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Charles Gilman called these Zephyr and Lama respectively, though by his description they cannot make the one‐step move that I'm not sure whether you're including. The latter also turns up as an Osprey in Expanded Chess

In wikipedia Fairy chess pieces they are the Osprey for DthenB and the Ostrich for AthenR

@Bn Em I meant a piece that takes the first 2 steps like a rook and then towards outside like a bishop. The osprey jumps as a dabbabah and then moves towards outside like a bishop. So they are not the same piece.

@Jean-louis

Agreed but these are not the pieces I am talking about. I'm saying a piece that starts like a rook for the first 2 steps and then it goes towards outside like a bishop. So this 2. Maticore would be able to stop or be blocked at wazir sqaures.

Ok so you are indeed including the 1‐step move among the movement possibilities — I suppose your ‘2.manticore’ is different enough from a lame/stepping/blockable osprey/lama (and mutatis mutandis for the ‘2.gryphon’) to merit a different name… maybe. If it's not being distinguished from a ‘true’ osprey/zephyr in a single game I'd be tempted to leave that name as is, though avoiding going too near overlexicalisation is a personal preference.

If the distinction does need to be made within a game (at which point the tradeoff changes imo), then ‘2.manticore’(/‘2.griffon’) is probably fine, if perhaps closer to the (presumably also present in a game featuring both of these) actual manticore/griffin than might be desirable, though I'm not really one to ask for original name suggestions (and M&B13 is apparently lacking names for lama/rook and zephyr/bishop compound with which we could (ab)use M&B8's ‘‐lander’ suffix). Perhaps a name based on lama/zephyr/osprey/ostrich/whatever you want to call them would be more apt? ‘Running Osprey’ isn't altogether without a ring to it…

I've been thinking a little about these pieces, as well as the ‘helical’ crooked riders that Fergus suggested here.

It seems to me these are instances of (modulo one detail, which I'll get to below) the same pattern that brought us the ‘modern’ elephant — i.e. the FA — wrt the original 2‐space‐diagonal Elephant: we have an original piece with a non‐coprime (as Charles Gilman would have it) leaping move and fill in the gap.

As such, it seems to me that, in line with mỹ initial intuitions in both cases, it's probably clearest imo to think of the helical pieces and the 2.bent riders as variations on respectively and lama–osprey/zephyr–ostrich rather than totally distinct pieces (or for that matter as immediate bishop/rook/queen or manticore/griffin derivatives)

The main difference between these and the modern elephant is that, the original piece having riding tendencies already, it seems more natural to have the ‘modern’ component be lame/stepping rather than leaping as in the elephant case. The ‘running’ elephant (as coined in the previous comment) would be a lame/stepping FA, or equivalently a B2.

I wonder whether there are many other piece‐types for which ‘running’ (or indeed ‘modern’) subspecies are useful? Running dababba‐/alfil‐/alibabariders, skip‐riders (panda/bear/harlequin), and slip‐riders (Tamerlane picket ⁊ al.) are just rooks/bishops/queens (and ‘modern’ ones the same but less blockable and this probably OP); running crooked dababba‐/alfil‐/alibabariders likewise reduce to lame contrabrueghels/‐proselytes/‐halcyons. Running alpacas/quaggas/okapis/⁊c. (i.e. alternating pairs of orthogonal and diagonal steps) — straight, curved, or switchback — are perhaps more promising, and not, imo, all too exotic; running nightriders/roses/nightfliers/‐sidlers/‐ladies, the same but starting with a single step, also bear considering, even if not strictly non‐coprime to begin with.

There's one other curious difference between the bent and crooked members of this family: as described, the bent ones can only make the remaining part of its move if the non‐coprime part is made in its entirety (i.e. the ferz/wazir move is to the exclusion of the rook/bishop one), whereas the crooked pieces must make both componets regardless (this difference is more pronounced when considering the time‐reversed versions, i.e. running contrazephyr/contraproselyte/⁊c.: the former is committed to a full alfil leap if it starts with a non‐zero rook move — the alternative would be the existing fimbriated griffon — while the latter has to make its final turn and ferz step lest it become equivalent to the aforementioned running crooked alfilrider (as well as curtailing its first, rather than its last alfil run; the pair with one time‐inverted but not the other is also possible, if a bit obtuse)). I'm not yet sure how best to describe that difference without special‐casing.

tl;dr: new category of pieces (tenatively named ‘running’) combining recent suggestions, with some further suggested extrapolations and some unanswered questions re semantics.

