Shortest-proof-game challenge

c5

If you're interested in that conversation, you can ask Arisktotle for where to find it. He knows quite a lot about the situation.

Every proof game is always unique in the sense that it is the only proof game consisting of those exact moves in that exact order Some diagrams have 1 unique proof game some have 1,000,000 unique proof games.

When proof game composers honor different shortest proof games for the same position they do that on the basis of another attribute. Like, there is 0-0 in one proof game, and 0-0-0 in the second one. Or, in one proof game all captures are made by a knight, in the other one by a bishop. Or, one proof game features an e.p. move, one a promotion and one a castling move (known as the Valladao task). Obviously it is easy to cheat on these attributes as there is always something different about 2 proof games, like "the 6th and 8th move". It only works when the distincttions are clearly the result of "intelligent design" of the puzzle and require composing skill.

"where order isnt considered"

I missed that - and I am glad I did Let's assume this is serious for a second. So when I have 2 proof games with the same moves - and one exception: the bishop travels Bf1-g2-f3 in the one and Bf1-e2-f3 in the other proof game - then I would have two uniquely different proof games? And not if I switched the order between say Bc1-d2 and Nb1-c3? Well, I agree it's not the same but certainly both are equally sloppy up to the 3rd decimal on the sloppiness scale!

Note that I can do these things on any random diagram. I locate all proof games which are "shortest" - let's say 9,123,456 SPG's - and then keep 1 from all sets with the "same moves" but different moves orders. That leaves me e.g. with 1275 SPG's. And then I announce to the world I have designed a diagram with 1275 "unique" SPG's! And I close off with the challenge to anyone to produce a diagram with more than 1275 unique SPG solutions! What an achievement!

I would like to honor Leither's position, since it has exactly four SPGs, one without castling, one with castling by White, one with castling by Black, and one with castling by both sides.

By the way, I had challenged Leither's claim of four SPGs since, after giving the position to Stelvio 1.6, I received the result "Found 2 solutions. The problem is correct." After Leither showed his four SPGs, I sent a Stelvio problem report. In his reply, Reto Aschwanden replied that I had found a bug in Stelvio, which he has fixed, and a new Stelvio version will be available in January with this fix included.

Indeed; I had realized this some time after posting, which is why I had said: "In hindsight, I realize that it is remarkably easy to create positions of this nature, and that I sound very stupid".

Although, it seems our understanding is slightly different. In your explanation, it seems that you interpret what I said as that each game with a different collection of moves is a "unique solution", and there could be multiple different solutions with that same collection of moves; therefore, one could technically take one solution out of those "multiple solutions that share the same collection of moves", and state that that specific collection of moves is a "unique solution". The more moves one makes, the more different possible ways to reach that position, which ends up creating a ridiculous amount of solutions with a "unique collection of moves", decidedly not impressive at all. In fact, I could probably randomly make 100 moves to reach a position, and it would have hundreds of solutions with a "unique collection of moves".

But that would truly be too easy. What I meant was that each "unique collection of moves" has a specific order that it must be played in, so there aren't alternate solutions with the same collection of moves; then, you couldn't "keep 1 from all sets with the "same moves" but different moves orders", because there are no other solutions with the same collection of moves. The key here is that no two solutions can share the same collection of moves, and that each solution cannot be reached in a different order.

This is still remarkably easy to do, so I still sound stupid.

Edit: I sound stupid for a different reason. A high quality position of this nature is difficult to create. My position is not a high quality position, however, more of an experiment.

also, to leither.... how is this simple?

it looks like you have to ensure that all moves have to be in a specific order for every solution, which seems reasonably tough

Here's an example of what I think Arisktotle means.

This is what my original intention was, where all possible solutions do not have an alternate order (hence, no "set of solutions with the same moves"). A high quality position of this nature is difficult to create, but the one I created is not an example of that; it is quite basic in comparison. To be honest, I was not really thinking properly when making the position. Perhaps it is best to not take the position seriously.

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.