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!

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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.

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