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I like anonymous commenter's opinion, but it can't be used for games, wich have riders of oblique leapers (knightrider, for example).

**Ben Reiniger**wrote on Fri, Aug 6, 2010 10:58 PM UTC:

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.

'On a cylindrical board, the Rook can move an infinite distance East or West...' - but on cylindrical board rook don't have to move infinite distance, if it's range is limited to 7 squares, it still can use all normal cylindrical rook moves (if board is 8x8, of course), so halfing cylindrial rook should be able to move up to 4 steps sideways.

Um... I fail to see how halfling knights would work just like normal knights. Normal Knights jump 2,1 but a Halfling knight would jump 1,1.

This is the best read on Halflings, having also good links to other Betza material, such as Avalanche(1977). Betza is compelled to re-study Chess Different Armies values affected by ''Halfling-ness.'' Betza concludes, ''...a Halfling piece is generally worth 0.6 to 0.66 of the value of the corresponding non-Halfling piece. Thus the Halfling Queen is worth a bit more than a Rook.'' Betza always thought Chess Unequal Armies, invented around 1980 and called CDA now, was the solution to save 8x8 at all costs, and predicted it would catch on to replace OrthoChess eventually. Deliberate humour and Betza are inseparable, but he meant it that Chess Different Armies was his premier variant.

One could have Halfling Knights as well simply by restating the rule as 'no Halfling piece can move more than half the distance to an edge (rounded up)', so a Halfling Knight could not move from the third rank to the first rank, and so on for each edge. This would prevent it from ever reaching the four corner squares, but it could get everywhere else. It's mobility is 4.375 (2.5 if a Knight is 3, 5/6 of the regular Knight's mobility), exactly equal to a Long Knights, as it has the same number of moves from each square as a Long Knight.

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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?