Theoretical Advantage in Chess960 Start Positions

One of the nagging questions about chess960 relates to the fairness of the different start positions. Do White and Black have the same chances from any initial position or do some positions naturally favor one color?

There's an interesting table at CCRL 404FRC : Downloads and Statistics (www.computerchess.org.uk) showing the results of computer vs. computer matches on chess960 start positions (SP). I extracted the data, plugged it into my database of start positions (see A Database of Chess960 Start Positions), and created the following table.

Most of the columns are self-explanatory, except maybe '%White' (percentage wins for White) and '%Score' (overall scoring percentage for White, i.e. one point for a win plus one-half for a draw).

SP	FEN	Gms	%Draw	%White	%Score
Highest Overall Score White
24	NBQNBRKR	42	28.6	76.2	90.50
868	QBBRKRNN	40	22.5	73.8	85.05
74	NNRKBBQR	44	34.1	64.8	81.85
424	RBNQBNKR	32	28.1	67.2	81.25
376	NBRKBRNQ	26	11.5	75.0	80.75
Highest Overall Score Black
92	NBNRKRBQ	28	3.6	41.0	42.90
222	NQRKNBBR	48	12.5	37.5	43.75
694	RQBKNBNR	34	17.6	35.3	44.10
82	BNNRKBRQ	34	17.6	35.3	44.10
396	QBRNNKBR	36	22.2	33.3	44.40
Highest % Draws
404	RBBQNNKR	34	47.1	35.3	58.85
488	QBRNBKNR	24	41.7	45.8	66.65
535	RNBKQNRB	44	40.9	47.7	68.15
426	RNQNBBKR	42	40.5	46.4	66.65
202	QNRKBBNR	40	40.0	55.0	75.00
Lowest % Draws
724	RBBKNQNR	38	0.0	47.0	47.40
92	NBNRKRBQ	28	3.6	41.0	42.90
754	BRKNNBRQ	26	3.8	48.0	50.00
839	RKBNRQNB	44	4.5	47.0	49.95
919	RKBRQNNB	38	5.3	50.0	52.65
Traditional Start
518	RNBQKBNR	28	21.4	39.3	50.00
Traditional Start (K&Q switched)
534	RNBKQBNR	22	31.8	43.2	59.10

At the bottom of the table I've included the traditional start position (SP518) for reference. Curiously, it weighs in at exactly a 50% score, although the expected result in games played between masters should give White a statistical edge. I've also included its first cousin (SP534) for comparison. As for the statistical validity of the table, I have no idea. I suspect there is not enough data to have much confidence in the results, but I can't say how reliable it is.

PGN game scores for the different start positions are also available at the CCRL 404FRC site. Assuming some statistical validility to the data, further avenues of investigation might be

• specific variations in openings that appear to be overwhelmingly favorable for White (e.g. SP024: NBQNBRKR) or moderately favorable for Black (e.g. SP092: NBNRKRBQ), and
  
• relationships between the start position of specific pieces (e.g. Bishops in the corners) and the overall scores.

I'm sure other ideas will present themselves. They always do!

***

Later: I discovered that my results were based on an erroneous assumption. The column labelled '%White', taken from the original data, was already calculated using one point for a win plus one-half for a draw. When I calculated my column '%Score', the results became heavily skewed in White's favor. I struck the erroneous portions of the original post and will redo the complete table in a future post. • Chess for All Ages (that's me) regrets the error.

***

Even later: I posted the corrected table on Advantage in Chess960 Start Positions Revisited.

Chess Movies, Chess Art, Chess Patents

Three new image galleries cover various aspects of chess in the real world.

• Chess in the Movies
  
• Chess Through the Artist's Eye
  
• Chess Patents

More: Links related to my About.com material.

Bias in the Soviet School

Watching Kasparov discuss Predecessors IV (see Kasparov (Live!) on Fischer - Gligoric), I was reminded that one of the themes running through Kasparov's Predecessors series is to track the Soviet School through its dominant position in chess. Even volume IV, subtitled 'Stars of the West', addresses this theme. During Kasparov's lecture at the London Chess Centre, his host Malcolm Pein asked him about a passage where Romanovsky wrote critically about Fine.

