27 October 2009

Tablebase 1 - Polugaevsky/Kasparov ½

Two years ago, in Tablebase 2 - Botvinnik 0, I gave an example of the difficulty that world class players can have analyzing certain endgames that computers solve in a second. Ever since then, whenever I encounter a nontrivial endgame with six pieces or less, I almost always subject it to the tablebase test. This next example is from the Petrosian chapter in Kasparov's Predecessors III, where he discussed Polugaevsky's career.

Amsterdam 1970
Polugaevsky, Lev

Gligoric, Svetozar
(After 73.Be4-b7
[[FEN "8/1B6/8/5p2/5k2/8/3r1PK1/8 b - - 0 73"]

In the diagrammed position Black sealed 73...Rd3. Polugaevsky wrote,

As I was leaving the tournament hall, I was inclined to think it was a dead draw. But, on delving into the secrets of the position, I found subtleties of which I would never even have dreamed.

Kasparov added,

A lengthy analysis enabled a plan of playing for a win to be found: Black must drive the Bishop from the a8-h1 diagonal and restrict it as much as possible by pursuit with the Rook, and at a convenient moment advance his Pawn f5-f4-f3.It is not at all easy for White to defend.

A tablebase confirms that the position is indeed a draw. The game continued 74. Bc6 Rc3 75.Bd5 Kg4 76.Be6 Rc5 77.Bb3 Kf4 78.Bd1 Rc6 79.Bh5 Rh6 80.Bd1 Rg6+ 81.Kf1 Rd6 82.Bh5 Rd7 83.Kg2 Rg7+ 84.Kf1 Ke4, which is also a draw. Gligoric made a mistake on his 102nd move, letting Polugaevsky force a win.

The moves given above, however, are not all the best. After 83.Kg2, the trusty tablebase tells us that White loses in 44 moves and that the moves 83.Be2 and 83.Be8 were the only sure paths to the draw. The problem with 83.Kg2 is that after 83...Rg7+ 84.Kf1, which is best play, Black should continue 84...Kg5 instead of 84...Ke4, which again allows the draw. The fastest winning sequence with best defense is then

84...Kg5 85.Be2 Kh4 {OM: Only Move} 86.Bc4 Kh3 87.Be6 Kg4 {OM} 88.Bd5 Rd7 89.Bc4 Rc7 {OM} 90.Bg8 Rc8 91.Bf7 Rf8 92.Be6 Re8 93.Bd5 Rd8 94.Bb7 Rb8 95.Bd5 Rb5 96.Bc4 Rc5 97.Be2+ Kh3 {OM} 98.Bf3 Rc1+ 99.Ke2 Rc3 100.Bh1 Kg4 101.Bd5 Rc2+ 102.Ke1 Rc5 103.Bb7 f4 104.Kd2 f3 105.Ba6 Kh3 106.Bf1+ Kh2 107.Ke3 Rc3+ 108.Ke4 Kg1 109.Ba6

With 109...Kxf2, Black wins the f-Pawn and forces mate in 17. I've indicated forced moves with 'OM'. In other positions there are either equivalent moves or slightly inferior wins by a more circuitous route. To play through the complete game see...

Svetozar Gligoric vs Lev Polugaevsky; Amsterdam 1970

...on Chessgames.com.

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