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Betza's use is earlier than Paulowich's, but if it has been used in fairy chess problems, the invention would probably predate Betza. What is your source on the Banshee name and its use in fairy chess? I tried to look up Banshee in A Guide to Fairy Chess by Anthony Dickins, but it wasn't listed.
All The Kings men mentioned Banshee. I now also discovered Jörg Knappen used it his CwdA army Fearful Fairies under that name
I found a link to All the King's Men in a guide by David Howe. Unfortunately, it just gives the name and description with no further information.
The name seems to be a invention by George Jelliss
Using the bash shell in Windows 10, I did a grep search on every issue of Variant Chess, and I didn't find any mention of Banshee. I did another search for Nightrider just to make sure I was doing it correctly, and I got a list of results. Since Jelliss's page is dated even later than Betza's and Paulowich's use of the piece, it's still unknown whether the piece goes back any further than Betza's game in 1995.
Pocket Mutation Chess calls this piece a Cardinalrider.
Wikipedia mentions a Banshee (BNN) piece type on more than one occasion. Here's one link:
https://en.wikipedia.org/wiki/Talk%3AFairy_chess_piece#Fairy_piece_values
Long ago (I think I then even mentioned this on CVP), the wiki on fairy chess pieces mentioned the Banshee (BNN) but apparently it has been largely edited out. The only mention of the Banshee currently (that I can see) is that it is sometimes given as another name for a Unicorn - this is said under the Unicorn entry (the one for (3D) Raumschach), which is a bit misleading since earlier elsewhere (before the edit I referred to) the Banshee had been explicitly given as BNN.
I've asked Mayhematics on twitter about the banshee piece
Edit: I've got an answer, he thinks the name was his (George Jelliss) ideaI've added the value and another name by Gilman. Is this page good enough for Piececlopedia?
I've made a few grammatical and layout edits, and Reviewed the page. For now it is a Piece article, pending Fergus's review for the Piececlopedia. I listed Betza as the inventor.
I added a link to the Bishop article and upgraded this to a Piececlopedia article.
Thanks Fergus. I am really proud for writing this
Information I have on this piece is ...
G. P. Jelliss invented a game called 'Twenty-First Century Chess' in 1991. In this game there is a piece that moves as a Bishop and Nightrider. Also in this game is a piece that moves as Rook and Nightrider.
See 'Variant Chess 6' April-June 1991, page 70. (This is a different game from Karl Munzlinger's game of the same name).
Unsure when he first invented the actual name 'Banshee', but the piece is there in his game. Dang it, now I'll have to research when he first used the name!! Link to how you can see 'Variant Chess 6' and other chess publications here ..
https://www.mayhematics.com/p/p.htm
edit>>> See this link here, by George Jelliss in 2002, 'Variant Chess Games' where the game is described and the name 'Banshee' is used (and 'Raven' for Rook + Nightrider) for his 1991 game. Look under 'T' for 'Twenty-first Century Chess'.
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Does anyone know who first 'invented' this piece?