Castling: The Longest Possibility

Continuing with the four types of chess960 castling that I listed in Castling: A Rook-only Example, the next example is an instructive case of the most common type of castling, where both the King and Rook move. The game started with SP937: RKRBBNQN. Note that the castling pieces are bunched together in the corner in the tightest configuration possible, 'RKR'.

After 22 moves, the players had developed all of their minor pieces, brought their Queens into play, and were ready to castle. The 'RKR' placement of the start position is still visible in the Black pieces.

Mainz 2007, Final Match, Game 2
Aronian, Levon

Anand, Viswanathan
(After 22...Bb5-d7)
[FEN "rkr5/pppb1nq1/3p2pb/3Pp2p/P3P2P/2P1NRP1/1PBB2Q1/RK6 w Aca - 0 23"]

White can castle O-O-O immediately, while Black, before castling ...O-O-O, needs to move the Rook on c8 to any square except d8. Black does, however, have another immediate possibility.

The next moves were 23.O-O-O O-O(!). Black's last move, castling ...O-O, shows the King and Rook making the longest possible castling move in chess960. It might easily be overlooked in the diagrammed position.

After castling, White's King and Rook were on c1 and d1, while Black's were on g8 and f8. With the next moves, 24.Rdf1 Rae8, both players brought the last undeveloped Rook into the game. The full score, courtesy of Chess Tigers, is

[Event "FiNet Chess960 Rapid World Championship"]
[Site "Chess Classic Mainz"]
[Date "2007/8/16"]
[Round "8"]
[White "Anand"]
[Black "Aronian"]
[Result "1/2-1/2"]
[SetUp "1"]
[FEN "rkrbbnqn/pppppppp/8/8/8/8/PPPPPPPP/RKRBBNQN w CAca - 0 1"]

1.e4 e5 2.Ne3 Ne6 3.Ng3 d6 4.c3 Ng6 5.d3 Ngf4 6.Bc2 g6 7.Rd1 Qg7 8.Ngf1 Nc5 9.g3 Nfe6 10.Nd2 Bg5 11.f3 f5 12.Ndc4 fxe4 13.fxe4 h5 14.h4 Bh6 15. d4 Nd7 16.d5 Nd8 17.Bd2 Nf6 18.Rf1 Bb5 19.Rf3 Ng4 20.Qg2 Nf7 21.a4 Nxe3 22.Nxe3 Bd7 23.O-O-O O-O 24.Rdf1 Rae8 25.b3 Nd8 26.Bd3 Rxf3 27.Rxf3 Rf8 28.Rxf8+ Qxf8 29.a5 b6 30.a6 Nf7 31.Qf1 Qe7 32.Nc2 Bxd2+ 33.Kxd2 Qe8 34. Qf6 Nh6 35.Be2 Kh7 36.Nb4 Ng8 37.Qg5 Qf8 38.Ke1 Qe7 39.Qxe7+ Nxe7 40.Nc2 Kh6 41.Na3 g5 42.Bb5 Bc8 43.Kf2 Ng6 44.Nc2 gxh4 45.gxh4 Ne7 46.Nb4 Kg7 47.Be8 Bg4 48.Na2 Bc8 49.Bb5 Ng8 50.Nb4 Ne7 51.Be2 Kg6 52.Nc2 Ng8 53.b4 Nf6 54.Ke3 Kf7 55.Bb5 Ke7 56.Bd3 Bd7 57.b5 Kf7 58.c4 Kg6 59.Nb4 Ng8 60. Bf1 Ne7 61.Be2 Kh6 62.Kf2 Kg6 63.Kg3 Kh6 64.Nc2 Kg6 65.Ne3 Ng8 66.Bf3 Nf6 67.Nc2 Be8 68.Bg2 Kg7 69.Kf2 Bd7 70.Kg3 Be8 71.Kf2 Bd7 1/2-1/2

Why did Aronian prefer castling ...O-O over ...O-O-O? That would be a good question for the grandmaster himself.

Castling: A Rook-only Example

While the rules of chess960 can be explained easily (see Fischer Explains the Rules of Fischer Random), the castling move sometimes leaves newcomers confused. In castling from the traditional start position (SP518: RNBQKBNR), the rule is usually explained, 'the King moves two squares toward the Rook and the Rook hops over the King'. There are additional conditions about the King not being in check or not moving through check, and these don't change for chess960.

