By default, we start searching a position with alpha and beta set to negative infinity and infinity respectively (a so-called infinite window).
Using an aspiration search, we make a guess as to the score that will be returned, say x, and set alpha and beta to x-d and x+d respectively, where d is some integer.
The guessed value of x is typically the score returned by the previous iteration of the search.
In order to provide an estimate to start with, the first few iterations are typically done with an infinite window.
If the true score is indeed within the narrowed search window, we will have saved time due to the additional cutoffs obtained.
If our guess was wrong, however, the score returned will be useless, and we must waste time searching the position again with an infinite window to obtain the true score.
The value of d should be set as small as possible while avoiding too many researches.
The optimal value will vary between programs, but typically a value of 50 centipawns is used.
Aspiration Search