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Update, June 2024. In May 2024 I found out Paradigm Chess30 can also be played on one fork of PyChess. You can play either with a human opponent or against Fairy-Stockfish. (It may soon be added to the official PyChess, but that's not sure.) What's more, following my proposal, that PyChess fork now includes Paradigm Chess1320 too! It has been working alright since 2024-06-04.
§1 Paradigm Chess30 is fun
This chess variant was invented by Lourenzo van Niekerk and Craig Willenberg (South Africa) in May 2020. It is not famous, but has huge potential. For me -- four years later -- it was an impressive discovery.
Paradigm Chess30 is mainly characterized by its unique special piece, the Paradigm dragon, which is a bishop-xiangqihorse hybrid. Dragons replace the bishops: each player has two dragons, and there's no bishop.
Paradigm dragons are strong major pieces: not so strong as queens or knight-bishop hybrids, but stronger than rooks. So, the knights are the only minor pieces in this variant: trading a dragon for a knight is mostly very bad -- but, as the only leapers, knights are often precious, or dangerous, based on points of view.
Paradigm is really interesting and enjoyable. It is a peculiar variant. Its flavour is very different from that of all the other chess variants I have tried.
paradigmchess30.com is the official website, and www.chess.com/variants/paradigm-chess30 is where you can find opponents and play. Try it! The available opponents will be very few, but some of them are good. They'll probably beat you -- well, not always. If you like being beaten by a computer too, play Paradigm on the Fairy-Stockfish playground, fairy-stockfish.github.io/online (click Open fairyground, then select paradigm in the drop-down menu Name -- it's without starting position randomization: you can modify the starting position, but it's not automatic).
§2 Paradigm Chess30 deserves to be tested and analysed
Paradigm Chess30 is extremely sober, entirely chess-like, with no redundancy at all. The typical Chess Dot Com variant player will typically dislike Paradigm. They love Four-Player Chess and XXL Chess; and Spell Chess, where you cast spells on the chessboard.
Anyway, my own judgements and opinions on matters of chess are not authoritative. I would like to find out if Paradigm Chess30 is really so good, beautiful, and innovative. Something like a Kramnik-plus-AlphaZero study would be what we need. Is Paradigm really more decisive (i.e. less drawish) than standard chess? I have no idea. I'm not sure, but I think that nobody has yet carried out a scientifically based analysis on this not-so-famous variant.
§3 About the name of Paradigm Chess30
Paradigm Chess30 is not a telling name. Well, the thirty part is, since it refers to the number of starting positions, exactly like Chess 960. But, why Paradigm? The official website reads: "The Paradigm Chess30 concept is an enhancement of MRL Chess Paradigm. The MRL Chess Paradigm concept was originally introduced to minimise the excessive number of draws", etc. And MRL stands for... who knows. But we know that "Lourenzo van Niekerk is the founder of MRL Chess Club based in Cape Town". So, we can say that it's called Paradigm for historical reasons. Paradigm Chess30 is the name chosen by van Niekerk and Willenberg, and that's it.
§4 The special piece of Paradigm Chess: name and appearance
I prefer to call them Paradigm dragons, because I prefer unambiguous words. If it's clear that we are talking about this chess variant, we'll simply say dragons -- but, be careful: the word dragon has a lot of other possibile meanings in standard chess theory, in shōgi (i.e. Japanese chess), and in chess variant vocabulary (for example, Miguel Illescas has proposed a variant similar to Seirawan Chess, awkwardly named Dragon Chess, where the dragon is the old trite knight-bishop hybrid).
I don't see the Paradigm dragons as a kind of bishops. They replace the bishops, but are not bishops. That of a bishop is only one half of their hybrid nature.
However, in the official website and reference sources, they are mostly called "Dragon Bishops". (What about the above-mentioned Illescas dragon? Is that a dragon bishop too?)
As for their appearance, the symbol is that of a bishop with the addition of well visible dragon elements: wings and claws. The bishop symbol with red-highlighted edges is an allowed alternative. For playing over the board, you may simply tie coloured ribbons around the bishop pieces, or something like that -- that's one of the inventors' suggestions.
