Obstruction

One of the very first things we learn is the value of each piece. Without this information it would probably take hundreds of games before we get an idea about which exchange is good or bad. However computers don't have this limitation. They only need to focus on playing chess. Besides they are also able to play very fast. Engines are perfectly capable of figuring out themselves the value of each piece and can even refine this by adding parameters like pair of bishops, position, endgame,...

This is how the traditional engines work today but I get the feeling that Alpha Zero and Leela don't define any value at all of the pieces. I didn't study the code of the programs but for sure mobility of the pieces plays a crucial role. So a piece which can't play, won't be taken into account. Below example illustrates this very well. This was the final position of my game against Marcel Vermaat (see comebacks part 2)

It is a dead draw but Komodo and Stockfish evaluate it totally wrong. Leela however detects that the 2 extra pawns can't move so shows it is completely equal. Counting material doesn't work here. Still I noticed that fortresses aren't necessarily recognized better by Leela. Mobile fortresses so in which pieces defend a zone, are still problematic to evaluate correctly even for this new type of engines.

Nevertheless looking at the mobility of the pieces seems a big improvement of the evaluation upon just counting material. Besides this reminds me of something I did when I started with chess. At that time I regularly tried to figure out on a piece of paper how the mobility influences the evaluation of a position. At a time when no computers existed, I chose a number of positions from a game and colored the squares which were controlled by the pieces. I only applied for a couple of months this method as it is very time-consuming and gives a very low return. Players often wonder when I say that more than likely I would be today a better player if I had access to a good coach. I wasted a lot of time in my childhood to try and error different methods. As an adult it is very hard to reclaim this lost time.

So for a human it makes no sense to figure out which moves will lead to the most positive gap between the mobility of both colors. Nonetheless there are a few themes you can find back in chess-literature which discuss mobility and can be implemented easily. One was introduced by late Mark Dvoretsky years ago in his concept of the superfluous piece. When 2 pieces of the same color are fighting for the same square this it can be useful for the other color not to exchange any of the 2 pieces. In my practice I got last year an opportunity to execute this theme. Although I was aware about it, I wrongly chose for something more ordinary.

Black to move

All my engines recommend Nd8 and consider it stronger than my standard developing move Rad8. So also classical engines do understand to some extend that mobility must be taken into account of the evaluation of a position.

Sometimes a piece is not only restricted in its mobility but it would be even better to not have it on the board at all. The own piece only obstructs. Basic examples are smothered mate and the back-rank mate (see e.g. When your chess pieces betray you). However there are also less clear examples of it. One of them I explained in one of my youth-lessons: 2 knights against 1 pawn.

[Event "A. Troitsky"] [Site "Study"] [Date "????.??.??"] [Round "?"] [White "?"] [Black "?"] [Result "1-0"] [SetUp "1"] [FEN "7k/8/4K3/5N2/8/3N1p2/8/8 w - - 0 1"] [PlyCount "27"] [CurrentPosition "7k/8/4K3/5N2/8/3N1p2/8/8 w - - 0 1"] 1. Nf2! Kg8 2. Ke7 Kh7 (2... Kh8? 3. Kf7 Kh7 4. Ne4 f2 5. Nf6+ Kh8 6. Nh4 f1=Q 7. Ng6#) 3. Kf7 Kh8 4. Kg6! Kg8 5. Ng7! {"Troitsky's standard maneuver which allows the knight to be transferred to e6. On e6 the knight is much more dangerous for the black king." - Dvoretsky} 5... Kf8 6. Kf6 Kg8 7. Ne6! Kh7 8. Kg5! Kg8 (8... Kh8 9. Kg6 Kg8 10. Ng4 f2 11. Nf6+ Kh8 12. Ng5 f1=Q 13. Nf7#) 9. Kg6 Kh8 10. Kf7! Kh7 11. Ng4 f2 12. Nf8+ Kh8 13. Nf6 f1=Q 14. Ng6# {"The pawn was advanced a lot. White managed to give mate anyway as the black king was already locked up from the beginning. If black had more freedom then he would've ran to a8 and the other white knight would've had insufficient time to support." - Dvoretsky} 1-0

Without the pawn it is always a draw but with it you risk to lose. The famous Troitsky-line explains us how far the pawn can be maximally advanced to keep winning chances with the knights. 

Another special case I mentioned casually in my article exchange pawn when standing worse. Brand-new international master Daniel Dardha proved a couple of months earlier once more that rook + bishop against rook isn't fun to defend see his game against Vincent Blom played in the Belgian interclub but sometimes it is with an extra pawn in any case lost.

[Event "Bundesliga 2016-17"] [Site "Munich GER"] [Date "2017.02.19"] [Round "8.2"] [White "Gerigk, E."] [Black "Lampert, J."] [Result "*"] [SetUp "1"] [FEN "8/8/8/8/8/2bkr1P1/5R2/3K4 w - - 0 73"] [ECO "C50"] [WhiteElo "2381"] [BlackElo "2500"] [PlyCount "36"] [EventDate "2016.10.15"] [Eventtype "team-tourn"] [Whiteteam "MSC Zugzwang"] [Blackteam "HSK"] [CurrentPosition "8/8/8/8/8/2bkr1P1/5R2/3K4 w - - 0 73"] 73. Rf1 {(Without the white pawn this would be a draw. However now it is strangely won for black.)} 73... Bd2 74. g4 {(Without the pawn white could force the draw here with Rf3.)} 74... Re2 75. g5 Be3 76. Rf7 Rb2 77. Rd7+ Bd4 78. Rc7 Rb1+ 79. Rc1 Rb5 80. Rc7 Rxg5 81. Re7 Rg2 82. Re8 Rb2 83. Rc8 Bb6 84. Rc6 Be3 85. Rd6+ Bd4 86. Rc6 Rd2+ 87. Kc1 Rf2 88. Kb1 Rb2+ 89. Kc1 Rb5 90. Rd6 Ra5 *

Parents regularly count material on the board of their child to get an idea if their position is good or bad. Only when you play chess at a certain level, you start to realize things are more complicated. So many exceptions exist that it makes little sense to judge a position by only looking at the value of the pieces.

Brabo