In chess960, the castling pieces move to the same squares as in SP518, but there are four distinct ways the two pieces can be moved:-

• by moving both the King and the castling Rook to new squares (as in SP518);
  
• by switching the King and the castling Rook on their squares;
  
• by moving only the castling Rook; and
  
• by moving only the King.

An instructive example of the third case happened in 2009 at Chess Classic Mainz (see CCM9: Nakamura, Grischuk, and Rybka for more about the event). The first third game of the final match between between defending champion GM Aronian and his challenger GM Nakamura started with SP666: RNKRBBNQ. After five moves, the players reached the following position.

Mainz 2009, Final Match, Game 1 3
Aronian, Levon

Nakamura, Hikaru
(After 5...Be8-d7)
[FEN "rnkr1bnq/pp1b1p1p/2pp2p1/4p3/3PP3/2N2NP1/PPP2P1P/R1KRBB1Q w DAda - 0 6"]

At this point, both players had probably already decided to castle O-O-O. This can eventually be done by hopping the Rook on the a-file over the King, but there is a small problem to be solved: the Rook on the d-file blocks the castling move and must be moved first. (The Black Knight on b8 must also move, but this isn't the focus of the current discussion.)

Nakamura played 6.Rd3. This move looks unusual until we recognize that its purpose is to free the d1-square for castling O-O-O. The game continued 6...Na6 (developing the Knight, which is also necessary for ...O-O-O) 7.a3 Bh6+ 8.Bd2 Bg7 9.Be3 exd4 10.Bxd4 Nc5 11.Rd2 Nf6 12.Ng5. White attacks Black's f-Pawn, while threatening a nasty fork on f7. Aronian solved both problems with 15...Rf8, a move which finally prepares ...O-O-O by clearing d8. Now both players whisked their respective Kings into safety with 13.O-O-O O-O-O.

The full score of the game, courtesy of Chess Tigers, is

[Event "CCM9 - Chess960 Rapid WCh"]
[Site "Mainz"]
[Date "2009.07.30"]
[Round "9.1"]
[White "Nakamura, Hikaru"]
[Black "Aronian, Levon"]
[Result "1-0"]
[SetUp "1"]
[FEN "rnkrbbnq/pppppppp/8/8/8/8/PPPPPPPP/RNKRBBNQ w DAda - 0 1"]

1.e4 e5 2.Nf3 g6 3.Nc3 c6 4.g3 d6 5.d4 Bd7 6.Rd3 Na6 7.a3 Bh6+ 8.Bd2 Bg7 9.Be3 exd4 10.Bxd4 Nc5 11.Rd2 Nf6 12.Ng5 Rf8 13.O-O-O O-O-O 14.e5 Ng4 15.f4 Ne6 16.Nxe6 Bxe6 17.h3 dxe5 18.Bxa7 Nf6 19.Ba6 e4 20.Qg1 Rxd2 21. Bxb7+ Kxb7 22.Qb6+ 1-0

This quick win in the first game set Nakamura on the path to winning the match in the third game gave Nakamura an insurmountable lead in the match.

***

Later: I don't what I was thinking when I wrote this. It was the third game, not the first!

World Championship Opening Preparation

How many top level chess games are won (or lost) during home preparation? Quite a few, it appears. Here are three well known examples from World Championship matches.

---

Karpov: 'a classic example of a battle which was decided entirely in the process of home preparation' ('Anatoly Karpov's Best Games' by Karpov; p.94)

Anatoli Karpov vs Garry Kasparov; World Championship Rematch 1986
http://www.chessgames.com/perl/chessgame?gid=1067222

See 14.h3.

---

Kasparov: 'I told my mother, "Just pray he will play the Ruy Lopez. Then he will be dead. Instantly."' ('The Day Kasparov Quit' by ten Geuzendam; p.45)

Garry Kasparov vs Viswanathan Anand; World Championship Match 1995
http://www.chessgames.com/perl/chessgame?gid=1018625

See 15.Nb3.

---

Bareev, Kramnik's second: 'We'd been given a firm directive to prepare this variation specifically. Unfortunately, the work went in various directions and although there were several of us, we didn't manage to analyse the position as much as we should have done, and we couldn't give a precise evaluation in all the lines.' ('From London to Elista', Bareev & Levitov; p.240)

Vladimir Kramnik vs Peter Leko; World Championship Match 2004
http://www.chessgames.com/perl/chessgame?gid=1309482

See 23.Qf2.

