strict means that I only care about the last position at in both game initial segments, but not necessarily same depth or length of segments (or sequence of moves) to be the same FEN. not caring about the 50 move clock by the way.. if one is gong to eliminate juicy ones just because same capture did not happen at same depth.

If there is an exact table of transposition with FEN at hand, or not far. I guess the segments ending on those earliest ones, would do.. I have seen tables about estimations, but i think those were bound calculations.

Any good link welcome.. otherwise. I was thinking of mirroring Carlsen bullet game where many moves were white shuffling king back and forth.

I can count to some extent, but I might have to go at it manually. 4 knights... they each, earliest, can move 2 square each , if we freeze all other pieces. (yes, it can be done, it is called legal chess). I kind of smell without computing the distinct combinations that in there, ought to be some transpositions.. Any pawn move is going to postpone such things I would guess. probably in ignorance.

The strict, is to avoid the transpositions from opening theory examples.. These are about a subset of strict transpositions, only those on opening theory worthy branches (or that may have been).

We do have exceptions for the very early mates, as tales for beginners, included in opening database frameworks, but what about the transpositions...

I just need the first one possible.. that means 2 distinct initial game segments.. yes.. overly precise words.. weird, maybe, but no harm to understanding, i hope.

This may be trivial, in which case, feel free to expand on the question.. but with shallowest in mind, and possibly not only those that annoy in some narrow repertoire preparation, where derailing is not what we might want because the trap or unprepared ness might be deeper. Caricature, sorry, not all repertoires preparation would be about that. And some strategies of preparation might be about having more landmarks in that opening blob (varying terms).

trivial I said. i did not have a board in my face.. now just went there.. split the board in 2 using the ambient plane vertical central line (i like to call this the lateral board symmetry axis, but since king and queen can be used as names for the resulting 4x8 panes).

just cycle the same K or Q side knights a la Carlsen. (you get a cycle yes, just don't do it too many times ok..:)
now consider a completely distinct sequence of moves, with the other K or Q side. you also get back. in 4 plies each.

not as insightful as deeper transposition.. ok.. maybe i should look into pawn moves, not much chance of cycling there.

those shortest transpositions. I guess i would need 2 pawns on each side.. different move ordering.. and voilà.

ok.. changing question to: please can you find the flaw in my here-post reasoning... I will past glorious SAN moves later. And any pointers to reviews or data analysis or combinatorics of transpositions from a more down to board point of view, like I just gave a taste. Or opening theory with specified database or framework of the sequences (a la lichess perhaps, the github repo i mean, for reproducibility potential) for having the entrant stuff allows to seize the sortant or results under such givens (not always shared in the results displayed). Those might have made studies with available FEN and criteria for transposition.

Anyone thinking that the pawn move or capture clock early in the game, should not filter away the definition of transposition? or that the position making the transposition should happen at same depth in each distinct sequence or if not same depth, then not a transposition. I think the human thinking challenge having the same diagram, turn to move, en passant vector code (hash?, keep forgetting), oh and castling right would be the same.

so, by FEN I mean real position not the fide rule termination conditional on move left one

en.wikipedia.org/wiki/Babson_task. This might involve transpositions, but is not about legal ones.. indeed it seems to be with the extra restriction of a mate at transposition position (the earliest from 2 distinct initial sequences of moves). reading.

The mate might be legal, but still not my simplest question. although part of my extended amended one for sure, with the mate condition added and specified.

quote from wiki (one page content)

> A Babson task (or simply Babson) is a directmate chess problem with the following properties:

> 1) White has only one key, or first move, that forces checkmate in the stipulated number of moves.
> 2) Black's defences include the promotion of a certain pawn to a queen, rook, bishop, or knight. (Black may have other defences as well.)
> 3) If Black promotes, then the only way for White towards a forced checkmate in the stipulated number of moves is to promote a pawn to the same piece to which Black promoted.

This is hard problem. interesting but I am looking for a simplest to less simple systematic approach.. does not have to be complete, as we know chess grows fast in combinatorial complexity in all sorts of target questions that might happen at depth.

ok in this monologue, (with some self-dialog flavor between posts), I forgot to explain why I even care.

Well I have this pet idea, that does not seem to fade, or still weathers all the new information that chess study and experience (amateurish, and limited hours, yes, but perseverant at my pace, and not just in zombie mode).

