28 September 2009

Chess960 @ Chess.com

On my main blog I've mentioned several times how much I like Chess.com (see Posts with label Chess.com). I was pleased to see a few months ago that the site now offers chess960. The kickoff was announced in Chess960 Explained!, where Mr. Chess.com himself (aka Erik) explains how to find a game. See also Forums > Chess960 and Other Variants.

27 September 2009

Arbitrariness in Chess Rules

I doubt that anyone can give a real reason why SP518 (RNBQKBNR) is the accepted start position for a game of chess, rather than SP534 (RNBKQBNR), shown in the following diagram. The only difference between the two positions is that the Kings and Queens are switched. Both SP518 and SP534 have the 'royalty' located in the center and both have the other pieces starting in a formation that, given the moves of those pieces, is superbly logical.

Start Position 534

Considering the two start positions objectively, there is no real reason why the Queen should start 'on her color'. The rule could be stated just as easily 'King on his color'. The start positions of the two pieces is an arbitrary decision that makes no real difference one way or the other. If the rules of chess had been codified as 'King on his color', chess opening theory would have developed exactly as it has over the last two centuries, and all of our chess books would have opening diagrams reflecting the switch in the positions of the Kings and Queens.

In chess960 the two start positions SP518 and SP534 are not equivalent. As I pointed out in A Database of Chess960 Start Positions,

SP534 is not a simple mirror image of SP518, the traditional start position. When castling O-O or O-O-O in SP534, the King and Rook end up on exactly the same squares as they do when castling in SP518: e.g. after castling O-O, the Rook ends on f1 and the King ends on g1.

It might not be as obvious as the case with the start positions of the King and Queen, but the rules of castling in chess also contain a big dose of arbitrariness. Suppose the castling rule in traditional chess were defined as follows:-

  • when castling O-O, the King ends on f1, the Rook on e1;
  • when castling O-O-O, the King ends on b1, the Rook on c1.

Other than the observation that it is a little easier to state the informal rule that we use to describe the castling move -- 'the King moves two squares toward the Rook and the Rook hops over the King' -- the new castling rule is just as logical as the traditional rule. The new rule could be stated informally as 'the King moves one square toward the Rook on the Kingside or three squares toward the Rook on the Queenside, and the Rook hops over the King'.

If you've thought about the castling rule in traditional chess ('two squares toward the Rook'), you probably realized that castling to the two sides does not produce identical positional considerations. Castling O-O-O has the advantage that the Rook ends up on a center file (the d-file), while castling O-O has the advantage that the King is located closer to the corner where it is a little safer. After castling O-O-O, a second move (Kc1-b1) is often played to move the King closer to the corner, while after castling O-O, a second move (Rf1-e1) is often played to bring the Rook to a center file. In either case, achieving the full advantages of castling -- safety the King and activate a Rook -- often requires an additional move. (*)

Looking the same way at the new castling rule ('one square toward the Rook on the Kingside or three squares on the Queenside'), the relative merits of the two types of castling have reversed. Castling O-O-O requires an additional move to bring the Rook to the center, while castling O-O requires an additional move to bring the King toward the corner.

Now let's say we define a variant where (a) we always start RNBQKBNR, but (b) in half the games we castle using the rule 'two squares toward the Rook', while in the other half we castle using the rule 'one square toward the Rook on the Kingside or three squares on the Queenside'. We have in fact defined a game where we play SP518 in half of the games and SP534 in the other half of the games. This is because our new castling rules have created a perfect mirror of SP534, with the King always starting on e1 instead of d1.

Looking at the other 958 start positions in chess960, it's easy to see that exactly half of the positions are mirrors of the other half, where the only real difference is the castling rule. We could just as easily have defined a game where (a) the King always starts on the Kingside, but (b) in half the games we respect traditional castling (O-O ends Kg1 and Rf1, O-O-O ends Kc1 and Rd1) while in the other half we use new castling (O-O ends Kf1 and Re1, O-O-O ends Kb1 and Rc1). This would result in exactly the same game as chess960, the sole difference being that the King always starts on the Kingside!

I'm not suggesting that anyone play using this half-and-half castling rule. I can imagine endless debates about which castling rule is actually in use for a specific game. What I'm suggesting is that chess960 is really chess480*2, where '*2' (meaning 'times two') denotes the two castling variants. Even if we were to restrict the number of start positions to two -- SP518 and SP534 -- we would have essentially doubled the number of opening variations available to us in traditional chess.

To repeat the point of my previous post, Chess960 Is an Evolution of Chess. It removes the arbitrariness of traditional chess rules, thereby increasing the complexity of the opening phase.


(*): Of course, the full range of positional considerations behind castling is more complicated than what I've stated. After castling O-O, the Rook might be better placed on a square other than e1, just as after castling O-O-O, the Rook might be better placed on a square other than d1. Similar considerations apply to the best square for the castled King. These complications don't change the direction of my argument; they just show how subtle chess (or chess960) can be.

