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The dragon is indeed a t[FR], in Betza's original notation. However, that part of it was never documented on the Betza Notation page (instead languishing on the Chess on a Really Big Board page, though it turns up elsewhere too), and is arguably a little underspecified, so H. G.'s XBetza (which is what the interactive diagram uses) specifies such multi‐leg moves in its own way. In this extension, FyafsF is indeed equivalent to the original t[FR]

The vulture afaict is mainly a longer‐range relative of George Duke's (and more recently Uli Schwekendiek's) Falcon, whose advantage over the bison (from a game design perspective) is its blockability — presumably the same is sought here. Unfortunately, due to the multiple paths to a given destination, it is quite complex to describe. Idk about the extra knight move though, that's perhaps a little gratuitous (presumably to make up for the basic vutlre's lack of maneuverability?)

I agree the birds are quite complex, if potentially interesting to play with? And whether the knight/elephant enhancements are truly necessary may be worth a playtest as well