---

There are many other examples and I'll add to the list as I encounter them.

***

Korchnoi: 'I ran up against a painstakingly analysed, prepared variation from which, by a direct attack, Karpov won. It was clear that the whole game, from beginning to end, was analysis. This was Karpov's best achievement in the match, but I found it strange that the Informator [Informant] jury should judge it to be the best game of the year. After all, there was no fight, no creativity.' ('Chess Is My Life', Korchnoi; p.108)

Anatoli Karpov vs Viktor Korchnoi; Moscow cf 1974
http://www.chessgames.com/perl/chessgame?gid=1067858

See 19.Rd3.

More on the Concept of Distance

In Randomness in Chess960 Start Positions (SPs), I noted that starting from the traditional start position (SP518: RNBQKBNR) there are exactly three other SPs that are a straightforward swap of two adjacent pieces, and I assigned them a distance of one (see that previous post for an explanation of the distance calculation). The next level of complexity, distance two from SP518, arises from slightly more complicated piece swaps.

• The first scenario is where two pieces separated by a single square are swapped. An example is SP518 with the Queenside Rook and Bishop swapped (SP226: BNRQKBNR).
  
  
• A second scenario is where two pairs of adjacent pieces are swapped. An obvious example is swapping both Rooks with the neighboring Knight (SP326: NRBQKBRN).
  
  
• A third scenario is where three adjacent pieces rotate one square within their little group. An example is shifting the Rook and Knight one square to the right, then the Bishop taking the place of the Rook (SP514: BRNQKBNR).

I imagine that the distance of a particular SP from SP518 has something to do with the number of moves to be played before the game starts to look like a 'normal' game starting from SP518. The maximum distance is ten, and there are nine such positions.

SP080: BBNNRKRQ
SP094: NNRKRBBQ
SP095: NNRKRQBB
SP879: QRKRNNBB
SP912: BBRKRQNN
SP928: BBRKRNQN
SP944: BBRKRNNQ
SP958: RKRNNBBQ
SP959: RKRNNQBB

It's worth noting that all nine SPs have the three castling pieces in the tightest possible configuration ('RKR'), and all but one (SP928) have the Bishops and Knights starting next to the piece of the same type. This gives them less of a random look than when the minor pieces are scattered haphazardly around the back rank.

I compared the nine SPs against my database of games played at Mainz, hoping to find an example game between two top masters. The only match I found was the following 2006 simultaneous game between supergrandmaster Levon Aronian and supermodel Carmen Kass.

Mainz 2006, Chess960 Simul
Kass, Carmen

Aronian, Levon
(After 11.b2xc3(xN))
[FEN "rkr2qbb/ppp1p2p/2n3p1/4Pp2/3N1P2/2P3P1/P1P4P/RKR2QBB b - - 0 11"]

The diagrammed position is obviously not from a traditional SP518 opening. With a Bishop buried on h8 and a vulnerable King, Black appears to be in trouble. Instead of 11...Nxd4, making the best of a dubious position, Black blundered with 11...Na5, losing material. Here is a partial game score, courtesy of Chesstigers.de.

[Event "CCM6 - Chess960 Simultan"]
[Site "Mainz"]
[Date "2006.08.16"]
[Round "?"]
[White "Aronian, Levon"]
[Black "Kass, Carmen"]
[Result "1-0"]
[SetUp "1"]
[FEN "rkrnnqbb/pppppppp/8/8/8/8/PPPPPPPP/RKRNNQBB w CAca - 0 0"]

{SP959} 1.f4 f5 2.g3 g6 3.Nc3 Nd6 4.e4 Nc6 5.e5 Nc4 6.Nf3 d6 7.d3 Nb6 8.d4 dxe5 9.dxe5 Nd5 10.Nd4 Nxc3+ 11.bxc3 Na5 12.Qb5 c6 13.Qxa5 Qd8 14. Qb4 Bd5 15.Bxd5 cxd5 16.Ne6 Qd7 17.Nc5 Qc6 18.a4 {Rest der Partie nicht nachvollziehbar} 1-0

For more about the event, see Chess Classic: Chess960 results, Anand and Aronian simuls. A photo of Kass just before the start of the game is in CCM6 Bulletin 04 [PDF],

Randomness in Chess960 Start Positions

Hikaru Nakamura's win at the 2009 Chess960 Rapid World Championship in Mainz (see CCM9: Nakamura, Grischuk, and Rybka) generated so much attention from American chess columnists that it might be worthwhile to collect them all in a future post. One reason for the attention was Nakamura's charisma; another was the event's unofficial designation as a 'World Championship'.