Someone just caught the drift of it, and I am eager but kind of energy limited.. I don't need the more terrifying opening name transposition to another name, or a tight combination of combinatorial criteria among the core rules, I want to have the minimal amount of things to put in a 2D plane to show how transpositions are naturally visible in the game world representation that is not carried by the 20 opening trees (well opening theory rarely uses all 20s, I keep thinking legal chess, maybe I should not? kidding). ̈

I am working on making the laziest version that would should the gist of what I have been needing to see to understand the lichess opening explorer and all manners of non-tree display of chess knowledge, but all inherited from the tree structure bottleneck representation (it obscures the position identity, in finite terms, and if allowing a zest of continuum notions, in your chess tea, it also prevents representing notion of similarity between positions, of which transposition are the acceptable discrete chess representation cases).

might need some math. that also transcend the tree of math specializations. or just life specializations.. (can't do them all).

Stay tuned... (hear twilight drone if needed. it might slide better).

"Portrait of a man in need of even more math..."

@MrPushwood said in #6:
> "Portrait of a man in need of even more math..."

It is more about using the right math for modeling the thing, wherever it might come from (if needed discover the math. solution to the problem such described).. A scientific approach, maybe from physics. Also, nothing that naive players would not naturally use internally, as we come to chess with such propension to make 2D maps of things.. I find natural, to think of some map of chess positions, where the positions could be assigned a point on the map.. and roads linking to other positions, being labeled by the piece that needs to change placement, to get there... many roads out of position, and more than one going in, possibly many such transpositions. Feels natural to me.. even without math. just that training with tools daily, can morph how we see things. no field invocation necessary.. professional deformation by the tools formatting the users perhaps.

github.com/SandroMartens/chess-opening-transpositions
It turns out that the shortest one is also an opening transposition. I have a bunch of sillier ones.

I prefer leaving names out of chess sequences, this added contorstion layer saturates my abilities to visualize what is happening. How lichess opening explorer decides to name openings, and if those name are just about the sequence, or as the following example, some opening names will have priority at transposition for the opening name attributed to a transposed position.

Here from the example provide by the link above (which has interesting things in it, all about opening names though, but i can pinch my nose and translate).

github.com/SandroMartens/chess-opening-transpositions#main-line (yes, the famous main line concept).

> Move Opening Name
> 1. d4 Queen's Pawn Game
> 1. ... d5 Closed Game
> 2. c4 Queen's Gambit

github.com/SandroMartens/chess-opening-transpositions#transposition-from-english-opening

> Move Opening Name
> 1. c4 English Opening
> 1. ... d5 Anglo-Scandinavian Defense
> 2. d4 Queen's Gambit

This is the choice that lichess has had to make given that its opening explorer is supposed to be about positions not sequences, at some point, if it can take a pure FEN as input, and still need to attribute a name to it, and there is only one slot for a string... well.. I think that is the constraint.. having multiple names going in and wanting a position to think about because that is really all what matters after the same position is reached in any game, at any depth. My confusion is about attributing an opening name to a position. I am not against... unique names for unique positions. And some explicit policy about with of the name collisions are going to supersede.

Here, it seems from the repository readme, and the titling above, that the concept of mainline has something to do with the same position changing name in explorer to that of the queen gambit. I guess, if there is only one position that gets its name and not a segment of move before or after we could deal.. named positions as unique position and unique names. like the book position hashing, for example. I get woozy when things start borrowing from each other. And that makes it hard to interpret the graphics that show real good work over in the repository. My ignorance likely to blame. But I think the results are perhaps a picture of lichess best attempts at digesting the opening theory and naming practices sources they have to work with.

I have not looked in the opneing repository to see if there is some emerging naming policy and systematic scanning of possible transpositions, and which names of seqeunces get the dibs on their inner position naming...

Anyway that is a 3 plies example. best answer.. I have funny ones some pairs of sequences to same position do not have same depth, and the wiki link or chess programming link both show known examples of opening named transpositions, (for those who thought that transposition have to happen at same depth from common root starting point. So it is likely that lichess opening explorer shows all the games visiting a queries position, not just those that have that position at same ply (I heard otherwise before, and was surprised). It also mean that FEN is too picky for defining transpositions.