Assuming anyone actually makes it through this, any thoughts?

Hello Bn Em,

I think the 2.manticore and 2.bishop are the pieces that start like a ranging piece and continues like another one. The Osprey for example does not do that. I'd name this R2 then B and B2 then R respectively. I am testing these in my next games. I think n.Matincore and n.Gryphon are good names for Rn then Bishop, and Bn then Rook. I think they are interesting exactly because they are blockable and playing them is more strategic because they have to be played after some pawn chains collapse.

The difficulty with viewing e.g. the 2.griffin/running ostrich as R2‐then‐B is that the obvious reading of that (in line with the obvious reading of full ‘rook then bishop’ — see also the large shogis' ‘rook‐then‐rook’ and ‘bishop‐then‐bishop’ hook movers) suggests that it could also make the Bishop move after only a single Wazir step, becoming effectively a compound of griffon and ostrich — what Gilman called a Fimbriated griffon (after a kind of outline in heraldry). Which is really quite powerful and not what either of us means afaict.

My view here is that the usual Ostrich (and Osprey) have a move along a given path, but the shortest of its moves is two steps — something it has in common with Tamerlane's picket, Alfonso X's unicorn, and indeed Shatranj's and Xiàng Qí's elephant. For the picket and elephant, the 2‐step move is non‐coprime, and so a one‐step move can be trivially interpolated: for the former this gives the familiar Bishop, while the latter gave a piece that was dubbed the ‘modern’ elephant (and of course with a modern dabbaba to match). For the unicorn it is less trivial (the knight has two possible interpolations) but extending the long‐range move backwards suggests orthogonal‐then‐diagonal over the alternative, giving our Manticore.

In the Osprey's and Ostrich's case, the 2‐step shortest move, as with the picket and elephant, is non‐coprime, and so the obvious interpolation lines up with your 2.bent riders. In the Osprey's case, the alternative exists of doing as with the unicorn and extending backwards, giving a ferz‐then‐bishop‐at‐90°, but fsr 90° turns seem (above‐mentioned hook movers notwithstanding) to be less favoured.

I don't disagree about blockability: what I have termed ‘running’, as opposed to the preëxisting ‘modern’, is explicitly blockable — though arguably calling them ‘lame/stepping modern’ os[prey/triche]s is just as descriptive. Fergus' helical pieces also differ from Charles' Proselyte ⁊c in being (by default) blockable, as well as interpolating.

As for 3‐or‐more.gryphons/manticores, it might indeed be interesting to have names for those (though they might begin to veer into being a little too exotic?), but it'd be equally useful imo to have names for the equally unusual threeleaper‐then‐bishop or quibbler‐then‐rook.

I was scrolling through some old comments and have found what Aurelian would call a 3.manticore posited by Sam Trenholme in this comment, alongside the ‘3.griffin’ and a bunch of others (the ’2.manticore’ or ‘running osprey’ is in there as well). No names alas, but still interesting to see these pieces having been discussed 12 years ago (almost to the day!).

It seems to me (on the topic of that thread) that simply the fact of having to count to three rather than either changing direction immediately or simply foregoing any counting altogether (griffon/manticore and hook mover/capricorn respectively) makes the ‘3.manticore’ non‐simple from a player's perspective; the ’2.manticore’/‘running osprey’ is kind of liminal in that respect — two‐step moves are still easily visualised and trivially interpolated — though even it is in some ways arguably more complicated than the component of Tim Stiles' fox and wolf, which only has immediate turns.

I agree that a piece that changes direction after 3 steps could be awkward to visualize. It would be worse, though, if the first step were a jump to the third square, because with a sliding move, you can easily see if a nearby piece blocks the movement.

On the other hand, with an initial leap the blocking would only be on a single diagonal, rather than having to check the nearby orthogonal squares as well. A tradeoff really, though in any case due to the ability to avoid nearby blocking pieces the t[HB] is probably too powerful (or, on small enough boards, too awkward) to use in (most?) games anyway.