Counting Viable First Moves

Over on the Chess960 Jungle blog, HarryO has come up with an interesting concept: Competition to find the SP with the highest number of viable first moves. He explains,

Discovered a start position SP today that has a ridiculous amount of viable first moves options! More than standard chess in fact, 15 in total. The absolute maximum number of first moves in some Chess960 starts is 21, but usually a large number of those can be [written] off because they are possible but theoretically too weak.

He then lists the 15 moves and reveals the methodology used to determine that number.

After a depth-24 search, Houdini-3 thinks that the variation in score between the best and worst first moves in that list is +/- 0.1 which is tiny. [...] In contrast, standard chess has at the very most 13 viable first moves but the variation in score is much bigger at +/- 0.43.

In other words, 1) Run your engine to a fixed depth on a certain SP, and 2) Record how many top moves have a similar evaluation. I imagine that different engines produce different results and that the results for one engine across all 960 SPs would probably tell us something new about the entire set of SPs.

SP491 QRNKBNRB

A few months ago I did a similar experiment that I recorded in a post titled First Move Diversity in Chess960. Working with a sample of real games between real players, most of them less than master strength, I calculated how many different first moves had been played with each SP. My sample was small by chess960 standards, so I'm not convinced the results showed anything conclusive. If the sample had been an order of magnitude larger, I could have also counted responses to the first moves.

For SP491 QRNKBNRB, I discovered that five different first moves had been played (shown here with the number of times each move was played):-

5: 1.g3
4: 1.g4
3: 1.d4
1: 1.Nd3
1: 1.Ng3

Note that the last move in this list, 1.Ng3, isn't even one of the 15 moves on HarryO's list. What move would I play in SP491? That's an exercise that I'll save for another post. In the meantime, it's also worth noting that SP491 was the position that appeared in The First Recorded Fischerandom Game, GM Bronstein - IM Douven 1996. Bronstein, who missed becoming World Champion by the narrowest of margins, played 1.d4.

Pieces in the Corner Square

Remember the following diagram? I developed it to illustrate A Framework for Chess960 Opening Theory. Its objective is to document different combinations of pieces and possible chess960 start squares.

The first column in the table, covering the a/h-files, represents one of the controversial aspects of chess960 : pieces that start in the corner squares. A corner square, having only three adjacent squares, offers fewer opportunities for development than the other back rank squares, which all have five adjacent squares.

A Rook in a corner square is not controversial. That is, after all, the setup used in traditional chess. Starting in the corner, a Rook doesn't interfere with the development of the minor pieces. It just waits patiently until an open file appears on the board, then heads for that file like a boat heads for open water. The first move of a Rook is nearly always along its back rank.

Once in a while a Rook is lifted to its second rank, where it gets active play laterally, but a lift to the third rank is rare. There is a stigma attached to the early two-step move of an a/h-Pawn, making that move psychologically difficult to play. Once in a great while, the blocking Pawn disappears on a capture or an exchange to its adjacent file, opening a file for the Rook immediately.

A Knight in the corner is not particularly controversial. It has only two choices for development, where the third rank on the adjacent file is often the natural move. Going to the second rank two files away requires another move to bring the Knight into full play. This is sometimes an attractive choice when the Knight continues to a central square, like the sequence Na1-c2-e3.

A Bishop in the corner is the most controversial corner placement. The first move of the Bishop can only be on its long diagonal, which requires moving the Pawn on the adjacent file. Even if this limitation can be considered a disadvantage, the Bishop is ready for action after a single Pawn move, which is a distinct advantage.

That leaves the case of a Queen in the corner. There are three ways to activate the strongest piece. I gave examples of diagonal development in a revent post, Opening Queen Swap in the Corner, although the early Queen exchange seen there is not typical.

The Queen can also be developed along its file, by moving the blocking Pawn one or two squares. Another recent post, Activating the Corner Queen, gave an example of a Queen developed vertically. This occurs more frequently than for the Rook, because the Queen obtains a new diagonal for its second move, thereby increasing its activity.

The most popular development of the Rook -- laterally along the first rank -- is perhaps the least popular for the Queen. It requires too many moves to get the Queen into the game, although it might be interesting to collect examples of this to see the circumstances under which it occurs.

There is a choice for any player who has trouble with these many possibilities for the corner square. Stay with the traditional start position. The corner Rook maneuvers are well known and there is little need for further thinking.

Activating the Corner Queen

The family of chess960 start positions (SPs) with a Queen in the corner is among the most challenging to play. There is no applicable principle from the traditional SP (RNBQKBNR) to serve as a guideline, so the players are on their own. Since 25% of all SPs (240 out of 960) have the Queen in the corner, the positions are seen frequently.