Mig Greengard, who won the CJA's Chess Journalist of the Year award in 2007 and who covers the elite players and their events, wrote two posts about Mainz that touched on chess960: Chess in the Mainztream and Nakamura 180 in Chess960. Although both posts received lots of interesting comments from his many followers, Mig is clearly no fan of chess960. In 'Mainztream', he called it by the old term 'shuffle chess', mixed up the 2007 event with last year's ('Aronian got some consolation revenge by beating Anand in the "Chess960" shuffle chess final last year and the Armenian is also back to defend his title.'), and added this in the comments:

Every year I forget how looking at these shuffle chess positions makes me queasy. In fact it looks like someone already threw up on the board. Often they boil down to relatively normal positions, but jeez. Soooo ugly!

This reminded me of another comment thread from 2005 that I encountered while preparing a preliminary Chess960 FAQ.

acirce: I tried to watch some of the Mainz Chess960 games live on ICC but the opening phase made me physically sick. I literally couldn't stand it. It was okay when they started to reach normal positions after 15 moves or so. • Gypsy: I believe you are telling it as it is (perhaps with just a little bit of dramatic license). This probably has to do something with the way we have trained our neural synapses. • (From Chessgames.com Fischerandom Kibitzing)

I've seen the same sentiment elsewhere, that random chess960 start positions (SPs) can provoke a feeling of queasiness or nausea. I'm not qualified to discuss the neurological underpinnings for this phenomenon, but I can comment on the randomness of the SPs.

***

I conducted an exercise to measure the difference between the traditional start position (SP518: RNBQKBNR) and the other SPs. I did this by calculating the number of squares between

• the position of each piece in a specific SP's start array, and
  
• the position of the same piece in SP518

For example, a start position with Knights on c1 and d1 would include a value of 1 for the first Knight (the number of squares between b1 and c1) a value of 3 for the second Knight (the distance between d1 and g1). If the same SP had a Rook on a1, it would get a value of 0, and a Bishop on b1 would get a value of 1.

Then I added up the values for all eight pieces in each SP. It turned out that all sums were even numbers, so I divided all results by two [see the footnote]. It follows that the sum of SP518 is 0, because all pieces are starting on their traditional squares. The results across all SPs were distributed as follows, where the first column is the total distance between the pieces in an SP and the same pieces in SP518, and the second column is the number of SPs with that total.

  0: 1
  1: 3
  2: 17
  3: 55
  4: 125
  5: 183
  6: 217
  7: 174
  8: 127
  9: 49
10: 9

The three positions where the total difference is 1 are SP230: NRBQKBNR, SP534: RNBKQBNR, and SP614: RNBQKBRN. You would expect SP534, the twin of SP518 with the King and Queen switched, to be in that list, while the other two positions are SP518 with a Rook and Knight switched. With eight pieces in the start array, you might expect more positions with only two pieces switched, but all other switches involve a Bishop and it is not possible to have both Bishops starting on the same color.

Does this method of classifying chess960 SPs give a reasonable measure of a position's randomness? I'll come back to that question another time.

***

Note: There is probably a simple correlation between the results divided by two and the minimum number of two-piece swaps to go from SP518 to the other SP, but I didn't see it before writing this post. If there is a correlation, I doubt it sheds any additional light on the subject.

Later: If I'd thought about it a little more, I would have realized that there is no simple correlation. The start position with Queen and light-squared Bishop swapped (SP533: RNBBKQNR) is distance two from SP518, but involves only a single piece swap.

CCM9: Nakamura, Grischuk, and Rybka

This year's Chess Classic Mainz has finished (see Preview: Chess Classic Mainz 2009 for links to the events on the official site) and, along with its coverage of the traditional chess events, Chessbase.com provided extensive reports on the chess960 events. For the top chess960 event, Chessbase reported on both days of the four-player, double round robin preliminary in

• Aronian dominates in chess960, and
  
• Nakamura's comeback,

and covered the winners of the three events in

• Nakamura wins Chess960 World Championship (includes a video clip),
  
• Grischuk wins FiNet Chess960 Open, and
  
• Rybka wins Chess960 Computer World Championship.

