[White "White (to move)"]
[Black "Black"]
[FEN "rnq1kb1r/ppp3pp/4pn2/4N3/2QP4/2N2P2/PPP3PP/R1B1K2R w KQ - 0 13"]

In this position, White can still castle, but Black cannot (having moved the king twice). Stockfish 10+ (depth 18) assures me that White has an advantage of +6.1, but I am unable to really see why the advantage is so great. I tried some continuing lines of play but Black can hold on to roughly equal material for a long time, so I do not even know how much of the advantage is due to a future tactical threat or merely a superior position.

I am hoping that there is some simple reasoning that is humanly understandable and does not require looking at all possible lines of play for the next 10 moves. Anyone can help?


It really is about king position, but also about how it affects the evaluation when it programmatically adds up the and compares the differences in mobility for each side's pieces. This is where you get the huge difference, and I think this is what you are looking for.

In each of the following lines, deemed best by Stockfish 11, you can see how little the black pieces can move. in particular, it is of note that in each case, the Ra8 and the Qc8 hardly move, and when the Qc8 finally does, it is just to sacrifice itself, or loses material on the move. The same for the Ra8 in the main line that follows. By comparison, look at the mobility of every white piece. The difference is enormous.

For example:

 [FEN "rnq1kb1r/ppp3pp/4pn2/4N3/2QP4/2N2P2/PPP3PP/R1B1K2R w KQ - 0 1"]

 1. Bg5 Be7 2. f4 Nbd7 (2... c6 3. O-O Nbd7 4. Rae1 Rf8 5. Nd3 Nb6 6. Qb3 Nbd5 7. f5 exf5 8. Nxd5 cxd5 9. Nf4 Rf7 10. Bxf6 gxf6 11. Rf3 Kf8 12. Rg3 Bd6 13. Ne6+ Qxe6 14. Rxe6 Bxg3 15. Qa3+ Kg8 16. Qxg3+ Rg7 17. Qd6) (2... Rf8 3. O-O Nbd7 4. Rae1 Nb6 5. Qd3 c6 6. f5 exf5 7. Rxf5 Kd8 8. Rff1 Qe6 9. Ng6 Qc4 10. Nxf8 Bxf8 (10... Qxd3 11. Ne6+ Kd7 12. cxd3) 11. Rxf6 gxf6 (11... Qxd3 12. Rxf8+ Kc7 13. Bf4+ Kd7 14. Rf7+ Kd8 15. Bg5+ Kc8 16. Re8#) 12. Bxf6+ Kc7 13. Be5+ Kd8 14. Qxh7 Nd7 15. Rf1 Qb4 16. Qh4+ Kc8 17. Qg4 Kd8 18. Qh4+ Be7 19. Qh8+ Nf8 20. a3 Qxb2 21. Rxf8+ Bxf8 22. Qxf8+ Kd7 23. Qf7+ Kd8 24. Bf6+ Kc8 25. Qe8+ Kc7 26. Qe7+ Kb6 27. Na4+) (2... Nc6 3. O-O Nxe5 4. fxe5 Nd5 5. Nxd5 exd5 6. Qxd5 Bxg5 7. Qf7+ Kd8 8. Qxg7 Be3+ 9. Kh1 Re8 10. Qf6+ Re7 11. d5 Bd4 12. Qg5 Ke8 13. Qh5+ Kd7 14. Qg4+ Ke8 15. Qxd4) 3. O-O Nb6 4. Qd3 Nfd7 5. Bxe7 Nxe5 6. dxe5 Kxe7 7. f5 Qd7 8. Qg3 Ke8 9. Rad1 Qf7 10. fxe6 Qe7 11. Ne4 Rd8 12. Nd6+ cxd6 13. exd6
  • 1
    It would be nice if you know how Stockfish is evaluating mobility, since that may very well provide a clearer explanation of how it is arriving at +5 score. – user21820 Feb 15 '20 at 15:01
  • 1
    @user21820 even though it is open source, and I could find the code, I am not a programmer, so I can only give this much. – PhishMaster Feb 15 '20 at 15:04
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    Oh I didn't know it's open source. I just took a look at the source code and I suspect I know the answer... – user21820 Feb 15 '20 at 15:17
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    I guess I am just not used to seeing Stockfish evaluation scores for positions like this where one side is stuck exposed in the middle. I didn't have much time to do more than glance through the source code, but I think your answer comes closest to explaining what Stockfish is seeing (evaluation source code), though I suspect it's more about "king danger" than "mobility", though surely the "trapped rook" contributes somewhat. – user21820 Feb 15 '20 at 15:57
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    @bof, No. The material contributes to the mobility plus, and lack of king safety for the black king. It is -3.02 without the Ra1. – PhishMaster Feb 15 '20 at 18:06

