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This item is a piececlopedia entry
It belongs to categories: Orthodox chess, 
It was last modified on: 2001-04-17
 By Peter  Aronson. Rhino. A set of pieces which combine the movements of the Mao with that of the Wazir.[All Comments] [Add Comment or Rating]
H. G. Muller wrote on 2019-07-10 UTC

Note that it must be trivially easy to checkmate a bare King with a Rhino, powerful as the latter is, in addition to covering two orthogonally adjacent squares. The checkmating applet cannot really do crooked sliders, but assuming that blocking doesn't play a significant role with only another King on the board, you can let it calculate a piece that directly leaps to the squares a Rhino would attack.

As is well known, the Gnu/Wildebeest, whose targets all fall on the Rhino paths, has no mating potential. This is due to a coincidental collision with the King. But just adding a single W move to the Gnu (say fW) already cricumvents this problem. So WNC, which is a subset of the Rhino (but leaping) already has an easy mate (maximally 19 moves).

The Mirror Rhino fares even better, as FN in itself has already mating potential (maximally 22 moves). The longer distance moves of the Rhino were only needed because without them no two orthogonally adjacent squares would be attacked.


KelvinFox wrote on 2019-07-10 UTC

@Aurelian Florea 

This is a Rhino where all Wazir movements are crooked compared to the previous one


Aurelian Florea wrote on 2019-07-10 UTC

So this is supposed to be a rhino-mirror rhino alternating?


KelvinFox wrote on 2019-07-09 UTC

A crooked wazir rhinoA weird piece idea where all wazir movements are crooked


George Duke wrote on 2015-12-18 UTC
What is the value of Rhino, asks author Aronson 14 yrs ago? Is it 3.0 like Knight or under at 2.8 or over at 3.3? We want to estimate not have long trials, any more than Carlsen thinks for only a moment Knight 3.0 and Bishop 3.2, then just makes the best move. This Rhino is direct link from Gilman's current revision of Chapter 16 "Diverging Further" in December 2015 <a href="http://www.chessvariants.com/index/msdisplay.php?itemid=MSmanandbeast16:">Man&B</a>. The estimate below also ties in with Muller's current research on Amazon. <p>Betza and Cohen in 1970s Tutti Frutti probably had Centaur and Champion at what we have today, but overestimated Amazon. That 64-square T-F is the only one time Betza ever used RN and BN. Tutti-Frutti is concept CV hardly worth playing. He disliked the 400-year-old Carreran pieces as I do. Use of Archbishop/Chancellor, as Capa calls them 100 years ago, almost always cutely paired has finally plummeted the last decade, but most variantists still put them in top 20 for historical importance.<p> The piece-types that cry out for research on values are short-range, such as Rhino or otherwise moderate value Crooked Bishop, those worth mere 2.0 to 6.5 let's say. They include over 1000 p-ts Gilman has invented or named. His one fault, Charles never estimates values. Other short-range or weaker pieces needing values are Joyce's Bent Hero and Shaman and all those in Christine Bagley-Jones Short-Range Project.<p> So what is value of Rhino and what is the logic? 3.3 value since it reaches 12 squares not only Knight's eight. Though blockable, Rhino has mating number of 2 to Knight's 3. The Mating Number and Value interact, the former settling the latter when low value holds. And these are the pieces that make the best CVs.

Jörg Knappen wrote on 2011-09-05 UTC
I suggest that you take a chess board, two kings and some piece representing the rhino (a knight works well for me) and try it out.

I must admit, that I didn't analyse the specific position nnz gave here, the placement of the supporting King is a bit awkward here. Both of your proposals to repair the situation work out fine.

For similar pieces: A gnu and a king can drive the king to the edge, but cannot give mate; the same holds for the quintessence (of quintessential chess).

Jeremy Lennert wrote on 2011-09-05 UTC
@J�rg:  I don't follow.  Unlike a rook, the rhino cannot confine a king to an edge without assistance.  In fact, it cannot confine the enemy king ANYWHERE without assistance--its attack pattern is porous.  The friendly king needs to stay close to the enemy king to plug the gaps.  It's not even clear to me that rhino+king could force the enemy king to an edge in the first place.



If you take the diagram nnz posted, the rhino delivers the check, so it must have been the last piece moved.  Which means the lone king's last move must have been from g8 to h8.

