30 December 2008

A Followup, an Error, and an Insight

In Theoretical Advantage in Chess960 Start Positions, I constructed a table showing chess960 start positions (SP) where the overall results appear to be extreme when compared to other start positions. Tom Chivers asked, 'do you have any interpretations of why these positions are the most/least violent?'. This was the same question I had after posting the analysis, so I'll tackle one of the SPs in this post.

Starting with the first position in that table -- SP024 NBQNBRKR -- I downloaded the PGN game scores from the source of the data (www.computerchess.org.uk) and analyzed the openings using chess software. Start position SP024 is shown in the following diagram.

Start Position 024

My first remark is that the number of games in the sample has increased from the 42 that I recorded in that earlier post to 46. That's an increase of four games in two weeks for just one of the 960 start positions. Computerchess.org.uk isn't standing still.

My second remark is that after analyzing the results for SP024, I realized that my calculations on the original table were wrong! The column '%White', taken from the source data, already included one point for a win plus one-half for a draw. This means that the overall percentage score for White in SP024 was not the 90.5% that I listed, but rather the 76.2% on the original data. I modified the original post to flag my error and to avoid misleading anyone else.

Believe it or not, I'm relieved to have made that error. An overall success rate of 90% for White from a specific start position would be a disaster for the acceptance of chess960. A success rate of 76% is bad enough. The current data, based on 46 games, gives 73.9% for White (+28-6=12), where the four most recent games split +2-2=0.

Looking at the openings used in the 46 games for SP024, I found that 19 started with the moves 1.Ne3 c5 2.d4 (or 1.d4 c5 2.Ne3, which is a transposition), where White sacrifices a Pawn on the second move. None of the sample games had Black accepting the sacrifice, because after 2...cxd4, the sequence 3.Nf5 Nc6 (forced) 4.Qg5, leaves Black with a bad game.

A close look at the initial SP024 position reveals that the e-Pawn is undefended, while the g-Pawn is protected only by the King. Both Pawns can be attacked in two moves by the Queen and the d-Knight (*). This is the SP024 equivalent of the Scholar's mate (1.e4 e5 2.Bc4 -- 3.Qh5 etc.) in traditional chess (SP518). When Tom Chivers observed in his comment that the dangerous start positions share the common feature of 'several Pawns unprotected and these can be easily attacked by the Queen and Bishop', he was on the right track.

Before tackling any other start positions, I'll redo my original table, but I expect the new results will be similar.

(*) - Is this an acceptable way to distinguish one Knight, the d-Knight, from its counterpart, the a-Knight?

1 comment:

Tom Chivers said...

Very interesting follow-up, thanks for it and I look forward to the next!