I touched on the topic of the corner Queen a few years ago in 'Fianchetto the Light Squared Bishop', where I quoted GM Seirawan saying, 'Unfortunately, because the Queens are buried in the corner, I don't see real tactics breaking out in the first dozen moves or so.' I don't believe that such positions are 'unfortunate'. There is no reason why fireworks need to occur immediately and good results often come to the player who is patient.

My previous post, Opening Queen Swap in the Corner, discussed a treatment of the corner Queen which doesn't happen often. I recently played another game which had a more normal treatment. It started with SP180 NBBRNKRQ and I had the Black pieces. Note that castling O-O is possible on the first move.

The first moves were 1.c4 c5 2.Nb3 Nb6 3.Nxc5 Nxc4 4.b3, reaching the position in the top diagram. Retreating the Knight didn't appeal to me, so I decided to play 4...b6, continuing the symmetry and offering a Pawn sacrifice. In my notes to the game, I wrote, 'Not sure if this is sound, but it's interesting!', a sentiment which arises frequently when I evaluate chess960 opening moves.

The critical line is the desperado continuation 5.Nxd7+ Bxd7 6.bxc4 Nd6 7.d3 Bc6, threatening the c-Pawn and keeping the initiative with Black. My opponent played instead 5.bxc4, and the game continued 5...bxc5 6.Bc2 O-O 7.Bb2 Bb7 8.O-O, reaching the bottom diagram.

In this position I felt that Black had a slight initiative. How is this possible? In fact, the move 6.Bc2 wasted a tempo because the Bishop is not posted any better on c2 than on b1. The b1-h7 diagonal is far more important than the a4-d1 diagonal. This observation helped to answer the key question: how should I develop the Queen. Since the Queen has no aggressive prospects on the a1-h8 diagonal, it can only come into immediate play via h6.

With this in mind I played 8...h5, reasoning that if White played similarly, Black's activity would occur first. The weakening of Black's Kingside (h-side for the purists) is secondary, because the h-Pawn can't be attacked. It might even play an aggressive role by advancing to h4.

Instead of 9.h4, White shielded the Queen on the long diagonal with 9.Nf3. I continued with the plan from the previous move and played 9...Qh6. After 10.d3, the time was right for 10...d5, opening the game. Black's Queen can transfer in one move to the Queenside (a-side), thereby supporting any tactical variations with the most powerful piece on the board. Meanwhile, White's Queen will languish in the corner.

Although the game lasted another 50 moves, Black was always in command and eventually won. The early activation of Black's Queen was the deciding factor.

Opening Queen Swap in the Corner

During the five years that I've been playing chess960 (see Thanks, Bobby for some general reflections), I've played around 100 games. Among my favorites are several games that I won with Black against good players, but one game in particular stands out.

The game was my first playing for a team, conducted under the system described in Parallel Games, two games against the same opponent with the same start position. Much to my dismay, the team was already losing 0-2 a short time into the match when our last board lost both his games by blitzing his moves. 'Overconfidence' was his excuse.

I won my game with White while the other team members played their games to an even result, so the team was one point down with only my game as Black remaining. The game started as SP861 RKNBRNBQ, a Queen-in-the-corner position. The first moves were 1.f4 f5 2.Nd3, reaching the position shown in the top diagram. Here I played 2...g5, planning the continuation 3.fxg5 e5, where Black has excellent play for the Pawn.

My opponent avoided this and the game continued 3.g3 gxf4 4.gxf4 c6 5.e4 fxe4 6.Qxe4 Nd6 7.Qe5, reaching the bottom diagram. White is hoping for an exchange of Queens on e5, repairing his Pawn structure and retaining the initiative.

Black can't avoid the Queen swap, but he can dictate the terms. I played the unusual idea 7...Ng6, when White has nothing better than 8.Qxh8 Nxh8. Black is not worse and has good play against the isolated f-Pawn. The game continued 9.Bg4 e6 10.Ng3 Kc7.

White launched a Queenside attack with the a-Pawn and castled O-O. Black repulsed the attack and launched a counterattack on White's weak Kingside, eventually winning a Bishop for a Knight. A long period of maneuvering set in and I finally converted my positional advantages into an extra Pawn. I wrote about the endgame in a post on my main blog, Simple Positions, Pretty Geometries.

The league's organizer, in a summary of the match, noted,

The cliffhanger of Section B delivered the teams New England [my team] and Team XLink who shared the victory with a result of 5-5. Funnily enough no draws occurred. Absolutely well worth seeing was the clash of two chess960 heavyweights at the first board. Mark with Black managed to defeat Carl in a model correspondence game.

It's always nice to win, but it's even nicer when the game has special value.