Castling Diversity in Chess960

After posting First Move Diversity in Chess960, I wondered if I could develop any sort of similar statistics for castling -- how many times did players castle to the same side, the opposite side, that sort of thing. What should have been a simple exercise turned out to be more difficult than I expected as I grappled with limitations in the database software I used. Excuses aside, here are the results I calculated on the same 4340 games collected for the 'First Move Diversity' post. First, here are the number of players who castled in each game:-

• 0: 1516 (no castling)
  
• 1: 1607 (only one player castled)
  
• 2: 1217 (both players castled)

These numbers are surprising. Of the 8680 opportunities to castle, more than 50% of the time a player did not execute the option. I went back to recheck my calculations and couldn't find any errors on my part, so the reason must be elsewhere. The 'First Move Diversity' post mentioned that there were 45 games abandoned before the first move was made. I discovered that there were nearly 150 more games that had been abandoned after only a handful of moves had been made. Indeed, short games account for many of the games where no castling occurred. How many, I can't say for sure.

Of the 1607 games where only one player castled, here are the counts for castling to one side or the other:-

• O-O:     883
• O-O-O: 724

Of the 1217 games where both players castled, here are the relevant counts for castling:-

• Both O-O:     659
• Both O-O-O: 313
• Both sides:    245 (both O-O & O-O-O)

It would be useful to compare these chess960 results with similar counts for traditional chess, but I didn't have time to do this. My gut feeling is that castling O-O-O occurs far more frequently in chess960 than in traditional chess.

It might also be useful to examine the castling patterns for the 56 different start positions of the King and Rooks (see Castling Patterns Visualized for a discussion of the basic patterns). Unfortunately, a sample of 4340 games probably isn't enough to produce valid results. I still might look at it if I find the time.

First Move Diversity in Chess960

When I start playing chess960 on a new site like The Lechenicher SchachServer (LSS), one of the first things I do is to check for a chess960 game archive. For LSS I found

Database with all LSS Chess960 tournaments finished up to and including December 2011. 4340 games.

After downloading the file, I imported it into a standard database (not a chess database) for further analysis. Taking averages into account, I expect a sample of 4340 chess960 games to have about 4-5 games per start position (SP). For the LSS games, I counted 858 SPs, meaning a little more than 10% of the valid chess960 SPs haven't been played in a single game.

Of the SPs that have been played, I was curious to know how many different first moves have been tried on average, so I produced the following table. It says that 55 SPs have seen only one first move, 228 SPs have seen two different first moves, and two SPs have seen nine different first moves.

1: 55
2: 228
3: 189
4: 198
5: 115
6: 51
7: 17
8: 3
9: 2

Not shown in the table are 45 games that had no first move, because the games were abandoned before any move was made. As you would expect, the 55 SPs with only one first move were mainly SPs which had fewer games on LSS. What about the two SPs with nine different first moves? Here they are:-

NNBRKBQR 9
RQKNBNRB 9

[Apologies for not adding the SP numbers, like 'SP001' or 'SP534'. Although these are calculated for all LSS games and recorded as a comment before the first move, the number is missing for many games. I could have worked around this, but it wasn't important for this current exercise.]

The second SP in the list ('RQKNBNRB') is in a class by itself. When I look at the counts of games having a particular SP, this is what I see for the first five in descending order (the counts are all even because LSS events are composed of two-game mini-matches where the opponents play both White and Black using the same SP):-

RQKNBNRB 42
NRNKRQBB 18
NRKQRNBB 16
RKNRQBBN 14
BRNBKNRQ 14

In other words, 'RQKNBNRB' was used in 42 of the 4340 games on the database. Why it was used more than twice as many times as any other SP is a mystery. The other SP with nine different first moves ('NNBRKBQR') is more normal. It is shown in the following diagram.

SP070 NNBRKBQR

Here are the nine first moves that were played on LSS, along with a count of the number of times they were tried (e.g. three games for 1.d4):-

3 : 1.d4
2 : 1.e4
1 : 1.b3
1 : 1.c4
1 : 1.f3
1 : 1.g3
1 : 1.g4
1 : 1.Nb3
1 : 1.Nc3

Where do I go with this data from here? I can't say for now, but I'm sure something will come to mind.

Updated Database of SPs (2013-01)

Has it really been nine months since I last updated my database of start positions? Apparently so, according to my previous post on the subject, Updated Database of SPs (2012-03). As the database grows, the work required to update it increases, so I'm going to try to do it more regularly, like every six months.

Castling into an Attack

My first complete chess960 game at The Lechenicher SchachServer (LSS) was another example of Castling Too Soon. LSS tournaments are round robin events made up of two game minimatches, where the opponents play both sides of the same start position. Against this particular opponent, the assigned position was SP608 BBRNQKRN. Note that castling O-O is possible on the first move.

In my game with White, I opened 1.c4 and my opponent played 1...O-O, reaching the position shown in the diagram. In the 'Too Soon' post, I pointed out the disadvantages of premature castling:-

• It's primarily a defensive move, which renders it somewhat passive, and
• it fixes the position of the King as a target for the opponent's pieces.

Both drawbacks apply here as well, to an even greater degree than that first example.

After 1.c4 O-O

In the current game, 1...O-O practically grants an extra tempo for development to White. Even worse, the castled King is under the gun of the Bishops which are well coordinated on adjacent diagonals. The game continued 2.b3 e5, where Black's second move also looks like a positional mistake. After an inevitable ...c5, the square d5 will be permanently weak.

I followed a simple attacking plan of Nh1-g3-f5, g2-g4, f2-f3, and Qe1-h4, eventually checkmating the Black King with 12.Qh7+. My game with the Black pieces isn't finished yet, but it has followed a similar course. White played 1.O-O and the White King was under attack before I had even played my first move.