A video wrapup of press conferences is on Nakamura 960 Champion [webcast.chessclub.com]. At 8:05 into the clip, Macauley Peterson asks a question about game two of the final Nakamura - Aronian match. The start position of the game is shown in the following diagram.

Start Position 451

Nakamura had Black, and the game started 1.b3 b5 2.f3 f6 3.d4 f5. When Peterson asked about 2...f6 and 3....f5, Nakamura replied,

The reason I played ...f6 is that at the start of the game I felt with the Bishops on a1 and h1 (and vice versa) that the key was going to be whose Bishops were better. White played 1.b3 and if I play ...g6, he trades off the Bishops and then I can't castle O-O, and whoever gets the first move there would have the stronger Bishop on the diagonal so that's why I played 2...f6. Then after 3.d4 f5 I felt that my Bishop was simply stronger than his because I control all the breaks in the center. I can play ...e5 or ...c5, so even though I lose a tempo I thought it was the right decision to play 3...f5.

A little later, discussing the same game, Nakamura added,

Game two was the one game where the general principle of playing in the center did not really apply. In certain positions you can play more for diagonals or play on the flanks as opposed to playing strictly in the center, but overall I felt that the main principle to follow is to play in the center.

Here is the PGN of that game, courtesy of Chess Tigers.

[Event "CCM9 - Chess960 Rapid WCh"]
[Site "Mainz"]
[Date "2009.07.30"]
[Round "8.1"]
[White "Aronian, Levon"]
[Black "Nakamura, Hikaru"]
[Result "0-1"]
[Variant "chess 960"]
[SetUp "1"]
[FEN "brnnkqrb/pppppppp/8/8/8/8/PPPPPPPP/BRNNKQRB w GBgb - 0 1"]

1.b3 b5 2.f3 f6 3.d4 f5 4.Nd3 g6 5.Qf2 Bf6 6.g3 Qh6 7.e3 Ne6 8.Qe2 Nb6 9.Nc3 a6 10.Nc5 Nxc5 11.dxc5 Qg7 12.Qd3 b4 13.cxb6 cxb6 14.Nd5 Bxa1 15. Nc7+ Kf7 16.O-O Bc3 17.f4 Bxh1 18.Kxh1 Qf6 19.Rbd1 Qc6+ 20.Qd5+ Qxd5+ 21. Rxd5 Rb7 22.Nxa6 Ra8 23.Nxb4 Bxb4 24.a4 Bc5 25.Re1 e6 26.Rd3 d5 0-1

I'll discuss other games from CCM9 in future posts on this blog.

A Dubious First Move with Black

The diagram shows the start position from a game I played recently at SchemingMind.com. I had the White pieces. The most striking feature of the position is the Bishop pair on the h-side aimed at undefended Pawns on the a-side. Note that the players can also castle O-O-O on the first move.

Start Position 095

Inspection of the games from CCRL 404FRC (see my post on Advantage in Chess960 Start Positions Revisited for a discussion of the data) showed that the engines' most popular moves were 1.Nb3, 1.g3, and 1.Nc3, but I liked 1.f4, which was the engines' fourth choice. My analysis of that move showed that Black had acceptable responses in 1...Nc6, 1...Nb6, 1...g6, and 1...f5, plus a few other moves. After 1...Nb6, I had to be careful about 2...Nc4, threatening mate.

Instead of those moves, my opponent played 1...c5, which looked dubious because of 2.g3, the move I chose; it threatens the other undefended Pawn. My opponent felt obliged to play 2...Rc7, ending any possibility of castling O-O-O. I continued to add to the pressure with 3.Nc3, and my opponent quickly fell into insurmountable difficulties. Here is the PGN, courtesy of SchemingMind.

[Event "Chess960: Pyramid challenge from bemweeks"]
[Site "SchemingMind.com"]
[Date "2009.04.21"]
[Round "-"]
[White "bemweeks"]
[Black "Buckaroo Bob"]
[Result "1-0"]
[Variant "fischerandom"]
[SetUp "1"]
[FEN "nnrkrqbb/pppppppp/8/8/8/8/PPPPPPPP/NNRKRQBB w KQkq - 0 1"]

1.f4 c5 2.g3 Rc7 3.Nc3 a6 4.Nb3 d6 5.Na5 Kc8 6.b4 g6 7.Qf3 Bxc3 8.Qxc3 cxb4 9.Bxb7+ 1-0

I think this is the first time that I won a chess game in nine moves.