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Refuting Fischer 07 February 2008

Bobby Fischer It is well known that Bobby Fischer considered the Karpov – Kasparov world championship matches to have been prearranged.
Not just the results, but the games themselves, move for move.
Fischer stated his views in an interview with an Icelandic radio station in 2002, and Yasser Seirawan provides an account of his experiences with Fischer in his outstanding book No Regrets.

After Fischer moved to Iceland in 2005, GM Helgi Olafsson, who, like Seirawan, did not share Fischer’s views, resolved to show him that his theories didn’t hold water. However, he soon discovered that changing Fischer’s mind was a difficult task. In late May 2005, Fischer showed Olafsson a position that he considered irrefutable proof that the games were prearranged. The position was from the ninth game of the 1984 Karpov – Kasparov match in Moscow.
Here is an ending with a slightly restricted bishop vs. knight and pawns on both wings. Karpov won the game as follows:
45.Ne3 Bb1 46.b4 gxh4 47.Ng2 hxg3+ 48.Kxg3 Ke6 49.Nf4+ Kf5 50.Nxh5 Ke6 51.Nf4+ Kd6 52.Kg4 Bc2 53.Kh5 Bd1 54.Kg6 Ke7 55.Nxd5+ Ke6 56.Nc7+ Kd7 57.Nxa6 Bxf3 58.Kxf6 Kd6 59.Kf5 Kd5 60.Kf4 Bh1 61.Ke3 Kc4 62.Nc5 Bc6 63.Nd3 Bg2 64.Ne5+ Kc3 65.Ng6 Kc4 66.Ne7 Bb7 67.Nf5 Bg2 68.Nd6+ Kb3 69.Nxb5 Ka4 70.Nd6 1-0

For comparison, Fischer showed Olafsson the game Saidy – Fischer (USA ch. 1963), which he said was clearly used as a model when the Karpov – Kasparov endgame was created. This is the position after White’s twenty-third move:

Here it is Black (Fischer) who has the knight. The two positions are very alike and the victory comes about in a similar fashion:
23…Nd7 24.Kf1 Nf8 25.Ke2 Ne6 26.Kd3 h5 27.Be3 Kh7 28.f3 Kg6 29.a4 Kf5 30.Ke2 g5 31.Kf2 Nd8 32.Bd2 Kg6 33.Ke3 Ne6 34.Kd3 Kf5 35.Be3 f6 36.Ke2 Kg6 37.Kd3 f5 38.Ke2 f4 39.Bf2 Ng7 40.h3 Nf5 41.Kd3 g4 42.hxg4 hxg4 43.fxg4 Nh6 44.Be1 Nxg4 45.Bd2 Kf5 46.Be1 Nf6 47.Bh4 Nh5 48.Be1 Kg4 49.Ke2 Ng3+ 50.Kd3 Nf5 51.Bf2 Nh4 52.a5 Nxg2 53.Kc3 Kf3 54.Bg1 Ke2 55.Bh2 f3 56.Bg3 Ne3 0-1
Fischer’s theory was that whoever composed the Karpov – Kasparov game could only have done so by using his ideas of how to win this type of position. It could not be based on an older game because this was the first demonstration of how to win such an endgame. Additionally, similar positions occurred so rarely that it was impossible it could arise by chance in such an important event as a championship match. Olafsson, however, had his doubts about Fischer’s win being the first in such a position.

Following his discussion with Fischer, Olafsson asked if I could find earlier examples of this type of win. My tool for the search was Chess Assistant and I used the three-million-game HugeBase as a starting point. I expected to make several searches, but I began by using material search (Search -> Material…) to create a list of all games where both sides had six pawns and one side had a knight and the other a bishop. The search criteria are shown in the following image:
In the “White” column of the “Material restrictions” panel, I set the “From” and “To” values for white pawns to six, meaning that we are looking for positions where White has exactly six pawns. Similarly, White must have exactly one knight. In the “Black” column, I require six black pawns and one black bishop. In “Total number of pieces” I set both values to sixteen, meaning that there must be exactly sixteen pieces on the board (including the kings).

All other values in this dialog box are set to their default settings. Since “Ignore colors” is selected the search will also find positions where Black has the knight and White has the bishop. The result is a list of all games where the material is equivalent to the positions shown above.

The search produced a list of a little more than 20,000 games, which I then used for all subsequent searches. This made them lightning fast. Next I wanted to produce a much smaller list of games that contained positions similar to the ones which Fischer had shown to Olafsson. As I wasn’t expecting to find many games, I wanted to ensure that I would find all those that could be relevant, so I decided to find the following types of positions.
On the top left we see the position from Saidy – Fischer. White has the bishop and the center pawns are on d4 and d5. The position on the top right is from Karpov – Kasparov, where White had the knight and Black had the bishop. The two positions at the bottom are similar, except that the pawn structure is mirrored vertically. The center pawns are now on e4 and e5, there are three pawns of each color on the queenside and two on the kingside.

I started by limiting the search to positions where none of the pawns had crossed the midline by more than one square. If I didn’t find what I was looking for, I could always relax this requirement and search again; note that in the diagrams above none of the pawns have crossed the midline.

There are at least two different ways to search for such positions in Chess Assistant:

  • Use a combination of advanced search (Search -> Advanced) and the material search shown above.
  • Use CQL.

