Limit of Calculation

I wonder how many moves ahead players can 'see' and calculate at each rating range, and the limits to this.  Looking at some master games it sometimes seems they can foresee almost everything, the most I can do is about 4 moves, when I have enough time.  Does anybody know any more?

No 4 is about my limit

1

It all depends on the position.  I had White in the following position over the weekend, and calculated it to a draw if Black responds with one of two legitimate first moves, and he did the one I figured out all the way to the end.

By the way, I should add, you know all those posts where I tell beginners not to worry about openings?  KNOW YOUR ENDINGS?  Here's why!  I know my Rook Endings, and especially stock positions.  Philidor's Draw, the Short-Side Defense, Lucena's Position (which I actually achieved the following round as Black on Sunday morning with a Black d-pawn, a Rook for each play, mine on the e-file, cutting off the White King on the f-file, and proceed to win.  White didn't play the most complicated moves that game, but had he, Lucena's position would have been executed - Instead I just won quicker.  KNOW YOUR ENDINGS GUYS!  Makes calculating them easier!

There are numerous problems with your question. One problem is you're assuming that rating and lookahead are strongly correlated. Another problem is the issue is looking through a *tree*, not along a single path. Another problem is that pruning the tree is as important as searching through it, and pruning is a nontactical skill. Another problem is that the needed distance of lookahead depends on the position. There are even more problems with your question. The issue is not at all simple, the answer is complex and is probably not even known in the chess community.

I must be a genius, I can easily calculate 6 moves ahead  (5 and a half, to be precise).

"Pruning the Tree". Thats a great phrase to use for instruction. Thank you.

Of course there are branched possible moves, and only some worth looking at.  But I wanted to know at the elite level roughly how far players could look.  It's sort of like those films where someone sees into the future then uses that information to stop bad shit happening.

i know a mate in six!

I can calculate right to the end of the game...where I lose 😕

If every move is forced, you can calculate forever. It's breadth, rather than depth, which makes calculation difficult. Put another way, it's no so hard to find possible candidate moves in a position you are physically looking at on the board, but much harder to find them in a position you are imagining in your mind potentially occurring a few moves down the line.

i made it!

Qf4+ works too but i dont know how to make an alternate correct!

mate in 6

Smothered mate

Trees are a computer science structure and pruning them is a basic concept of game theory and problem solving.   In a nondeterminstic problem (like chess) where you cannot calculate every possible outcome in a reasonable length of time, you discard search paths that are not useful.  For example, your move leads to being checkmated, forced: conclusion: discard this move if there are alternatives. 

As far as humans go, its a mix of lookahead and theory.  Good players can look ahead to a degree, even evaluate multiple lines, or solve an endgame, etc.  In a complex mid-game, though, they must combine look-ahead with potential, doing things like looking for weak spots to attack or defend and building a combo around positional evaluation rather than attempting to consider every possible move when there may be many hundreds of options for the next 4 or 5 moves.

Kasparov says that the *typical* lookahead needed is 4-5 moves...

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(p. 48)

Without a doubt, the question I am most often asked is "How many

moves ahead do you see?" As with most such questions, the honest an-

swer is "It depends," but that hasn't stopped people from asking or gen-

erations of chess players from concocting pithy replies. "As far as needed"

is one, or "One move further than my opponent." There is no concrete

figure, no maximum or minimum; in a way, it's like asking a painter how

many brushstrokes he uses in a painting. Calculation in chess is not one

plus one; it's more like figuring out a route on a map that keeps changing

before your eyes.

(p. 50)

   In a complicated game this tree of analysis usually stays within a

depth of four or five moves--that is, four or five moves for each player,

(p. 51)

or eight to ten total moves. (We call these half moves: one move for

white and one for black equals one full move.) Unless there are special

circumstances--a particularly dangerous position or a key moment in a

game--I know from years of experience that's a safe, practical amount of 

calculation.

Kasparov, Garry, and Mig Greengard. 2007. How Life Imitates Chess: Making the Right Moves, From the Board to the Boardroom. New York, NY: Bloomsbury USA.

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However, it is aso clear that GMs can and do calculate many more moves ahead in tactical positions (or endgames) when it is needed. In the following tactical position, Kasparov as White saw 10 moves ahead to know that Black was going to run out of checks, which allowed Kasparov to win when he allowed himself to be checked during that period...

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(p. 1)

      Lesson 1

      Tactical Play

The subject of our book is tactics. But where should we

begin? How can we convey to the reader the tactical ideas

which exist in a sharp position?

   The following example shows how a single misstep can be

fatal:

      Diagram 1

      Kasparov - Pulagaevsky, Moscow 1979

Black to move

1. ... Rxe5?

(p. 2)

This is a natural move, but it leads Black into a trap. Black

had to play 1. ... Kxg7 2. Rg1+ Kh7 3. f6 Rg8 4. Rxh6+ with

only a slightly better endgame for White.

2. f6!

   This move simultaneously covers g7, attacks the rook at e5,

threatens Rc8+ and the promotion of the g-pawn as well as Rxh6

and Rh8+. This makes it much more powerful than a mere

double attack!

2. ... Rf2+

3. Kd3   Rf3+

4. Kd4   Re4+

5. Kxd5  Re8

6. Rxh6  Rf5+

7. Kd4   Rf4+

8. Kc5   Re5+

9. Kb6   Re6+

10. Rc6

   And Black resigned because he has run out of checks.

   The example we have just examined shows how important it

is that each player properly evaluate all concrete threats.

Although White's king was subject to many checks, he had

properly calculated that in the end it could escape.

You beat me to a response. Yes, "pruning the tree" is a technical term, so I can't be credited for a creative new term. Here's a diagram showing pruning of a move tree, where the double lines show branches being disconsidered:

Well in either case, when i am teaching kids opening principles, they always seem to not get the purpose.....using the phrase "to prune the tree" will help them visualize.....Although maybe ill use "trim" as they might not know what prune means