Kasparov: Let's not forget that Romanovsky had to write bad things about Western players, especially American players, because in the Soviet Union we had to criticize foreigners for being passive, non-creative, non-attacking, and only the Soviet chess style deserved praise. Romanovsky wrote some nasty things about Fine just before the AVRO tournament in Amsterdam. [1938; reads from Predecessors IV (p.33)] 'The Fine-Flohr style is fundamentally alien to the creativity of Soviet masters.'

Pein: Sounds like good, solid propaganda, Garry, but is there any truth in it?

Kasparov: Before the tournament [Romanovsky] said, [reads another passage from the same page, where Romanovsky is not identified as the author] 'Fine's practical play is fundamentally remote from tactical trickery, resourcefulness, and playing for complications. Because of this Fine loses very rarely, but also usually he only wins against masters who play weaker than him.' That was written before the tournament. In the first five rounds of AVRO, Fine scored 4.5, beating Botvinnik in the first round, then beating Euwe, Flohr, and Reshevsky. While writing the book I came up with some statistics. I'm not sure, but I think Fine is the only [non-World Champion] who had a positive score against World Champions. There are some players who had one or two games, but I'm talking about a player who had 25 games against five World Champions and a +3 score, which is quite impressive, when one talks about him only beating 'weak players'.

Kasparov went on to mention that Leonid Stein also had a positive score against World Champions and, speaking of records, that Reshevsky played 11 World Champions and Najdorf played 10.

Kasparov: Reshevsky was a real threat to the Soviet domination. He couldn't win a candidate tournament, but he had some great moments. In 1955, he beat Botvinnik in a four game USSR-USA match in Moscow. In the center of Moscow, in front of Soviet Union officials, he beat Botvinnik 2.5-1.5. That counts for something.

When I finish with Chigorin, whom Kasparov discussed in Predecessors I, I'll come back to his points about Fine, Flohr, and Reshevsky; plus maybe Romanovsky and Stein.

Kasparov (Live!) on Fischer - Gligoric

The game mentioned in Fischer - Gligoric, CT 1959 is the same game discussed in a clip featured in one of my earliest Video Friday choices: Kasparov's Birthday. Thanks to the kibitzers at Chessgames.com (see link in that first Fischer - Gligoric post) for pointing out that much more of the same Kasparov talk is available on Garry Kasparov at the London Chess Centre (LCC; www.chess.co.uk), where 'Clip 6', the last in the LCC series, is the same clip that I found on YouTube. Kasparov used the LCC visit to promote the just published Predecessors IV, where he discussed -- in 'behind the scenes' style -- the writing of the book.

Chess with Rhythm

Chessvibes.com isn't the only chess site producing high quality videos about Chess on Blip.tv. Here's one from the French magazine Europe Echecs.

Dresden Closing Ceremony (2:32) • The Medal Winners

You can find their Episodes Archive at

• europe-echecs.blip.tv

plus the Episodes Archives of other well known chess personalities at

• macauley.blip.tv, and
  
• chessstrategies.blip.tv

It looks like Blip.tv is the site of choice for serious producers of chess videos.

Chess Magazines on Google

Well, not really. There are, however, a number of magazines with references or articles (it's not clear which) about chess available via Google. The new feature is packaged as a subset of Google books...

Books 1 - 10 of 684 on chess
http://books.google.com/books?lr=&q=chess&as_pt=MAGAZINES&as_brr=0

...where the search is restricted to magazines. Considering how many different titles and issues have been published since the dawn of the magazine age -- Wikipedia dates the first 'general-interest magazine' to 1731 -- that's not a lot of magazines with a reference to chess.

There are even fewer that are unquestionably about chess itself: Books 1 - 10 of 11 on chess intitle:chess. Of those, Popular Mechanics and Popular Science account for half.

Even interesting titles can be misleading. The title Chess players, 'a set of precise, gently mocking miniaturist illuminations, as intricate as the chess game at its center' (New York Magazine, 5 Jun 1978, p.86) is about Satyajit Ray's film The Chess Players; Chess, 'keeps getting revived and revised, but seems deader every time' (New York Magazine, 24 Feb 1992, p.132) is about the musical; and Hillary Rodham Clinton Awards $60,000 Donation to Restore Chicago's Chess (Jet, 15 Nov 1999, p.30) is about Chess Records recording studio.

