Longest checkmates

[Kirill Kryukov]

Hi everyone! I am making a web-page where I list longest checkmates in different endgames. Purpose:
1. Get excited about the checkmate length and be able to immediately see the example position.
2. Those positions can be used to test if a chess engine is accessing particular tablebase.
3. To get a clue about what endgames are more interesting.
4. I (or anyone) may use those positions to compose some studies.
5. It's fun.

Come and take a look.

I realize that this is not new information. I simply list those checkmate lengths and example positions all on one page for convenience. Any comments of suggestions are welcome.

The page is incomplete, I'll work on it more as I have time. Also any help will be appreciated.

[guyhaw]

This initiative is very welcome: more light could be shone on these positions deep in the firmament of the chess endgame where no human otb player is likely to go or return from.
All the known maxDTx (DTC, DTM, DTZ, DTZ50) stats are available in my spreadsheet at http://www.icg.org --> Game-specific info --> Western Chess --> Endgames.
I have a file of all 3-5-man DTM-maximal positions (wtm/btm, 1-0 & 0-1) created by Peter Karrer some years ago: you are welcome to this.
It would be good to have .pgn files of lines produced by DTM-minimax strategies, i.e. by a SM-vSM+ strategy-pair in my notation, see the ICGA_J papers on this.
I also have a file 3-5-man DTC-maximal positions (wtm/btm, 1-0 & 0-1) created by Christoph Wirth from his own EGTs: you are welcome to this.
A piece of work not done yet is to identify the intersection of the Karrer and Wirth positions-sets. A position which is both DTC- and DTM-maximal is 'more special' in a sens. Also, a line produced by an SM-C-vSM+C+ strategy-pair is 'more special' than a line produced by a SM-vSM+ or SC-vSC+ strategy-pair.
To convey more information in a line of play, the unique and uniquely-DTx-optimal lines can be marked. I prefer to avoid !! and ! for this, as these are customarily indications of subjective pleasure/surprise at a move: I have used " and ' before, leaving open the possibility that a '-move is later marked a "-move if alternative winning moves merely allow the loser to force the winner back to the moved-from position.
Anyway, you are welcome to any help I can provide.
g

[Kirill Kryukov]

Hi Guy, thanks for comments and information! My page will have very simple format, easy to read and enjoy. Your XLS file is very extensive of course, I may refer to it in future.

I have a file of all 3-5-man DTM-maximal positions (wtm/btm, 1-0 & 0-1) created by Peter Karrer some years ago: you are welcome to this.

Thanks, I already found all 3-5-men DTM positions by myself using Wilhelm. I did that in 2004. If I did not have them, I would be happy to use your data.

It would be good to have .pgn files of lines produced by DTM-minimax strategies, i.e. by a SM-vSM+ strategy-pair in my notation, see the ICGA_J papers on this.

Yes, it would be good.

I also have a file 3-5-man DTC-maximal positions (wtm/btm, 1-0 & 0-1) created by Christoph Wirth from his own EGTs: you are welcome to this.

I am not interested in DTC at the moment. But thank you anyway!

A piece of work not done yet is to identify the intersection of the Karrer and Wirth positions-sets. A position which is both DTC- and DTM-maximal is 'more special' in a sens. Also, a line produced by an SM-C-vSM+C+ strategy-pair is 'more special' than a line produced by a SM-vSM+ or SC-vSC+ strategy-pair.

This is just toying, I think. Right now we are more in need for some more easy information to attact the general chess enthusiasts' attention to endgame tablebases.

To convey more information in a line of play, the unique and uniquely-DTx-optimal lines can be marked. I prefer to avoid !! and ! for this, as these are customarily indications of subjective pleasure/surprise at a move: I have used " and ' before, leaving open the possibility that a '-move is later marked a "-move if alternative winning moves merely allow the loser to force the winner back to the moved-from position.
Anyway, you are welcome to any help I can provide.
g

I have been thinking about incorporating the 50-moves rule into tablebases. As we know, Nalimov bases wash their hands here so all work on detecting the 50-moves draw has to be done by engine. What do you think is the best way to construct 50-moves-rule-aware tablebases?

[guyhaw]

I think WILHELM can be used to produce the required SM-vSM+ lines.

The defined metric DTZ50 (with the '50' subscripted) recognises the 50-move rule: see http://www.tinyurl.com/law6k for the papers. For any position that can be won by limbo'ing under the 50-move rule, DTZ50 provides the number of moves to 'move-count zeroing' under the limbo-constraint.
It is not just a matter of setting DTZ to 'draw' if DTZ>50: there are, e.g., plenty of 'wins' in KBBKNN which are not achievable under the 50-move rule because they drop into a KBBKN position with DTZ>50. There are KQPKQ wins with DTZ=1 and DTZ50=50 (!): plenty of examples like this in the JT/GMH paper (see below).

John Tamplin has computed DTZ50 EGTs for all 3-5-man and 6-man-P-less endgames. He used Marc B's GTBGEN program which can create DTC, DTM and DTZ EGTs without or with recognition of a (general) k-move rule. The work was written up in two papers at 'law6k'.

It was Marc B that argued for a programming and production-run investment in DTZ50, given that I'd defined the DTR & DTZR metrics but those DTR and DTZR EGTs would not be created for a while. DTR is the metric one gets if the attacker not only wishes to win but to limbo under as many k-move rules as possible. See 'law6k' again. The idea is that DTR tells you by how much you are failing to win your game under a k-move rule, and therefore how much your fallible opponent has to concede to hand over the win.
DTR EGTs are therefore conceptually better than DTZ50 ones which don't do this. DTR-based endgame strategies also deliver more 'natural' play as they tend to avoid needless sacrifices (as have actually been seen otb between FRITZ & JUNIOR playing KRRPKR), and premature captures or P-pushes.
g

[GMX]

nice idea!

