Problem with the SP or with the Engines?

Continuing with Proof of Concept with HarryO, in Waving a Yellow Flag I discovered that SP408 and its twin SP749 give lopsided results for White in engine-vs-engine play. Is this because of a problem with the SP or a problem with the engines?

HarryO and I set out to play the SP in the comments to a post on his blog: Non-Random Chess 960 Trial Game 6: SP408. He chose to play 1.d4, the same move played in 64 of the 112 CCRL games, and which had garnered a success rate of 75% for White. The resulting position is shown in the following diagram.

SP408 RBQNBNKR after 1.d4

Now it was my move. I noted in my first comment,

From CCRL I'm seeing 1.d4 with a WLD score of +44-12=8. The two most important variations are 1...c5 with +22-9=6 and 1...Ng6 with +20-2=0. Those are terrible stats for Black.

Later I added,

After 1.d4 c5 2.d5, the most popular move is 2...c4. It's not a bug. The engine is trying to prevent c2-c4, which creates a strong center for White. Note that White has also moved the same Pawn twice, but the second move is very strong because it limits the movement of the Black Knights. I don't think 1...c5 is playable.

On top of that, I don't like 1...Ng6. It commits the Knight to a less than optimal square and leaves White a free hand in the center. I appreciate that it prepares ...O-O and guards the weak e-Pawn, but neither of these objectives is a priority.

I finally decided to play 1...d5, a move which had not been tried in any of the 112 CCRL games. HarryO played the critical move 2.c4, against which I had prepared 2...Nde6. The move depends on the correctness of the tactical sequence 3.cxd5 Nxd4. We played through move 16, and although Black never achieved full equality, he was never in real danger of losing in the opening.

Looking again at the comments we made while making the moves, I am impressed by our general discoveries about chess960. After the game, HarryO expanded the anchor post to highlight some of the unusual variations that might have been played.

Our next game started with the twin of SP408: Non-Random Chess 960 Trial Game 7: SP749. It has the same sequence of pieces, but in reverse order -- only the castling considerations are different. The first two moves for each side mirrored the ideas discovered in SP408. White varied first, playing the equivalent of 3.e3. This put less pressure on Black and when we finally abandoned the trial on move 15, Black had achieved equality and was perhaps even somewhat better.

Getting back to the initial question -- Were the lopsided CCRL results 'because of a problem with the SP or a problem with the engines?' -- I'm convinced that it's a problem with the engines. A discussion of why they go wrong would be a good topic for a future post.

Proof of Concept with HarryO

HarryO and I are playing our eighth chess960 opening now. We've played so many moves over the last six months that I've lost track of what I've covered on this blog and what remains open. Here's a summary of the games to date.

We started off with a test of Non-random Fischer Random, where the players actively choose the start position (SP) themselves, rather than rely on a random process. We played two games, taking a different color in each game. Links to HarryO's posts, where the moves and running commentary can be found, are marked HO; links to my posts are marked MW.

• SP384 BBQRNNKR • HO: Non-Random Chess960 Trial; MW: The Barbecue Positions
  
  
• SP393 QRNBBNKR • HO: Non-Random Chess960 Trial Game 2: SP393; MW: A Clash of Styles (good comments here)

Although the non-random trials worked well enough, we decided to tackle several specific SPs that appear to push the chess960 concept to its limits. Our methodology involves playing enough moves to determine that Black is not overwhelmed in the opening and emerges with a playable game.

• SP000 BBQNNRKR & SP959 RKRNNQBB • HO: Non-Random Chess960 Trial Game 3: SP000 (or SP960 depending on who you talk to) & Non-Random Chess960 Trial Game 4: SP959; MW: Extreme Barbecues
  
  
• SP468 RBBNNKRQ • HO: Non-Random Chess 960 Trial Game 5: SP468; MW: The KQR Corner Family & Deferring the Castling Option

Toward the end of last year, I wrote a post that flagged other problematic SPs: Waving a Yellow Flag. HarryO proposed tackling those and we were off again.

• SP408 RBQNBNKR • HO: Non-Random Chess 960 Trial Game 6: SP408; MW: Twin Research (introduction to SP; no discussion of trial game)
  
  
• SP749 RKNBNQBR (twin of SP408) • HO: Non-Random Chess 960 Trial Game 7: SP749; MW: TBD
  
  
• SP868 QBBRKRNN (in progress) • HO: Non-Random Chess 960 Trial Game 8: SP868; MW: TBD

Looks like I still need to cover SP408 and SP749. To date we haven't found any SPs that are hopeless for Black, but that doesn't mean they are easy to play.

Of Knights and Start Squares

After finishing last week's post on win/draw percentages for the pieces on different start squares -- Pieces, Start Squares, and Scores -- I created more tables for pairs of similar pieces. For example, what is the win/draw percentage for Bishops starting on the a- and b- files versus starting on the a- and d- files? While I was doing this, I discovered another geometry that I had bever noticed before. I'll introduce it with a question.

How many chess960 positions are there where the Knights start on the a- and b- files? Of the six remaining squares, three are available for one Bishop and three are available for the other. Placing the Bishops leaves four squares for the Queen. Putting this together means there are 3 x 3 x 4 possible positions, for a total of 36 positions.

How many positions are there where the Knights start on the a- and c-files? If you answered, 'also 36 of course!', then you're wrong. When the Knights start on a- and c-, they are both starting on the same color square. This leaves four squares for one Bishop and two squares for the other. Since 4 x 2 x 4 = 32, there are fewer chess960 positions than for the Knights' a- and b- configuration. The same is true for all start patterns with the Knights on the same color.

I thought I had already seen all of the start position anomalies, but this was a new one for me. I wonder if there are any others that I've overlooked.

Pieces, Start Squares, and Scores

It seemed like a good idea at the time. The CCRL data (see the right sidebar under 'Resources' for a link), last captured on this blog for Waving a Yellow Flag, is very straightforward: start position (SP), score for White (%), draws (%). Why not calculate the average % for different pieces starting on different files?

The following table shows the results. For example, Bishop starting on the a-file scores 51.55% for White overall and draws in 20.51% of the games.

Although the numbers look like statistical noise, a few patterns might be significant. According to the table, Bishops starting in the corner win less for White than when starting on other squares. Bishops on b/g-files draw less. Knights in the corner win more. Queens in the corner draw less.

Why only 'a good idea at the time'? I expected to see something more convincing.