19 January 2013

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:-


[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):-


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.


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.

1 comment:

GeneM said...

Mark, you are on to something I care about, even though you don't much care about it.

** What would be the best "second heavily reused start setup".

Desired Attributes:
1. Lower draw rate.
2. More opposite wing castling games.
3. No bishops start on any corner square.
4. White's two knights start on the same shade of square.
5. Closer to no advantage for White.

** 6. Broadest variety of good first moves and thus opening systems; least redundancy.

GeneM , 2012/Jan/23