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Adrian King's Typhoon(1999) and another large cv of his or two has that exact Bishop 1,2, or 3 maximum called Bishop's Dog. I defined that, as soon there is the third step allowed, the variant piece is considered Bishop, limited Bishop, whether up to three or four or five or more. Three would be still short-range. It became of interest to mention because of comparable three steps, mandatory not optional, of also non-leaping Falcon from year 1992. That was 1996 article become cvpage 2000 write-up in revision. There the 1,2,3 Bishop is described the last section. I sort of doubt either prolific specific-cv specialists Betza or Gilman ever uses this 1, or 2, or 3 Bishop yet. And according to King's wording at Typhoon, several large Shogis do not. Betza covers the restriction for Rook or Bishop in Funny Notation. For example, Glenn Overby's 2003 essay, ''A number N after a capital letter limits the described move to N spaces.''
ah 'Bishop's Dog' thanks!! yes name comes from the shogi piece 'Lion Dog' which moves 1 to 3 squares on the queen lines. I've been coding a lot of shogi pieces lately and there isn't a piece that moves like this, which is pretty amazing because there are heaps of short range sliders in shogi variants.
In fact, a bishop limited to 3 steps can be found in Taikyoku Shogi (The monster version) under the name Rikishi (Wrestler). On the other hand, a piece named Rikishi or Wrestler with different moves occurs in Tai Shogi and Maka Dai Dai Shogi: Here it is a limited bishop who can move also one square horizontally. In Ko Shogi, the Rikishi or Wrestler is lion mover. So sticking to Bishop's Dog for the limited bishop is probably the best choice. This also gives me the opportunity to advertise Derzhanski's list again: http://www.chessvariants.org/piececlopedia.dir/whos-who-on-8x8.html The huge advantage of this list that you can actually find pieces when you know how they move; either by searching the move notation or by estimating their strength and scanning the appropriate strength region.
ah ha, thanks for info on 'Wrestler' in Taikyoku Shogi!! i had seen this piece in this game but i just assumed it moved like it does in Tai Shogi and Maka Dai Dai Shogi. That's excellent, thanks again.
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