So, the simple way to reason out that white is winning is to look at the safety of black's king. White has a very simple plan of developing their bishop to g5, castling and then breaking open the center (either with d5 or with f4-f5, the latter seeming a bit stronger since it forces the a2-g8 diagonal open for white's queen to cause mayhem). After this, white's rooks will be placed on the central files, leaving black's king in mortal danger.

If we try to find moves that hold on for the moment for black, then it's possible to play the bishop out to either e7 or d6, or it's possible to move pawns. Note that no matter what black tries to do, they cannot prevent white from realizing their plan. Black is simply too passive and tied down (due to their obligation to defend e6)

A major problem for black is of course that they cannot castle to put their king to safety, but it's worth noting that even if black still had the option of castling, the kingside wouldn't be a very safe haven due to the f4-f5 break, since the e6 pawn would then be pinned and lost immediately with the black king on g8.

  • I understand the imminent danger for Black's king. What I don't understand is why Stockfish 10+ thinks it is such a big advantage, more than a rook's worth. I have never before seen Stockfish assign such a large value unless there is a tactical advantage corresponding to about that many 'points'. Passed or queening pawn yields 10+ or 64+ score. Here on the other hand I played 10 moves down the best line provided by Stockfish and its evaluation remained stable throughout at +4 to +6, so I suspect there is some persistent tactical threat that I am just not seeing. – user21820 Feb 15 '20 at 12:48
  • user21820 what kind an answer are you looking for? You say you want an human understandable one, but your comment here sounds like you want an explanation not of the chess position, but of the computer evaluation. Are you looking to understand the position as a human or trying to understand how stockfish evaluates? – Michael West Feb 15 '20 at 15:15
  • @MichaelWest: I see a few possibilities: (1) There are a few tactical threats that result in material gain of about +5 for White, and there is a sure way to get to them even if Black can delay it for many moves; (2) White can establish a specific good position no matter the response of Black; (3) Neither of the above hold, and the computer evaluation of +5 is actually an artifact of the evaluation heuristic. If (1) or (2) holds I expect a humanly understandable explanation. I just looked at the source code after Phishmaster pointed out that it is open source, and it seems (3) holds. – user21820 Feb 15 '20 at 15:20

The advantage is positional. It is not material nor tactics that are about to happen.

It is harder for many players to understand positional advantages. But the computer understands is quite well.

Most average players see material advantages but only see positional when it is a looming mate or other drastic advantage.

Looking at every line of play would not make it clearer if you are not able to grok the positional advantage.

What may make it clearer is more experience. Some people never reach that level. Some like Fischer get their quickly.

The big thing here is that black cannot castle and his king is in the middle. Black has an isolated pawn that needs defending. White owns the centre. White is better developed. And white is a pawn up.

Yes, black can defend quite well here, and with club players might even draw. But between GMs or computers it is just a matter of technique and white should win without any problems.

Technique is that magic ingredient GMs use to convert a positional advantage to a win. Although often in the end a positional advantage will result in tactics that win material too and sometimes mate.