(Since normal bishops are absent, it's also possible to use the regular bishop symbols or pieces. Well, you always have to remember which variant you are playing, even with no reminder. When you play Torpedo on Chess Dot Com, for example, pawns look like ordinary pawns... though they're so fast and dangerous! -- When I tried Paradigm on the Fairy-Stockfish playground, the dragons were real dragons, but looked like bishops.)
§5 Paradigm Chess30 and fischerandomization
Paradigm Chess30 has randomized starting positions, with 30 possibilities. These are not a subset of the famous 960, since no colour-bound piece is present.
With reference to the nice table at the beginning of the section Similar variants in en.wikipedia.org/wiki/Fischer_random_chess, for Paradigm Chess30 we should cross out "Bishops opposite color" and, instead, tick "King and rooks fixed on traditional starting squares".
But... What if we freed the king and the rooks from their starting squares, and applied the very principles of Fischer Random to Paradigm Chess30? Personally, I like 960 very much. I find that Chess 960 castlings are most delightful.
The starting positions of fischerandomized Paradigm Chess, with no constraint on colour-bound pieces, will be many more than 960. But, exactly... how many? The Wikipedia table is not comprehensive, and I couldn't find the missing information anywhere on the web. (About twenty-five years ago I learned combinatorics at school, but I'm afraid that I've forgotten everything.)
Anyway, I spotted another nice and useful table, the Läufertabelle (Bishop table) in the German-language Wikipedia, de.wikipedia.org/wiki/Schach960. We learn that Fischer Random has 16 possibilities for the bishops, and this table displays the 16 possibilities, grouped by 4. If you observe the table and think of a version without the colour-bound constraint, it becomes clear that you have to add 3 possibilities in the first group, 2 more possibilities in the second group, another one in the third group, and none in the fourth (last) group. Therefore, for what we may label as the two-bishop coefficient, the total is 22 instead of 16. For the other six pieces, the different combinations with Fischer Random rules are 60 ("60 verschiedene Kombinationsmöglichkeiten für die sechs Figuren").
60 × 16 = 960
60 × 22 = 1320
So, I'm looking forward to playing Paradigm Chess1320, how I suppose it should be called! Precisely the principles of Fischer Random, with Fischer Random castling -- which is not a random castling, of course.
(Is it possible to set a fischerandomized version of Paradigm Chess, as a custom variant, on www.chess.com/variants/custom? Either 960 or 1320, that makes little difference. 960 is ok! Well, it's possibile, more or less, almost... This way. Go to "Edit rules", tab "Mix & match": select "Chess 960" and then deselect it [!]; put "NQRΔ" in the field "Pawn promote to". Go to "Edit position" and replace the four bishops. Choose the clock setting, and click "Play!". -- As for PyChess, see the June 2024 update at the top of this page!)
Now, I have made up the following pun... Couldn't we call it Paradise Paradigm Chess? That's because the number 1320 reminds me of Dante's Paradise, written in those years -- the author died in 1321. Paradigm Chess30 is great and perfect in itself, but Paradigm Chess1320 might prove really heavenly.
§6 Gli scacchi Paradigma, in italiano
Giochiamo a Pàradaim Trenta? Io farei anche due partite a Fischerandom Pàradaim, cioè a Pàradaim Mille, Pàradaim Mille-e-rotti, Pàradaim Pàradais o Pàradais Pàradaim che dir si voglia... In Italian, we can keep the English word Paradigm, or translate it as Paradigma. Gli scacchi Paradigma, gli scacchi Paradigma 30 (trenta). The dragon can be called either drago or dragone. I prefer the latter. Il dragone, il dragone Pàradaim. Se promuovi a donna, è stallo: promuovi a dragone!
(As a member of the Zerocalcare generation, I remember "Dragone!..." with the intense voice of Pegasus, worriedly shouting at his noble and generous friend Sirio. Sirio il Dragone. -- Actually Pegasus has a personal name, Seiya, but we didn't know, and Shiryu has no relation with the star Sirius, con la stella Sirio... I cavalieri, le sacre armature: there were no saints, no cloths, etc., and Saori Kido was called Lady Isabel. We were all girellari -- girellai, girellaiuoli --, but we were sometimes sort of happy.)