Shortest-proof-game challenge

People all over the world who use Stelvio for proof game verification would be grateful if they knew that your position was responsible for the removal of a significant bug from the program. It isn't known how many other positions may have been improperly analyzed, but yours is the first to be reported and to inspire a correction that will appear in the next released version.

Actually I haven't studied Leither's 4 proof games - I reacted on the general concept of proof games where the move order doesn't matter which was in Leither's original post on this. Which is apparently not what he intended. If what n9531l1 says is true than we'd have 4 SPG's separable by an "attribute" or "theme", something the composing community would applaud. But apparently that is not true either. So I can only conclude that within the themes are many more proof games honoring the theme and the length but not the move set. For instance there might be a 1000 proof games without castling and for just one move set there happens to be one move order. All the other 999 proof games without castling exist as well but they contain some moves which can be reordered. Can someone explain how I could ever find the one with one move order and reject the other 999? Then I would have to assess all 1000 proof games, right? And I would have to be sure there is no other move set which features just once among the remaining 999. How do you explain this to any solver?

To be clear, it is different when there are not 1000 but just 1 shortest proof game for each theme. That would be great!

To be clear, Leither's original post (#5805) didn't say move order doesn't count. On the contrary, he claimed that all his position's four SPGs have a unique sequence of moves. I pointed out in the following comment that they would have to, since any particular solution has a unique sequence of moves, or it wouldn't be that solution.

What is it about what I said that leads you to say it is apparently not true?

In the chess composition world, the term "proof game" actually refers to a problem type where unique play is required to reach a specific position. Within this PG genre, problems with more than one unique solution is also normal. This sounds like a contradiction, but in practice, it's easy to tell apart a correct PG with distinct solutions and an unsound PG with dualised play. Typically (though not always), the intentional distinct solutions begin with different first moves and the two precise sequences involve notable thematic changes, whereas in a faulty PG, there are just minor variations (duals) in the play.

For some examples of PGs with two solutions, see my 2-part introduction to the genre, Proof Games. PGs with three distinct solutions are very rare: see this blog with two examples.

The PG-solving program Euclide does a good job in distinguishing between sound PGs with multiple solutions and cooked PGs. Whatever algorithm it uses, it seems like an "objective" test that matches what human problemists tend to agree on. For instance, the Fool's mate position given in post#5899 is totally uninteresting as a PG and it's indeed marked as "cooked" by the software.

Leither's 4-solution PG is very interesting in showing four different castling possibilities, despite its weakness of having many moves repeated across the four parts. I think it's a fine achievement. Euclide's verdict is that it's sound: "4 distinct solutions".

Thanks, Rocky. You mentioned that PGs with three distinct solutions are very rare, so I assume that's also the case for those with four distinct solutions. Are you aware of any besides the one we now have thanks to Leither's position?

P.S. I'm assuming Stelvio will agree with Euclide once the bug is fixed that caused it to find only two solutions.

Well, I learned something new today! Would you say #5893 is a better example of a position with multiple distinct solutions?

The bug fix for Stelvio is pretty neat. Now I can feel like I was a part of something useful

Yes, I wasn't aware of other examples with 4 solutions from a single setting (twin settings are a bit different). I've just checked on the Schwalbe database and found a PG in 8.0 moves where the stipulation is "2 solutions, each with 2 variations". Here there are 2 different starting moves and each splits into 2 variations. It's kind of moot whether this counts as 4 solutions. By the same token, Leither's PG, because of the same starting move throughout, can be described as having 1 solution with 4 variations. This is why problemists like me who compose multi-solution PGs much prefer different starting moves.

Yes, that's a more clear-cut example, with different starting moves and notable changes, especially the original vs promoted knight on b8. Quite a stroke of luck that the second solution was unintended!

I guess I will now have to study the 4 (or are there 3?) solutions in order to react but obviously Euclide will not approve of 4 proof games when there are countless alternatives as was suggested. When the 4 proof games are really the only ones - with the themes as described - it's a perfect SPG challenge - as I wrote from the beginning. Move sets are irrelelevant but obviously the proof games should be as different as possible - especially the starting moves. Once the first moves diverge that commonly happens naturally for the remainder.

Unfortunately I have no proof game solver and decided to rely on your texts. Not that accurate I conclude.

Btw - as Rocky wrote - the retro-community commonly refers to proof games as unique move sequences for this type of challenge - but that is precisely what is different for this whole topic. Almost 100% of the content here is about (shortest) proof games which are not unique which means that all of you need to be very precise when making distinctions and exceptions in your texts. Btw2, there are other places in the retro-domain where the concept "proof game" means just that - without uniqueness. Uniqueness is only associated with "shortest proof games" - but not in this topic on chess.com.

Are there 4 solutions, or only 3? #5905 doesn't leave me with any doubt about this.

I think it's a good thing that uniqueness doesn't have to be only associated with SPGs in this topic. That would rule out interesting questions like the one discussed here a while back on positions that have more than one SPG and a longer proof game that is unique.

It would be interesting to know Euclide's verdict on this position. The output from Stelvio 1.6 says "Found 4 solutions. The problem is correct. Solving time: 00:00:01 seconds."

Apparently it makes no distinction between solutions based on their starting moves.

Ah yes, there were many posts on it, starting with #5895! In the world of composition SPGs are only associated with uniqueness - but with a twist as Rocky and I indicated. When you differentiate them on a theme there may be a unique SPG associated which each one of the thematic options (like a common problem may have 4 variations for the AUW promotions). Without such a theme they are merely a set of extra "bad luck" SPG's.

The problem is that on this site SPG's also refer to non-unique SPGs and from Leither's language on move collections - which do not matter - and without reference to a theme. I could only deduce that he had constructed some set of random proof game solutions. Had he used Rocky's language, it would have been clear straight away. So there was a miscommunication. I probably could have resolved it by finding the 4 solutions myself (or seeing #5905) but I didn't want to waste the time on what looked like a sloppy challenge and commented on the "move collections" in the text.

Btw, I wrote "4 (or 3)" only because someone mentioned 3 somewhere and it didn't matter for the issue. To prevent someone shouting "there were 3!".

I knew and accept that you use the term SPG different from the retro-community but that will also open the door to the occasional misinterpretation when it is about text rather than just diagrams. Never know how many SPG's you will find inside a post!

Just quickly checked the 4 solutions in #5905 and concluded the quartet does not pass the composition test for forking proof games. Almost always they fork on the first move (that's why it's hard to make 3 or 4) unless there is some justification for delaying it. I have never seen one but there always are when you have a "good storyline". I recall having seen an A-to-B proof game which does not start on game move 1 but that takes us further from home as does every new condition or complication.

Of course, I had acknowledged that the challenge was sloppy shortly after posting the position, so here's a challenge that isn't. Can anyone here construct a position with at least 2 unique solutions that differ from move 1?

Did you mean in addition to the one already mentioned by Rocky which has four solutions with two different starting moves, and the one you constructed at #5889?

Yes, a number a people can do it. Here's a short one constructed by François Labelle.

Proof game in 5.0.

I think Leither wants us to engage our workbench rather than consult our encyclopedias.

I think so too, but he didn't word his question as a challenge. If he had said "you" instead of "anyone", it would be a challenge. (And I wanted to show the one from Labelle, since I think it's neat.)