More on Displacement and Distance

Responding to my post on 'Bizarre Castling Rules'?, HarryO suggested examining the R***K**R positions (see Non-Random Chess960 Trial Game 9: SP864 after 4)...e6), e.g.

1) Do these 18 starts allow [full] Queenside and Kingside castling strategies or are they restricted in some way? [...]

with the further restriction that

The main culprits we should investigate are the six SPs with Knights on the same color probably starting with the four N*N SPs.

I had some difficulties to compare the different positions, so I created a chart in the same style I used in The KID Family Goes the Distance.

With the left Rook (zLR), King, and right Rook (zRR) fixed to their original squares, the list includes SP518, while the 'distance' (Dist) from that position to the other positions is typically low. It turns out that HarryO's suggested positions can be identified easily from a calculation based on the displacements of the pieces (zLR, zLN, etc.).

For example, the first position in the list, SP414, has the left Knight (zLN) displaced by one square and the right Knight (zRN) by three squares. The sum of these -- four squares -- is an even number; the Knights start on different color squares, because they start on different color squares in SP518. For the second position in the list, SP430, zLN = 0 and zRN = -3. The sum of these displacements (using their absolute values) is an odd number, so the Knights are on the same color square (N*N in SP430).

[By similar reasoning, the combined displacements of the Bishops must always be an even number. The Bishops are on different color squares in SP518, a requirement that holds for all chess960 positions.]

Of the 18 positions in the R***K**R family, HarryO is right in pointing out that only six have the Knights on the same color. That means twelve positions have Knights on different colors. Why the imbalance in the two cases? Because Knights on the same color mean there are fewer possibilities for placing the Bishops.

Another curiosity of the same type is the number of positions in the family where a Knight starts on the same square as SP518. There are eight positions where zLN = 0, but only six where zRN = 0. Why the difference? Because in R***K**R, the left Rook and the King are on the same color as the right Knight. This again limits the choice for placing one of the Bishops.

That's all nice to know, but it doesn't tell us anything about the dynamics of the different SPs. Some practical tests will be necessary to do that.

A Two Pawn Gambit for Black

Along with the game featured in my previous post, Dynamic Imbalances Are Instructive, I played another unusual game in the same LSS event. The start position, SP305 BNQBRKRN, is still visible in the top diagram, where my opponent opened with 1.b3.

Here I had the idea to sacrifice a Pawn by playing 1...e5, which my opponent accepted with 2.Qa3+ Be7 3.Qxa7. The game continued 3...Na6 4.Qe3 b5 5.Qh3, when I sacrificed a second Pawn with 5...O-O 6.Bxe5, reaching the bottom diagram.

What's the compensation for the two Pawns? Black is better developed and will gain further time by threatening the Bishop on e5 and the Queen. The Knight on a6 will come into play via c5 (less likely is b4), after which the move ...Qa6 will initiate an attack on the Queenside. The move ...f5 will activate both Rooks and threaten to advance into White's Kingside, supported by the light-squared Bishop on the long diagonal.

All of these objectives were met in the following moves: 6...Ng6 7.Bb2 f5 8.e3 Nc5 9.Ng3 Qa6. Black sacrificed two more Pawns with 10.Nc3 f4 11.Nh5 Ne6 12.Be2 fxe3 13.dxe3 Qa5 14.Bxb5 Bb4 15.Bxd7, when White was no longer able to cope with the pressure. Short of time, he blundered on the 19th move and promptly resigned.

My note to my first move said, 'Not sure it's sound, but it's definitely interesting!' That's one of the attractions of chess960. There are new ideas to be tried as early as the first move.

Dynamic Imbalances Are Instructive

Studying traditional chess often yields benefits in chess960. One obvious area is the endgame, where the old chess and the new chess are virtually indistinguishable. Another crossover occurred while I was working on the series Practical Evaluation on my main blog, in particular the topic 'material imbalances'.

I was playing White in a game on LSS that started as SP009 QNNBBRKR. One of the problems both players have is how to castle. I took a leaf from some ideas documented in a previous post -- Extreme Barbecues -- and decided I would lift the f-Rook up the f-file, thereby getting it out of the way in order to castle O-O. That explains my first moves, 1.f4 d5 2.e3 e6, reaching the position shown in the top diagram. Black has played a couple of normal developing moves.

