14 September 2017

A Difficult Tablebase Position

Tablebase (TB) positions make for an interesting class of endgames. While best play in most TB positions is obvious to a good player, some positions defy accurate analysis even for world class players. A recent example is a tiebreak game from the fourth round of the 2017 World Cup, currently being played in Tbilisi, Georgia.

TB games between top players are particularly difficult to annotate. On the one hand, we can't criticize a world class player for not knowing an esoteric endgame which has probably never occurred in his previous experience. On the other hand, we can't pass without comment on positions where one or both players overlook a winning or drawing continuation.

An additional problem is that every single move by either player leads to a new branch of the TB's tree of variations. The TB doesn't explain the winning plan; it just lists moves together with their eventual evaluations. It is the annotator's job to make sense of the moves played and to explain why they work or not.

Another question is how a position compares with similar positions. If we shift a TB position a file to the left or right, or a rank up or down, how does the evaluation change? Similarly, if we leave the Pawn structure the same, but move the Kings (or other pieces) to completely different squares, how then does the evaluation change?

This blog's most recent TB post was Q vs. 2B in TCEC Season 9 Superfinal Followup (December 2016). For this current post, the TB position is R+P vs. B+P, shown below. It helps to know that R vs. B is almost always a draw.

After 47.Rb6-b5(xP)

Here is the PGN for the full game, followed by a brief analysis of the critical positions reached during the game.

[Event "FIDE World Cup 2017"]
[Site "Tbilisi GEO"]
[Date "2017.09.13"]
[Round "4.2"]
[White "Aronian, Levon"]
[Black "Dubov, Daniil"]
[Result "1-0"]
[ECO "D85"]

1.d4 Nf6 2.c4 g6 3.Nf3 Bg7 4.Nc3 d5 5.cxd5 Nxd5 6.e4 Nxc3 7.bxc3 c5 8.Be3 O-O 9.Be2 b6 10.Qd2 cxd4 11.cxd4 Bb7 12.e5 Nc6 13.h4 Qd5 14.h5 Rfd8 15.Rc1 Qa5 16.h6 Bf8 17.e6 f6 18.O-O Qxd2 19.Bxd2 Nxd4 20.Nxd4 Rxd4 21.Be3 Rdd8 22.Bb5 Bd5 23.Bd7 g5 24.f4 Bxh6 25.fxg5 Bg7 26.Bd4 fxg5 27.Bxg7 Kxg7 28.Rf7+ Kg6 29.Rxe7 Rf8 30.Re1 Bxa2 31.Bb5 a6 32.Bd3+ Kf6 33.Rxh7 b5 34.Rh6+ Ke7 35.Rh7+ Kf6 36.e7 Rg8 37.Rh6+ Kf7 38.Rh7+ Kf6 39.Be4 Rae8 40.Rh6+ Kf7 41.Bc6 Bc4 42.Bxe8+ Rxe8 43.Rxa6 Rxe7 44.Rxe7+ Kxe7 45.Kf2 Kf7 46.Rb6 Be6 47.Rxb5 Kf6 48.Kf3 Bf5 49.Rc5 Bd3 50.Ke3 Bf5 51.Kd4 Bb1 52.Rc1 Bg6 53.Rc6+ Kg7 54.Ke5 Bb1 55.Ra6 Bc2 56.Rd6 Kf7 57.Rf6+ Kg7 58.Rf2 Bb1 59.Rb2 Bd3 60.Rd2 Bb1 61.Ke6 Be4 62.Re2 Bd3 63.Rd2 Be4 64.Ke5 Bb1 65.Rd4 Kf7 66.Ra4 Bc2 67.Ra5 Bb1 68.Rc5 Kg6 69.Rc1 Bd3 70.Rd1 Bc2 71.Rd2 Bb1 72.Ke6 Be4 73.g3 Bb1 74.Rb2 Bd3 75.Ke7 Be4 76.Rb6+ Kg7 77.Rb5 Kg6 78.Rb4 Bc2 79.Kf8 Kf6 80.Kg8 Bd3 81.Rd4 Bc2 82.Rd2 Bb1 83.Rf2+ Kg6 84.Rb2 Bd3 85.Rb6+ Kf5 86.Rb4 Kf6 87.Rd4 Bc2 88.Rd2 Bb1 89.Rf2+ Kg6 90.g4 Be4 91.Rd2 Kf6 92.Rb2 Bd3 93.Rb6+ Ke5 94.Kg7 Kf4 95.Rb4+ Be4 96.Rxe4+ Kxe4 97.Kg6 1-0

47.Rxb5: The diagrammed position shows the first TB position reached in the game, where the Pawn capture starts a countdown for the 50-move rule. The TB says, 'Given optimal play on both sides, White will win in 72 moves.' The main variation undoubtedly includes moves that reset the 50-move count.

47...Kf6: The first mistake, giving White a win in 47 moves, which is just inside the 50-move rule. For the next few moves both players find the right plan and make the best moves.

51....Bb1 52.Rc1 Bg6: Both players make a suboptimal move. This is followed by a long sequence of moves which maintain the status quo. White fails to make progress, while Black does not let the position deteriorate prematurely. The TB consistently indicates that White wins in around 30 moves.

73.g3 Bb1: White makes a Pawn move, thereby resetting the 50-move count. Unfortunately for White, the move hands Black a TB draw. Unfortunately for Black, he fails to take advantage of the opportunity and moves into another lost position. The double blunder starts another long sequence where White often lets Black escape with a draw, but Black overlooks the chance and plays into yet another lost position. The right plan for White revolves around a timely g3-g4, while Black needs to prevent this.

92.Rb2 Bd3: White again overlooks the win (the TB says 92.Re2 is the fastest) while Black misses the only move to draw (92...Ke5). After this, White plays accurately to score the win although Black overlooks opportunities to prolong the game for as long as possible.

A discussion of the winning plan in this game and an overview of similar positions in other endgames with R+P vs. B+P would take too much time for a single post. I suppose that someone could even write a book on the subject.

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