So:  black king g8, white king h6.  In order to force the king into the corner, the rhino needs to be some place that attacks both f8 and f7, and to deliver the checkmate it also needs to be able to reach e7 in one move.  That pattern of three adjacent squares does not appear anywhere in the rhino's movement diagram.  You can't rewind the position shown even one move.  Therefore, the rhino cannot force the exact position shown.

HOWEVER, a similar mate might still be possible; the rhino could also deliver the mate from c6 or a5.  A rhino at e5 threatens f7 and f8 and can also reach c6 to deliver the mate.  Perhaps you might also do better to locate the friendly king at g6 instead of h6.

So the exact diagram nnz posted is not possible without collusion, but I still don't know whether it's possible to force a mate or not.  My suspicion is not, but I haven't given it extensive thought.

Jörg Knappen wrote on 2011-09-05 UTC
@charles: ... but can the rhino and the king force this position?

Yes they can, and they can do so easily: Essentially, after forcing the opposite king to the edge of the board, the rhino pushes forward using the wazir move.

Charles Gilman wrote on 2011-09-03 UTC
'...but can the rhino+king force the opposing king into this position?'
Good point - the diagram works for a Gnu too, but it doesn't follow that a Gnu can force mate.

Ben Reiniger wrote on 2011-08-26 UTC
...but can the rhino+king force the opposing king into this position?

Peter Aronson wrote on 2011-08-26 UTC
Yeah, I was overly pessimistic about the Rhino's mating potential. Jorg has also pointed this out earlier. Thanks!

nnz wrote on 2011-08-25 UTCExcellent ★★★★★
'On an eight by eight Chess board, I don't believe a Rhino or a Mirror-Rhino plus a King can mate a King, but a Double-Rhino plus a King can. A Monster should be able to mate unaided.'

I'm pretty sure an ordinary Rhino can, like so:

 d   e   f   g   h
---+---+---+---+---+
   |   |   |   | k | 8
---+---+---+---+---+
   | R |   |   |   | 7
---+---+---+---+---+
   |   |   |   | K | 6
---+---+---+---+---+
   |   |   |   |   | 5

Correct me if I'm wrong.


Charles Gilman wrote on 2011-02-24 UTC
Since I have been reviewing my Man and Beast series, and many members have been commenting on Leaping/Missing Bat Chess, it has occurred to me that Curved pieces alternating Wazir and Ferz steps do indeed belong in the 'Rhino' group of pieces, and a reference to the Curved pieces and the use of effectively a Curved Double Rhino in L/MBC would be a worthy addition to this page. The Curved pieces too start off with the Mao or Moa or Moo move. They also retain the constant turn of 45° of the Crooked pieces, unlike the Rose which alternates the angles of two different Crooked Nightriders.

Garth Wallace wrote on 2009-12-02 UTC
Whoops, I was thinking of the one-step versions, but that passage is about the sliding versions. My mistake!

Charles Gilman wrote on 2009-12-02 UTC
None of this page's long-range pieces are switching. The Rhino's first three destinations are those of the Wazir, Knight, and Camel. Knight plus Camel equals famously triangulating Gnu. Likewise the even destinations (exactly as with the Mirror Rhino) are destination of the Nightrider - a straight linepiece like the Bishop and Rook and so able to make two moves in the same direction and return in a single move the same length as the two together.
	Indeed not even a Waverer, a Rhino restricted to moves of odd numbers of steps, is switching as a Camel move can be reversed in four Wazir ones. Nor is a Feverer, a Mirror Rhino so restricted, as a Ferz move can be reversed in two Zebra ones. It may be more difficult when what I am for short calling Camel/Zebra moves are stepping ones here, but it is posible.

Garth Wallace wrote on 2009-11-30 UTCExcellent ★★★★★
Is the mirror-rhino really worth less than a rhino? I would have thought that the fact that it is not color-switching and can return to its starting space in an odd number of moves would give it a boost.

Jörg Knappen wrote on 2009-11-28 UTCExcellent ★★★★★
The Rhino inspired a new chess piece, the Teutonic Knight having the first three steps of the Rhino with the ability to jump.

The Rhino is an interesting and inspiring piece and this article is well written.


