16 December 2008

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).

Highest Overall Score White
Highest Overall Score Black
Highest % Draws
Lowest % Draws
Traditional Start
Traditional Start (K&Q switched)

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.

1 comment:

Tom Chivers said...

Interesting . . . do you have any interpretations of why these positions are the most/least violent (etc)? I'm not surprised to see several NNs in the highest scoring positions for white; when they leave several pawns unprotected and these can be easily attacked by the queen and bishop . . . trouble. But others I couldn't guess at the problem.