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Expanded Chess. Here's the preset:

https://www.chessvariants.com/play/pbm/play.php?game=Expanded+Chess&settings=default

Thanks!...

What would the Xbetza notation be for the Osprey?

That would be DmpafyafsW . That is, you have to extend the two-leg part of the Griffon (yafsW) by prefixing an extra step that can both move and hop (mp) so that it effectively jumps. (mpafW would just be a cumbersome notation for D, glueing two colinear W steps together, but here you are forced to base the move on W/F because in the final leg you want to make single steps.)

what would be betza notation for Knight then Camelrider?

CC would do. (C0, LL or L0 should also work)

I meant the bent rider that moves as Knight first and then camelrider

I meant the bent rider that moves as Knight first and then camelrider

Ah, I misunderstood that. I am afraid this is not possible in XBetza. The problem is that you cannot repeat a set of legs in XBetza to make it a rider, only the basic leap of the atom. This forces use of the Camel atom, but there is no way you could write a Knight move as Camel moves, as the Camel is color bound. (Camel and then Nightrider would be possible, as a Camel can be writte as two Knight moves.)

It could be made possible by allowing parentheses with a repeat count on groups of modifiers, meaning that group could be repeated an arbitrary number of times. (I.e. x(y)4zA = xyzAxyyzAxyyyzAxyyyyzA .) Of course on a board with a finite size you know the maximum number of steps the rider leg could have, and write it as a combination of lame leaps to every possible destination. After all, R = WafWafafWafafafW... . Likewise you could write NalmparNalmparalmparN... , writing the Camel leap as two Knight leaps, transparently glued together at a move-or-hop intermediate square. A short-cut notation for this could be N(almpar)0N , where the 0 means arbitrarily many. (Or you could just use a large number.)

what would camel-then-nightrider be?

There are more pieces that fit that description, but for the one that would move e1-f4-g6-h8... a 'transparent' intermediate g2 could be slipped in. This would make the trajectory bend left 90 degrees at g2 and then right '45' degree at f4 to continue as Nightrider. Problem is that what is left after e1-g2 would become right after e1-f3, so you would have to split it into left-handed and right-handed chiral moves with the aid of an initial hl or hr. This would then give ChlmpalyfrNhrmparyflN , where the y causes range toggle from leaper to slider. (A convention that the meaning of l and r should be swapped on oblique atoms (or effectively oblique sequences of orthogonal/diagonal legs after the first s modifier) when the move starts left-handed would allow us to shrink that to CmparyflN . But the diagram does not implement that.)

Problem is that such tricks would not work on irregularly shaped boards, or boards with holes, as the 'transparent' (mp) intermediate might hit a hole. This could be solved by allowing intermediate legs to stray off board through an o modifier, so that true transparance can be specified as mpo.