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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.''