26 September 2009

Chess960 Is an Evolution of Chess

Over the last few weeks I've investigated the evolution of two important rules in chess. The first rule governs the initial position:-

The second rule governs castling:-

I didn't pick these two rules at random. Together they constitute the sole difference between traditional chess (aka SP518: RNBQKBNR) and chess960. A frequent objection to chess960 is the emotional argument, 'It's not really chess!', which is only true if we consider chess to be exactly the game defined by FIDE's Laws of Chess (appropriately called 'FIDE Chess' by certain people).

The laws are found in FIDE's Handbook under section 'E. Miscellaneous': E.I.01A. Laws of Chess, where, contrary to the belief of the 'It's not really chess!' crowd, we also find in E.I.01B. Appendices the rules of chess960, which were added earlier this year. [Am I the only person who thinks it odd that FIDE classifies the laws of chess under 'miscellaneous'?]

In my lengthy quotes from Murray on the origins of the two rules, I included his summaries on other rules that have evolved through the centuries -- the moves of the pieces, the Pawn's initial move, Pawn promotion, en passant, stalemate, the bare King. These show that the similarities between traditional chess and chess960 are more significant than the differences.

21 September 2009

Murray on the King's Leap, Italian Style

Unlike the excerpt I gave in Murray on the King's Leap, Spanish Style, I've extracted in entirety Murray's section on the Lombard (Northern Italy, including Milan) game. His notes on the King's Leap also represent a more substantial portion of the material in the section (p.461-463).

As for the mention in the last paragraph that 'details will be found on a later page', this refers to the material I covered in More on Castling in Chess.

20 September 2009

Murray on the King's Leap, Spanish Style

The material in Davidson on the King's Leap seems to have been taken mainly from Murray. In the preface to his book, Davidson wrote,
At first I was afraid that my book was to be sheer plagiarism. But I was encouraged by the discovery that if you steal your ideas from one author, that is plagiarism; whereas if you lift them from many, that is research.

If he were alive today, Davidson would undoubtedly be a keen blogger.

Murray described the King's Leap in separate sections in his chapter on 'The Mediaeval Game'. One section addressed chess in Spain, another addressed chess in Italy. Here's what he had to say about the Spanish game (p.457-461).

In fact, except for point (4) in the second part, most of the material I've excerpted has nothing to do with the King's Leap. I've left in the rest to establish the period covered, to show Murray's own sources (MS. Alf. is the Alfonso manuscript and is well described on other Web pages), and to overview the rules of the pre-modern game at that time, particularly the Queen, the Bishop, and the Queen's leap.

19 September 2009

Davidson on the King's Leap

In both The Origin of Castling and More on Castling I quoted several mentions by Murray of the King's Leap. Here's what Davidson had to say about the move in 'A Short History of Chess' (p.22):
The King's Leap. It occurred to early chess players that if in actual practice a mounted soldier could escape capture by leaping over his enemy, the King, who presumably would also be mounted, could escape in the same way. The King was surely as potent as one of his own Knights. And so there was introduced in Sanskrit chess the King's leap -- a privilege of moving like a Knight. This is still the rule in the Malay peninsula where once during the game (usually when "checkmated" -- or to escape checkmate) the King may leap like a Knight. [...] An initial two-move leap for the King was permitted in European chess down to the 13th century.

For more about Davidson, see The Origin of the Initial Position and More on the Initial Position. In his chapter on the Rook, he tied the leap to castling (p.48):

Castling. The root of castling is the King's leap [described above]. There were two forms of this leap. In the first, the King could jump once like a Knight. In the other, he had the privilege of going two squares on his first move. The latter form of the "King's leap" was the practice in European chess down to the 13th century.

In the North African variety of Arabic chess, the King was put into a safe corner by a two-stage procedure. First he moved into the second rank. Then the Rook was brought into the King's original square and simultaneously the King went to the Rook's corner. This was the embryo of modern castling and its development from there proceeded along logical lines. [...]

From North Africa [castling] crossed the Mediterranean along the trade routes and its first appearance in Europe was in Italy toward the close of the 15th century. For a while, Italy was the only country in Europe which used castling in chess play. As the Arabic crescent waxed around North Africa and crossed Gibraltar, the chess practices of the Moslems entered Spain and in the 16th century castling was the rule in Spanish chess. By this time, however, the Arabs had consolidated the maneuver into a single move, so that one-move castling was practiced on the Iberian peninsula and two-move castling on the Italian peninsula.

By 1630 castling was known in France, Britain, and Germany, though because of its dual ancestry, there was for a while some confusion as to the technic. [...] By the end of the 17th century, castling in the modern manner was a fixed rule of chess.

Davidson had a tendency to explain historical facts by speculative musings (e.g. 'It occurred to early chess players...' above). I've removed most of these from the quotes I selected.

14 September 2009

More on Castling in Chess

Following up The Origin of Castling in Chess, I'll continue with Murray (p.830) where I left off in that previous post (p.811-812 as mentioned in Murray's first paragraph).

Note the frequent mention of the word 'leap', a rule that was a carryover from the precursors of modern chess. I'll cover that in another post.