Now I became attached to an idea that I couldn't get out of my head. It started with 3.f5. In my notes, I gave it '!?' and commented, 'Looks interesting, but is it sound? Willing to take the risk to find out...' My opponent played the obvious moves and the game continued 3...exf5 4.Rxf5 Nd6 5.Rxd5 Bc6 6.Rc5 b6, reaching the bottom diagram where the Rook is effectively trapped. Now I sacrificed the exchange with 7.Rxc6 Nxc6 8.O-O.

It looks like White is simply down the exchange with a single Pawn as compensation. According to IM (now a GM) Larry Kaufman's database research, this is more accurately calculated to be a 0.75 advantage for Black. As compensation, White has the Bishop pair (a 0.50 advantage for White) and two unopposed center Pawns (a 0.20 advantage for White). Since -0.75 + 0.50 + 0.20 gives Black a trivial advantage of -0.05, the material is almost equal. On top of this, both sides are approximately equal in development, with Black perhaps having a slight edge.

The game lasted until move 49, during which time the material imbalance transformed to a Bishop for White versus three Pawns for Black (plus other matched pieces for both sides). Although the result was a draw, the shifting dynamic imbalances were both fun to play and instructive.

'Bizarre Castling Rules'?

From 'Counterplay / Readers Respond', Chess Life (CL), July 2013:-

CASTLING IN CHESS960: ANOTHER APPEAL FOR SIMPLICITY

Chess960 is a noble, but flawed attempt to force players to start thinking from the very first move of the game. The biggest problem with Chess960 are the bizarre castling rules. For anyone not familiar with Chess960, consider the following, which is just one bizarre aspect of “castling.” Depending on the opening setup, when castling, the king can move anywhere from five squares to zero squares to minus one squares (yes, the king can actually move in the opposite direction than it normally would). It would be difficult to teach this maneuver to anyone not familiar with standard chess. A variant called Chess480 seeks to simplify these castling rules, but in doing so creates some of its own issues.

I propose a variant which achieves the goal of eliminating memorization of openings while avoiding the failings of both Chess960 and Chess480. This variant, which I have dubbed Chess18, has a randomized opening setup just like its “predecessors.” The difference is that the rooks and the king start on the same squares that they do now so that castling remains exactly the same as it is now— problem solved!

An additional benefit of Chess18 is that it avoids the situation in Chess960 where with some opening setups White can attack an undefended black pawn with her first move.

When Bobby Fischer met with former FIDE President Kirsan Ilyumzhinov to propose the switch to Chess960, Ilyumzhinov advocated “step-by-step” changes mindful of the heritage of chess. Well, here is such a step.

David Couture, via e-mail

CL also provided a response:-

Chess Life asked Damian Nash, a two-time Utah state champion who ran small Chess960 tournaments at the U.S. Opens in 2010 and 2011, and also conducted small break-out sessions on the topic, to reply:

David Couture hits the nail on the head. Bizarre castling rules are a serious problem with Chess960 (Fischer Random). His solution is novel: Leave the rooks and king on the same squares as classical chess, thereby keeping familiar rules intact. Chess18 is a logical first step toward the evolution of the world’s greatest game, expanding opening books by a factor of 18. Another interesting alternative is “Moab Random,” a form of pre-chess that replaces castling (already a bizarre move in classical chess) with the much simpler ‘evacuation’ of the king to any empty back-rank square.

Kudos to Mr. Couture and other game theorists who attempt to wrestle chess out of the grip of the brilliantly obsessive memorizers at the top, who hold Ph.D. equivalents in opening theory. Consistent with Bobby Fischer’s hope for the future of the game, Chess18 could help return chess to the vastly larger audience of brilliant tacticians and strategists worldwide; at least for a little while, until opening jargon catches up. In classical chess, opening experience usually trumps raw talent. But in ChessX, as X increases, natural ability and sound strategy will yield progressively better results.

What do you think? Are 'bizarre castling rules' the 'biggest problem with chess960'?