I preferred CQL for two reasons. First, because it is simply the most powerful search tool available, and second, because it allows me to store the searches (CQL queries) as text files. These are then easy to modify when you want to alter the search criteria. Note that you can also save other types of searches in Chess Assistant, but CQL queries are easier to manipulate once you master the basics.

The CQL query below is a modified version of the one I originally used. It consists of two main sections. In the first, we see a repeated use of the :piececount keyword. This is used to specify the number of different types of pieces on the board. The second section of the query describes the location of the pieces by using so-called piece designators.

The :piececount keyword is best understood by looking at a couple of examples.

    :piececount B 1

This matches a position where there is exactly one (“1”) white bishop (“B”) on the board. Note that this doesn’t say anything about the number of other types of pieces. White pieces are specified using uppercase letters (P, N, B, R, Q, K) and the black ones using lowercase letters (p, n, b, r, q, k). You can also specify several different types of pieces by enclosing them in square brackets:

    :piececount [NRQbrq] 0

This matches a position where there are no rooks or queens on the board and also no white knight or black bishop. In other words, the only allowed pieces are pawns, white bishops and black knights.

The piece designators describe the position of the pieces. In the simplest case, when a piece must be on a specific square, we can write it like this:


This means that there must be a white pawn (“P”) on d4. If we want to search for a white pawn on a2, a3, a4 or a5, we can write it like this:


Note that you can put several piece designators on the same line in a CQL query as shown below. The most mysterious piece designator in the CQL query is the following:


This piece designator matches a position where there is a white bishop (B) on a dark square. The squares listed in the brackets are all the dark squares on the board.

Here is the whole query and, as you can see for yourself, it is mostly composed of :piececount keywords and piece designators. The comments (starting with a semicolon and reaching to the end of the line) show where each of the two main sections begin:

     ; The number of pieces
     :piececount B 1
     :piececount n 1
     :piececount P 6
     :piececount p 6
     :piececount [NRQbrq] 0
     ; The location of the pieces
     Pd4 pd5
     P[a2-5] P[b2-5] P[f2-5] P[g2-5] P[h2-5]
     p[a4-7] p[b4-7] p[f4-7] p[g4-7] p[h4-7]

I described the basic structure of CQL queries in the December 2007 column, including the “match” and “position” keywords. The :flipcolor and :flipvertical keywords, which you can see near the end of the query, are very powerful. If you look at the four diagrams above, I would only find positions similar to the one on the top left without these keywords. The effect of :flipcolor is to transform the query so that it also finds the positions shown on the right hand side and :flipvertical allows me to find the types of positions shown at the bottom. So, with the help of these two keywords, a single CQL query allows me to find the four types of positions that are illustrated above.

The next step was to run the CQL query. Selecting “Search” on the menu bar and then “CQL search” displays a dialog box where the query can be typed in (or pasted) as shown here.
To start the search click “OK”. After about five seconds the search produced a list of 242 games: 132 draws and 110 with decisive results. Next I looked at the 14 games that were played before Saidy – Fischer. Out of these, four ended in a draw, others were trivial wins and some were badly played. So perhaps Fischer was correct after all. Maybe he had been the first to show how to win such positions, since the winning method was not trivial.

The oldest game was Herzog – Eliskases from 1934, but it was a trivial win. The second oldest game was Levenfish – Kotov, (Leningrad 1939). This is the position in the game located by the CQL query.
Levenfish won the game using a method reminiscent of the way Fischer won against Saidy.
31…Bc6 32.Kf1 Ke6 33.Ke2 Kf5 34.Kf3 h5 35.Nd1 Bb5 36.Ne3+ Ke6 37.Kf4 Be2 38.f3 Bd3 39.Nd1 Bf1 40.g4 Bb5 41.Nc3 Bc6 42.b3 hxg4 43.fxg4 Kf7 44.Nd1 Bd7 45.Ne3 Be6 46.Nc2 Bc8 47.Nb4 Bb7 48.g5 Kg7 49.Nd3 Bc8 50.Ke3 Kf7 51.Nf4 Bb7 52.Kd2 Bc6 53.Kc3 Bb7 54.b4 Ba8 55.b5 a5 56.Kd3 Bb7 57.Ke3 Ba8 58.Nd3 Bb7 59.Nb2 Bc8 60.Na4 Bd7 61.Nxb6 Bxb5 62.Nxd5 fxg5 63.hxg5 Bc4 64.Nc3 Ke6 65.Ke4 Kd6 66.d5 Kc5 67.Ke5 Ba6 68.d6 Bc8 69.Nd5 Bf5 70.Ne7 Bd7 71.Nxg6 Kb4 72.Nf8 1-0

Another interesting game was Fairhurst – Keres (Hastings 1955). Realizing that my task was complete, I called Olafsson and sent him all the games I had found. I wondered how Fischer would react when he saw the games. Yet I didn’t have to wait long. Olafsson called me after meeting with Fischer, who had recognized the Fairhurst – Keres game when he saw it. After going through the games Olafsson was pleasantly surprised by Fischer’s reaction: “Unbelievable! Wow, great research.” and then he laughed. He never mentioned this position again to Olafsson, clearly feeling that his theory about the game being prearranged had been refuted.

Dadi Jonsson.

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