If your computer suggests a move that violates all your logic, try to refute it by exploring variations. Though this might seem like a thankless task, it will help you reach a fuller understanding of the position.

Chess computers use a search function and an evaluation function to calculate many possible moves for both sides in a given position. These programs have advanced algorithms to reduce the time spent searching a position.

## Game tree

A game tree is a dynamic, hierarchical data-structure consisting of nodes (also called vertices) and directed edges (also called arcs). Nodes represent the chess positions that result from each white or black move. The edges indicate a possible transition from one node to another. A chess computer will use the game tree to decide its moves by applying the minimax algorithm, which minimizes the expected loss for either player in a worst-case scenario.

A chess computer will start by constructing the game tree from its current position. Then it will assign a value to each node in the penultimate level. It will then select the nodes that have the best value based on its evaluation function. This is a simple way to choose the best move.

There are many ways to calculate a game tree, and the process is often done in layers. Each layer contains a number of states, each of which has a value corresponding to its probability of being selected as a move by the chess computer.

The early chess computers struggled with the game tree because it took too long to search and compare the different states. It was also difficult to incorporate subtle chess knowledge into the evaluation function. Eventually, it was found that limiting the lookahead to a certain depth and combining it with domain-specific knowledge could solve these problems.

## Alpha-beta pruning

Alpha-beta pruning is a process that reduces the time it takes to search for good moves in computer chess. It is a modification of the Minimax search algorithm, which uses alpha- and beta-cutoffs to prune branches of the game tree that are not optimal. It also reduces the number of moves that need to be examined in order to find a good move.

The alpha-beta pruning process is based on the fact that, at some depth ahead, both players will always maximize board value by playing their best. Hence, there is no need to explore these parts of the game tree any more. Alpha-beta pruning eliminates this unnecessary exploration by removing parts of the tree that can be guaranteed better by either player. This is accomplished by setting the values of alpha and beta to -Limit and +Limit respectively.

Using this technique, the total number of nodes on average that need to be evaluated is O(bd/2), instead of O(bd). This reduction in search time increases the efficiency of the algorithm. This is especially important when computing resources are limited or the player is impatient to wait for results. The effectiveness of this algorithm can be enhanced without sacrificing accuracy by employing cheap heuristics such as the killer heuristic, which ensures that moves that capture pieces are examined before other moves.

## Killer moves

A killer move is a quiet move that doesn’t capture anything, but produces a large advantage for the player making it. A killer move is a good way to reduce the search depth of a position and is a key element in modern chess engines.

Chess computers have many different ways of analyzing a position and determining who has the advantage. For example, they can analyze material, space, pawn structure, plans, and more. They also use specialized hardware to calculate moves and build a game tree.

The strongest chess engine currently available is AlphaZero, developed by Google DeepMind. However, it is not yet available to the public. The next strongest engines are Stockfish and Komodo, which are free to download and use. Both engines have improved dramatically over the last decade, thanks to stronger processors and better chess analysis databases.

The best chess programs use several techniques to speed up their searches, including killer moves, killer heuristic, and priority to captures. These help to ensure that the best moves are searched first, rather than later. This reduces the overall search depth and makes alpha-beta pruning much more effective. These techniques are important, because a bad move at the start of a tree can halt progress. This is especially true for a heuristic such as the history heuristic, which keeps track of the moves that repeatedly cause beta cutoffs at a particular depth and places them near the top of the move list.

## Variations

A chess computer can analyze many different variations of a chess position. It will try to find the strongest move, based on calculation, and will also consider other factors like material, space, pawn structure, and plans. It can also look at the advantages of each side, as well as their drawbacks. This analysis is done using a game tree. It is used to find strong moves in the opening, middle-game, and endgame. It is also important to remember that chess isn’t just about calculation, it’s about understanding the ideas behind the moves.

A computer can theoretically calculate all the possible chess moves, but in practice, this would take too long with current technology. It would also require a lot of storage. Therefore, chess programs use optimization techniques to speed up their search. These include heuristics, forward pruning, and search extensions. These methods reduce the amount of time spent searching for good moves, but they need to be used carefully because over extending or reducing search depth can lead to missing good moves.

Several chess variants have been developed that expand the board to three dimensions or more. These are often based on modern warfare or fantasy and science fiction themes. For example, Raumschach is designed to reflect aerial and submarine warfare, while 5D Chess with Multiverse Time Travel incorporates the idea of parallel worlds. Other chess variants expand the pieces to different sizes or introduce new rules for movement, capturing, and winning conditions.