a knight, 3.33 points to a bishop, 5.1 points to a rook and 8.8 points to a queen.	Chess\Eval\MaterialEval
Overloading	A piece that is overloaded with defensive tasks is vulnerable because it can be deflected, meaning it could be forced to leave the square it occupies, typically resulting in an advantage for the opponent.	Chess\Eval\OverloadingEval
Passed pawn	A pawn with no opposing pawns on either the same file or adjacent files to prevent it from being promoted.	Chess\Eval\PassedPawnEval
Pressure	This is a measure of the number of squares targeted by each player that require special attention. It often indicates the step prior to an attack. The player with the greater number of them has an advantage.	Chess\Eval\PressureEval
Protection	If a piece is unprotected, it means that there are no other pieces defending it, and therefore it can be taken for free resulting in a material gain. This indicates a forcing move in that a player is to reply in a certain way. On the next turn, it should be defended by a piece or moved to a safe square. The player with the greater number of material points under protection has an advantage.	Chess\Eval\ProtectionEval
Relative fork	A tactic in which a piece attacks multiple pieces at the same time. It is a double attack. A fork not involving the enemy king is a relative fork.	Chess\Eval\RelativeForkEval
Relative pin	A tactic that occurs when a piece is shielding a more valuable piece, so if it moves out of the line of attack the more valuable piece can be captured resulting in a material gain.	Chess\Eval\RelativePinEval
Space	This is a measure of the number of squares controlled by each player.	Chess\Eval\SpaceEval
Square outpost	A square protected by a pawn that cannot be attacked by an opponent's pawn.	Chess\Eval\SqOutpostEval

The evaluation features are used in two heuristics classes: Chess\FenHeuristics and Chess\SanHeuristic. The former allows to transform a FEN position to numbers while the latter transforms an entire chess game in SAN format to numbers.

use Chess\FenHeuristics;
use Chess\FenToBoardFactory;
use Chess\Function\CompleteFunction;

$function = new CompleteFunction();

$fen = 'rnbqkb1r/p1pp1ppp/1p2pn2/8/2PP4/2N2N2/PP2PPPP/R1BQKB1R b KQkq -';

$board = FenToBoardFactory::create($fen);

$result = [
    'names' => $function->names(),
    'balance' => (new FenHeuristics($function, $board))->getBalance(),
];

print_r($result);

Array
(
    [names] => Array
        (
            [0] => Material
            [1] => Center
            [2] => Connectivity
            [3] => Space
            [4] => Pressure
            [5] => King safety
            [6] => Protection
            [7] => Discovered check
            [8] => Doubled pawn
            [9] => Passed pawn
            [10] => Advanced pawn
            [11] => Far-advanced pawn
            [12] => Isolated pawn
            [13] => Backward pawn
            [14] => Defense
            [15] => Absolute skewer
            [16] => Absolute pin
            [17] => Relative pin
            [18] => Absolute fork
            [19] => Relative fork
            [20] => Outpost square
            [21] => Knight outpost
            [22] => Bishop outpost
            [23] => Bishop pair
            [24] => Bad bishop
            [25] => Diagonal opposition
            [26] => Direct opposition
            [27] => Attack
            [28] => Overloading
        )

    [balance] => Array
        (
            [0] => 0
            [1] => 12.4
            [2] => 0
            [3] => 3
            [4] => 0
            [5] => 0
            [6] => 0
            [7] => 0
            [8] => 0
            [9] => 0
            [10] => 0
            [11] => 0
            [12] => 0
            [13] => 0
            [14] => 0
            [15] => 0
            [16] => 0
            [17] => 0
            [18] => 0
            [19] => 0
            [20] => 0
            [21] => 0
            [22] => 0
            [23] => 0
            [24] => 0
            [25] => 0
            [26] => 0
            [27] => 0
            [28] => 0
        )

)

A chess game can be plotted in terms of balance. +1 is the best possible evaluation for White and -1 the best possible evaluation for Black. Both forces being set to 0 means they're balanced.

use Chess\SanHeuristic;
use Chess\Function\CompleteFunction;

$function = new CompleteFunction();

$name = 'Space';

$movetext = '1.e4 d5 2.exd5 Qxd5';

$balance = (new SanHeuristic($function, $name, $movetext))->getBalance();

print_r($balance);

Array
(
    [0] => 0
    [1] => 1
    [2] => 0.25
    [3] => 0.5
    [4] => -1
)

🎉 Chess positions and games can now be plotted on charts, queried for Data Mining purposes and processed with machine learning techniques.