  • I understand the positional advantage. What I don't get is what Stockfish is evaluating about the position that gives it such a consistent large but not that large value over a long period of time. Maybe only the programmers can answer that... The thing is that if the position is so bad for Black, it should not be only around +5, but around +10 or more. Yet Stockfish seems to be counting something in particular. – user21820 Feb 15 '20 at 14:58
  • Stockfish and all engines see a lot more than we do. In many AI type programs not even the programmers know why their program gives the answer that it does. Some programs do not now give the full advantage it sees way in the future but only the current advantage. And what does a stockfish point mean anyway? Does anyone have a conversion table between material advantage and positional advantage? Is there another table that take position and material and spits out an overall advantage? The position is about as bad as stockfish said IMHO and my intuition as a very old player and was right. – edwina oliver Feb 15 '20 at 15:07

If you look at the static evaluation of the position in Stockfish, White gets an advantage of 4.17. The top factors in this position are are:

+1.23: King danger. This measures various things, like whether the king has a pawn shelter, how many checks are available, and how many pieces are threatening the area around the king.

+0.77: Piece value bonus. This is the extra pawn.

+0.76: Piece square table bonus. A bonus (or penalty) is given to each piece based simply on what square it's currently on. The knight on e5 is getting a bonus while the knight on b8 is getting a penalty.

+0.48: Mobility. A measure of how many squares are available for each piece. Squares defended by enemy pawns are not counted, and for the queen squares defended by a weaker enemy piece are not counted.

+0.38: Outpost bonus. The White knight on e5 gets a bonus for being on an outpost, and there's also a bonus for the other knight because it can reach the outpost on e4 in one move.

There are also various smaller factors, like Black's isolated pawn, but these are the main factors in the static evaluation of this position.


I checked the position on Lichess' analysis and looked at the source code on Github. On Lichess' engine, the evaluation is +5.8 (Stockfish 10+ depth 22).

  • If we give castling rights to the black king, the evaluation drops to +3.4.
  • If we then take out the pawn on f3 (restore material balance), the evaluation drops to +3.1.
  • If it's black's move (one tempo given to Black and taken away from white), the evaluation drops further to +1.6
  • If we now put the black Queen back to d1, the evaluation drops to +0.8
  • If we put the center pawn back on d2, the evaluation is now +0.3, which is more or less the starting evaluation for a chess game.

From this we can infer that the main factors in this evaluation are:

  1. King safety
  2. Development/mobility and initiative
  3. Material imbalance (one extra pawn)
  4. space (defined by Stockfish as the number of safe squares on your side - the area behind your pawns counts double)
  • Sorry but that kind of comparison is completely unconvincing and possibly misleading. It fails to show that there is no tactical threat, especially since you changed so many things. PhishMaster's comments that taking away the White bishop still yields an advantage for White, while taking away the A1 rook results in a −3 score for White, is much more convincing, if you want to judge anything by such kind of numbers alone. – user21820 Feb 16 '20 at 9:52
  • If you want to test the relative effect of the factors, you would have to change the code to remove the bonus for each factor separately, and recompile and see what the new evaluation is in each case. I don't have the time or motivation to do that, and I don't expect anyone to either. But certainly changing the board doesn't prove anything. – user21820 Feb 16 '20 at 9:56
  • I looked at the lines after every change to make sure I was not creating any tactical opportunity. I think my approach is more telling then randomly creating a major material imbalance by removing a rook or a bishop. The most accurate way of finding out why Stockfish gives this evaluation would be to run the position through in debug mode and find the exact values of each variable. There should be no need to mess with the code. However I am not a C++ guy and it would take too much time for me to set up an environnement and compiling the code from source just to answer this question. – Sylverdrag Feb 16 '20 at 19:16
  • You're not getting the point. I said that you failed to show that there is no tactical threat in the original position. Once you change the position a bit, any sharp plays would very likely vanish. So you have no reason to claim that the resulting lower evaluation is not due to such a sharp play vanishing. – user21820 Feb 17 '20 at 1:36

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