Even when a reference is ostensibly about chess, as in 'By a simplified, pictorial method, this course teaches you how to play chess in one evening! Pictures, diagrams and examples make everything clear.' (Popular Mechanics, Mar 1947, p.82), it turns out to be an ad for Chess Review magazine. A few weeks ago I mentioned LIFE Photos on Google in Google Images. It's still more interesting, but I expect Google Magazines to get up to speed quickly.

The Google juggernaut rolls on...

A Database of Chess960 Start Positions

Now that I'm comfortable with chess960 concepts, I thought it would be useful to have a small database of the 960 valid start positions. This would let me answer some simple questions like 'how many positions are there with such-and-such characteristics'. I set out on a web search to find the base data relating the 960 start positions (SP) to their corresponding setup string, for example, relating position 518 (SP518) to the traditional chess setup RNBQKBNR. I looked at 20-odd sites, came up empty handed, and decided it would be faster to generate the data myself. Since the basic algorithms are explained on Wikipedia pages, I studied them for the details, and 30 minutes later had my database.

Wikipedia entries often suffer from an excess of detail, and the chess960 pages are no exception. Constructing a random chess960 start position is easy. Confining yourself to White's first rank, first you place a Bishop at random on one of the four light squares and the other Bishop at random on one of the four dark squares. Then you place the Queen at random on one of the six remaining empty squares, followed by the two Knights on the five remaining squares. That leaves three empty squares where you must place the King and Rooks so that the King has one Rook somewhere to its left and the other Rook to its right. When you are done with the White pieces, you place the Black pieces on Black's first rank so that they mirror the White pieces. Then you place all of the Pawns on their respective second ranks.

You can use almost any simple game of chance to choose random squares; dice and cards work well if you repeat a step returning an invalid number, e.g. larger than the number four when placing a Bishop. Coin tosses work if you're comfortable with binary numbers (aren't we all?) and you could even use yarrow stalks or a ouija board if you're comfortable with divination.

The standard accepted numbering of the 960 start positions uses a clever scheme that cycles through the 16 possible setups for the Bishops (4 x 4) and the 60 possible setups for the Queen and Knights (6 x 5 x 4, divided by 2, to factor out the duplication of the Knights). After generating the 960 positions and mapping them to their standard numbers, I loaded the data into my database and created an external page with the most important info...

Chess960 Start Positions
http://www.mark-weeks.com/cfaa/chess960/c960strt.htm

...Armed with the table, I realized I could use it to refine my initial web search and locate other web pages to check my work. First I found 37 chess960 positions on Opening experience : Fischer Random Chess (Chess960). One of its positions didn't match my numbering (SP246), but I quickly determined that it was an error on that page. Then I found another copy of all 960 positions on Fischer random chess setups. This matched my results perfectly and gave me confidence that my work had been correct. I then used my database to answer simple questions like

With the King and Queen on the central files (the d-/e-files), which positions are symmetric? By symmetric, I mean that one type of piece (R, B, or N) is on the a-/h-files, another is on the b-/g-files, and the remaining piece is on the c-/f-files.

Logic says there should be 12 such positions, but how are they numbered? My database says they are numbered like this...

SP323 • BNRQKRNB
SP326 • NRBQKBRN
SP332 • NBRQKRBN
SP339 • BNRKQRNB
SP342 • NRBKQBRN
SP348 • NBRKQRBN
SP515 • BRNQKNRB
SP518 • RNBQKBNR
SP524 • RBNQKNBR
SP531 • BRNKQNRB
SP534 • RNBKQBNR
SP540 • RBNKQNBR

Of course, SP518 is one of those positions, but it's also worth noting that SP534 is similar to SP518, with only the King and Queen switched on the central files. Here's a diagram of SP534.

Start Position 534
The Queen is NOT on her color!

This is a good time to clarify a point that sometimes confuses newcomers to chess960. SP534 is not a simple mirror image of SP518, the traditional start position. When castling O-O or O-O-O in SP534, the King and Rook end up on exactly the same squares as they do when castling in SP518: e.g. after castling O-O, the Rook ends on f1 and the King ends on g1.

Along with identifying the 12 symmetric start positions my database taught me a few other things about the family of valid chess960 start positions. I'll leave that discussion for another post.

***

Note: Listed under 'STRATEGIC CONCEPTS' on Chess Blog Carnival 1/09, where I'm described as 'a support beam of the chess bloggers'. Call me 'Mr. Beam'?