H. G. Muller wrote on 2009-10-24 UTC
Ah, OK, I see. The description is a bit confusing, and I thought that 'basic move of the Rhino' actually meant how it moved. Sorry about that.

Jörg Knappen wrote on 2009-10-24 UTC
In fact, mating with the mirror-rhino can be more complicated than mating with a simple FN, because
the additionaly attacked zebra square provides lot of stalemate traps. A key position in the mirror-rhino's mating manoeuvre is the following:

Black King on a1,a2,or b1; White king on c3, mirror-rhino on f6.  Black to move.

Only now the white king can complete the confinement of the black king

--- BTW, the rhino is not colourswitching at all, it is a slider continuing its way after WN squares to
C NN2 .... Adding the wazir to the Gnu essentially gives it the can-mate property.

H. G. Muller wrote on 2009-10-22 UTC
A color-alternating piece with mating potential? You must be joking.

For the purpose of mating a bare King, the mirror Rhino is equivalent to the (FN), which has mating potential of boards upto 16x16 (where it takes 100 moves), see:

http://www.chessvariants.org/index/listcomments.php?subjectid=12x12_checkmate

Jörg Knappen wrote on 2009-10-22 UTC
I tried it out and found that both the rhino and the mirror rhino can mate a single king with the help of their own king. There are no special manoeuvres involved, the mating goes relatively straightforward.

Joe Joyce wrote on 2007-11-21 UTC
Hey, George, you didn't notice the hint of chagrin and a delicate sarcasm in that statement of mine? To boldly invent the rhino for the umpteenth time doesn't do a lot for one's image. Imagine my thrill when I found out the Muse of Redundancy had visited me with another used idea.

But to put together a little system that pops out pieces like that among other common and some very rare and unique pieces isn't all that bad. [I may need to continue that thought on your 91.5 Trillion thread, George]. 

I do have to disagree about independent invention of ideas, though. It has happened repeatedly throughout history, and will happen more and more in CVs because there are more and more of them. With luck, people with experience will catch the duplications. But this doesn't lessen the creativity of the designer, merely the bragging rights... :-)

George Duke wrote on 2007-11-20 UTCExcellent ★★★★★
At Aronson's Rhino piece description, Joe Joyce enunciates the doctrine of re-inventing the wheel in immediately preceeding Comment. ''I actually think it can be good that people re-invent the basics. How's that for putting a good spin on re-inventing the wheel?'' As for piece values, Aronson points out Rhino can reach twice the squares as Nightrider, but the latter is more valuable in our estimation. Ralph Betza is credited with inventing Rhino, Mirror Rhino, and Double Rhino. Obfuscation mentions Aronson and Friedlander as independently 'inventing' one or more of them, but we do not buy that. Betza invented them, unless someone comes up with examples or documentation of other earlier uses. That is because invention credit is determined, generally in all fields, by assumption that someone 'skilled in the art' is more or less omniscient of relevant prior uses, or should so be aware of them, or subject to them if unaware. Occasional actual simultaneity, or overlap in time before publication, is another matter (maybe like Newton and Leibnitz in Calculus). So many efforts are also why it becomes harder to invent chess variations and pieces for the time being. There is simply more to be studied first, although recent prolificists apparently choose to study less pre-existing CVs. Hence for now not so good quality as before. Double Rhino is multi-path, namely two-path beyond its first square. Charles Gilman's Comment April 2004 here adds at least four more pieces after these hippogonally-directed move directions.

Joe Joyce wrote on 2007-08-21 UTC
I believe the first sentence in 'History' in this piece write-up sums up my feelings: ' This family of pieces has been invented more than once. '
I actually think it can be good that people re-invent the basics, because each person is a fresh look, and sometimes we get something brand new. [How's that for putting a good spin on re-inventing the wheel?]
For being such interesting and constantly re-occurring pieces, the NW and NF are not seen all that much in variants, that I've noticed. You'd think they'd be used more; the NK or centaur shows up several places. I suspect it might be that people find breaking the move of a piece that's already a bit awkward and very short range into tiny pieces and doing the pieces one at a time is annoying. Or maybe I'm totally wrong, and have overlooked games with these pieces.

Jeremy Good wrote on 2007-08-21 UTC
Joe Joyce, I thought this entry might interest you a little bit.

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