How are humans good at chess? It is estimated that the total number of legal positions in chess is somewhere between 10^40 and 10^50. This is of course an enormous number. Computers today with reasonably good chess software can sometimes look 20 moves ahead to find the best continuation.

But (most) humans are incapable of such calculations. After each move, it is practically impossible to compute all the ramifications and variations. Therefore a move made by a human being is expected to be a very poor move indeed.

But this is not the case: looking at GMs games, those people are able to find the ''best'' moves recommended by top engines such as Stockfish, even though they obviously are not calculating billions of combinations per minute.

So what makes humans good at chess, if they are unable to see into the vast space of future variations? When looking at what GMs do better than amateurs, what I usually find is better ''intuition'' or ''feeling for the position''. But these can't be quantified. And GMs are obviously not psychic. So how can they find the best move most of the time? Chess masters often insist that they are not following an internal ''algorithm''. So what on Earth are they following?

How can humans be so good at chess?
Herbert Simon touched on this question. He received the Turing Award in 1975 and the Nobel Prize in Economics in 1978. His primary research interest was decision-making and is best known for the theories of "bounded rationality" and "satisficing". 

Satisficing is a decision-making strategy or cognitive heuristic that entails searching through the available alternatives until an acceptability threshold is met. Simon used satisficing to explain the behavior of decision makers under circumstances in which an optimal solution cannot be determined.

In his paper Theories of Bounded Rationality (1972), Simon used "the game of chess as a microcosm that mirrors interesting properties of decision-making situations in the real world." Here are some useful quotes.


  On the average, at any given position in a game of chess, there are
  about 30 legal moves-in round numbers, for a move and its replies, an
  average of about 10^3 continuations. Forty moves would be a not
  unreasonable estimate of the average length of a game. Then there
  would be perhaps 10^120 possible games of chess. Obviously the exact
  number does not matter: a number like 10^40 would be less
  spectacular, but quite large enough to support the conclusions of the
  present argument.
  
  Chess players do not consider all possible strategies and pick the
  best, but generate and examine a rather small number, making a choice
  as soon as they discover one that they regard as satisfactory.


The limits of rationality in chess.


  (...) three limits on perfect rationality were listed: uncertainty
  about the consequences that would follow from each alternative,
  incomplete information about the set of alternatives, and complexity
  preventing the necessary computations from being carried out. Chess
  illustrates how, in real world problem-solving situations, these three
  categories tend to merge.


Satisficing and optimizing.


  The terms satisficing and optimizing (...) are labels for two broad
  approaches to rational behavior in situations where complexity and
  uncertainty make global rationality impossible. In these situations,
  optimization becomes approximate optimization - the description of the
  real-world situation is radically simplified until reduced to a degree
  of complication that the decision maker can handle. Satisficing
  approaches seek this simplification in a somewhat different direction,
  retaining more of the detail of the real-world situation, but settling
  for a satisfactory, rather than an approximate-best, decision. One
  cannot predict in general which approach will lead to the better
  decisions as measured by their real-world consequences. In chess at
  least, good players have clearly found satisficing more useful than
  approximating-and optimizing