12 September 2009

The Origin of Castling in Chess

Along with the rule governing the initial position in chess, which I covered in two posts on The Origin and More, the other rule differentiating chess960 from chess is the rule governing castling. Where the chess960 rule for the initial position is designed to deliver a richer set of possibilities at the beginning of a game, the rule for castling is designed to steer the game back to positions which are more 'chesslike'.

Murray believed the rule for modern castling arose from the necessity to standardize the rules as players from different localities travelled to compete with each other in an 'even contest'. From his 'History of Chess' (p.811):

I've left the points about stalemate and en passant in the excerpt because Murray's four points are his complete account of the local differences in chess in the 16th century. It was also easier to leave them in than to take them out!

07 September 2009

More on the Initial Position in Chess

In Origin of the Initial Position in Chess, I reported the opinion of chess historians that the initial position in modern chess has its roots in the oldest known version of the game, Indian chaturanga. In the initial positions of both games, the Pawns occupy the second rank, the King and chief counsellor (the Queen in modern chess) occupy the center files, and the three other pieces are placed symmetrically on the flanks of the first rank.

Davidson speculated that the three flank pieces occupy their positions (RNBxxBNR) because that is the most efficient arrangement for an army. Murray, on the other hand, was not so sure ('History of Chess', p.46):

To emphasize Murray's central idea: 'There is no obvious reason why the remaining pieces should be arranged in any particular way, and the existing arrangement (RNB) was probably only arrived at after experiment'. In A Database of Chess960 Start Positions, I pointed out that there are only twelve symmetrical positions with the King and Queen in the center. Of these, there are six with the King on e1 and the Queen on d1.


The move of the modern Bishop wasn't developed until the late 1400s, and could not have been a factor in chaturanga. Experience with chess960, however, shows that when the Bishops start in the four corners, they are often exchanged quickly. I made another observation which might be relevant in Undefended Pawns in Chess960 Start Positions.

Taking SP518 (RNBQKBNR), the eight Pawns are defended in a pattern that looks like 1-1-1-4-4-1-1-1; the a/b/c and f/g/h Pawns are all defended exactly once, while the d/e Pawns are each defended four times. This symmetric result for SP518 is partly because the King and Queen protect the same number of Pawns from a particular start square. It turns out that there is only one other SP that has the same start profile as SP518, its 'twin' SP534 (RNBKQBNR), where the King and Queen swap places on the central squares.

Another variant, which is not a legal start position in chess960, is what Murray called a crosswise arrangement. This is where the King and Queen (or her equivalent) start not on the same file, but where the King starts on the same file as the opposing Queen. This arrangement is seen in certain oriental chess variants. Has it been tried in modern chess?

[For a general discussion about the evolution of chess from chaturanga to the modern game, see The Origin of Chess.]


Later: Re the 'crosswise arrangement', on p.360 Murray gives the moves for a complete game where the Kings start on e1 and d8. White castles Kg1 and Re1; Black castles Kb8 and Rd8.

05 September 2009

The Origin of the Initial Position in Chess

The rules of chess and of chess960 differ in two ways: (1) the initial setup of the pieces, and (2) the rules of castling. How did these particular rules of chess come about? In this post I'll cover the initial setup.

From Murray's 'History of Chess' (p.27; in the third line, the 'same conclusion' is that chess was first developed in India):

From Davidson's, 'A Short History of Chess' (p.7):

Sanskrit Chess. When the game first entered the pages of history, it was called chaturanga and was played in western India. Than, as now, the board was made up of 64 squres, eight by eight. The chessmen represented an Indian army and the name was derived from a Sanskrit word for 'army'. Chaturanga literally means 'four arms'. Chatur is Sanskrit for 'four' and is the ancestor of the Latin word quattor (visible in such English words as 'quartet'). The other half of the term, anga, meant 'arms', and it was in military Sanskrit precisely as we use it in military English. Thus we speak of the 'arms' of the service, meaning its components, such as infantry, cavalry, artillery, and so forth. These are the 'arms' (the very word 'army' has the same origin). The old Indian army was composed of four 'arms': chariots, elephants, cavalry, and infantry; and the word chaturanga meant 'the four arms', that is, the army as a whole.

In the battle line of the Sanskrit army, the chariots were posted on the flanks, while the king and his prime minister stationed themselves in the protected and important center of the line. The cavalry were also deployed on the flanks but nearer the center to permit fast wheeling-in movements. The lumbering elephants were stationed just off center. This is the traditional battle line of all armies -- and for that matter, of a football team, too. Speed on the flanks, power in the center. Finally the foot soldiers were ranked in the front line, then, as now, bearing the brunt of battle. Thus chaturanga was an effigy of a battle.

A little later, Davidson explained that the elephant was the ancestor of the Bishop. The title page of his book tells us that he was a 'Major, Medical Corps Reserve, United States Army', thereby putting his remarks into context.

The conclusion of both authors is that the initial position has carried over virtually unchanged from the 7th century A.D. Murray, however, gave no explanation for the sequence of the three pieces on the flanks. I'll come back to that point in another post.