A Rook on the square a8 of an empty 8x8 board could move to a1, adistance of seven squares. According to the rule, "half, roundedup", a Halfling Rook could move four squares in that direction, toa4; and next turn it could move only two squares in that direction,to a2; and so it would need three moves to reach a1. This exampledemonstrates a special weakness of Halfling pieces -- they havetrouble reaching the edge of the board, and in fact cannot move tothe edge of the board except by taking a one step move. Thus the newChess proverb will be "When hounded by halflings, hide on the edge."
There are two possible kinds of Halfling pieces, relative halflingsand absolute halflings.
A relative halfling White Rook on a8 could not capture a Black Pawnon a6, because a normal Rook would only be able to move two squaresSouthwards (and thereby capture the Pawn), and the Halfling can only movehalf that far. Although it would be futile to chase the Pawn, theHalfling Rook can intercept it if the rest of the board is empty, bymoving to b8, b4, b2, and a2. Alas for the poor Halfling, the Pawncan capture it on b4; and so, the Pawn wins against the HalflingRook in this miniscule endgame study.
An absolute Halfling Rook on a8 can simply capture the Pawn. Itsrange is half of what a normal Rook could move on an empty board,and so it could move as many as four squares to the South. Ofcourse, even the absolute Halfling Rook cannot force mate in the K+Rversus K endgame -- but at least the Halfling Q can do so.
All my examples and discussions from here on will be about absoluteHalflings. Relative Halflings have a confusing move, that is, it'svery easy to make mistakes and try to make illegal moves with them;and relative Halflings also are very weak, as they can capture onlyat short range.
All my examples and discussions will be about Halflings, as opposedto Thirdlings and Quarterlings and Octolings and Duodecalings --however, such pieces are possible, and can have interesting uses inchess variants.
Halfling ChessIt is obvious that the rule of Halfling movement immediately definesa game that must be named Halfling Chess. The Pawns cannot make atwo step advance, Knights still move as they always did (one stepKnightwise), the Rooks, Bishops, and Queens are Halflings of thesame type. Castling is evidently illegal. One could argue thatCastling is a special move of no distance, of course, but the judgehas ruled that Castling is illegal. Halfling Chess is obviously aplayable and enjoyable game, and one can safely predict that peoplewho like to play Shatranj or DemiChess will also like to playHalfling Chess. It is equally obvious that Progressive HalflingChess and Avalanche Halfling and so on are playable games, and willsuit players of different tastes.
The limitation of distance may have particularly piquant effects ingames such as Halfling Dynamo Chess, or Halfling Conversion Chess.
The Halfling Chess army is presumably decisively stronger than theDemiChess army, even though both armies try to be "half strength",and one reason is that the Halfling Knight is exactly the same asthe normal Knight. Things can be somewhat evened up by using aCrabRider instead of the normal Demichess Crab, but the additivenature of piece power probably still leaves the Halflings decisivelystronger.
The Halfling Nutty Knights will be stronger than the HalflingFabulous FIDEs, because the short range pieces are not handicappedby their Halfling halving. The Halfling Colorbound Clobberers andthe Halfling Remarkable Rookies also gain in strength relative tothe FIDEs, though they do not gain as much as the Nutty Knights do.Finally, the Halfling Forward FIDEs are probably still a good matchfor the Halfling Fab FIDEs. (Knights versus Clobberers is probablyalso a good game.)
On a cylindrical board, the Rook can move an infinite distance East orWest; and so, therefore, can the Halfling Rook.
On an 8x8 board, the empty board mobility of the Halfling Rook isprecisely 8.0 because when it can move 4 spaces North, it cannotmove South at all, and when 3 North is possible, the greatestSouthing is always 1; and so on.
Allowing for the fact that the board is not always empty, as perhttp://www.chessvariants.com/d.betza/pieceval/betterway.html , weget a value of about 6.0 for the average real mobility of theHalfling Rook; and interpolating 0.77 (the ratio of 6.0 to 7.88)into the chart given inhttp://www.chessvariants.com/d.betza/chessvar/pieces/shortrook.htmlwe find that the Halfling Rook's mobility gives it a likely valuethat is midway between the value of a R3 and the value of a R4.
In other words, the numbers predict that a Halfling Rook has verynearly the same value as a FIDE Knight, which is worth somethingbetween 60 percent and two thirds of a FIDE Rook.
Where the Halfling Rook has 0.77 times as much empty board mobilityas the FIDE Rook, the Halfling Bishop has a mere 0.6 times the emptyboard mobility of the FIDE B. However, a high percentage of itsmoves are short, and its mobility allowing for the presence of otherpieces is proportional -- and so it seems safe to take a shortcutand say that a Halfling piece is generally worth 0.6 to 0.66 of thevalue of the corresponding non-Halfling piece.
Thus, the Halfling Queen should be worth a bit more than a Rook.These are theoretical values which have not been play-tested, butare likely to be reasonably accurate.
So far, I have presented a new and unprecedented rule of movement, achess variant that uses it, several likely candidates for goodmatchups in different-armies games, and a good try at estimating thevalue of pieces using the new rule. That should be enough for oneday.
- Halflings: Corrected Calculations.
- Halflings 2.
Categories and Details
CreditsBy Ralph Betza.
How about a piece that moves like a relative halfling rook, then turns 90 degrees and moves an additional step?
For naming I suggest the zeknight, a pun on Zeno's paradox. Any ideas on piece value?
I like anonymous commenter's opinion, but it can't be used for games, wich have riders of oblique leapers (knightrider, for example).
Well that brings up a question: should moves be as considered fractional in Charles's sense, or in a component-wise sense as the anonymous comment suggested? I suppose the article's statement of unchanged knights answers this for the variant, but couldn't the component-wise version be just as interesting?
I can also answer the anonymous question about Halfling Knights. The Knight move is coprime, that is, its coordinates have no common factor except 1 (also true of Camel, Zebra, Giraffe, Antelope moves). Therefore no move is a fraction of it and half of it gets rounded back up to the whole move.
What if a particular game on a cylindical 8x8 board bans null moves (in that case, a Rook moving an exact multiple of 8 steps)? Would a Halfling Rook on such a board be barred from moving any multiple of 4 steps? Or would it be able to round up half a 7-step move to 4 steps - and half a 15-step move to 8 steps? If the latter, the Halfling Rook would actually be stronger than the standard Rook! Perhaps the Rook would have to be made Halfling first and the null move ban then be applied.
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First Created: Thursday, March 1st, 2001
Last Modified: Thursday, March 1st, 2001
File Timestamp: Wed, 14 Jul 2021 17:37:28 -0400
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