Just a small remark: position given as an example for KRPkbn is absolutely illegal. Is there any other mate in 204 or the limit is 203?

[guyhaw]

This is a tricky one. As there is no general algorithm for saying whether a position is reachable from the initial array or not, the weeding out of unreachable positions has not been attempted by Thompson, Wirth, Nalimov or Konoval - to name but four.
This is fortunate in a way as it makes the respective sets of statistics comparable or more comparable.
However, when it comes to 'shortlists' of positions such as the maxDTx positions, the maxDTx mzugs - or just the mzugs (if there aren't too many), one can see that the position one wants to focus on might be clearly unreachable.
I've always reported maxDTx and maxDTx-mzug (depths and counts) without checking for unreachability, on the grounds that I'm bound to miss one some day. However, if I see one, I note that it is unreachable but don't change the nominal stats. I hope that's a good pragmatic.
g

[Kirill Kryukov]

nice idea!

Just a small remark: position given as an example for KRPkbn is absolutely illegal. Is there any other mate in 204 or the limit is 203?

Thanks GMX! Yes, there are many illegal or unrealistic positions there, I don't try to remove them. For example, there is also a number of positions with two bishops of the same color.

It is interesting for me to see the longest possible checkmate line with given configuration of pieces.

Is there any other mate in 204 or the limit is 203?

I don't know. You can try to search using "Wilhelm" program.

[guyhaw]

I asked Tim Krabbe whether an actual game had ever featured two same-colour Bishops on the same-coloured squares.
He found about 30 in a database of 2m games, but "none of them were serious". So, effectively, it has never happened.
This is not of course an argument for not removing such positions from the EGT statistics. g

[Oded Ross]

This is just toying, I think. Right now we are more in need for some more easy information to attact the general chess enthusiasts' attention to endgame tablebases.

I am a chess enthusiast who with a particular liking of chess oddities and records, and this page is my favorite part on the site
Is it still a work in progress? Any estimation about completion of 6-man EGT longest DTM?

This initiative is very welcome: more light could be shone on these positions deep in the firmament of the chess endgame where no human otb player is likely to go or return from.
All the known maxDTx (DTC, DTM, DTZ, DTZ50) stats are available in my spreadsheet at http://www.icg.org --> Game-specific info --> Western Chess --> Endgames.
I have a file of all 3-5-man DTM-maximal positions (wtm/btm, 1-0 & 0-1) created by Peter Karrer some years ago: you are welcome to this.
I also have a file 3-5-man DTC-maximal positions (wtm/btm, 1-0 & 0-1) created by Christoph Wirth from his own EGTs: you are welcome to this.

The excel file you made containing both their works is superb. I often refer to it. Can't remember where I downloaded it from.
Is there any similar sheet for 6-man EGT? The closest I found was one made by Ken Thompson, but it contains only DTC and is highly incomplete with pawnless EGT only.

nice idea!
Just a small remark: position given as an example for KRPkbn is absolutely illegal. Is there any other mate in 204 or the limit is 203?

Thanks GMX! Yes, there are many illegal or unrealistic positions there, I don't try to remove them. For example, there is also a number of positions with two bishops of the same color.

There is a clear distinction between an illegal position such as this one, and an unrealistic one - and frankly, RRR-Q for example is just as unlikely as same-colour Bishops for White. I see why an algorithm of pruning these out would be hard to make.

I asked Tim Krabbe whether an actual game had ever featured two same-colour Bishops on the same-coloured squares.
He found about 30 in a database of 2m games, but "none of them were serious". So, effectively, it has never happened.
This is not of course an argument for not removing such positions from the EGT statistics. g

I think the double negativity causes the meaning of the sentence to be the opposite of what you meant to say

[Kirill Kryukov]

This is just toying, I think. Right now we are more in need for some more easy information to attact the general chess enthusiasts' attention to endgame tablebases.

I am a chess enthusiast who with a particular liking of chess oddities and records, and this page is my favorite part on the site
Is it still a work in progress? Any estimation about completion of 6-man EGT longest DTM?

If you refer to my "Longest Checkmates", I am not doing anything about it at the moment, but I might complete the page in future. Also, the longest possible DTM in all 6-piece endings is already known, since the tablebases are computed and available. My page is just showing the example maximum DTM position for each ending. In any case, I am always happy to see any EGTB-related activity.

[ernest]

spreadsheet at http://www.icg.org

The excel file you made containing both their works is superb. I often refer to it.

icg.org now sends you to... International Crisis Group

[Oded Ross]

spreadsheet at http://www.icg.org

The excel file you made containing both their works is superb. I often refer to it.

icg.org now sends you to... International Crisis Group

Yeah I've noticed... But I did find out where did I find these excel sheets - John Tamplin's site, which is one of the many links in Kirill's online tablebases page. Highly recommended.

If you refer to my "Longest Checkmates", I am not doing anything about it at the moment, but I might complete the page in future. Also, the longest possible DTM in all 6-piece endings is already known, since the tablebases are computed and available. My page is just showing the example maximum DTM position for each ending. In any case, I am always happy to see any EGTB-related activity.

I don't know of a more convenient place that shows these stats than your page. It's interesting and sometimes funny (as I wrote on this chess site, one can think when do two queens and a rook take 32 moves to mate a lone knight ) to see the max DTM position (as opposed to just know what is that number) for every setup, not just the 200+ moves ones. I hope you'll have the time to finish it some day (and for that matter 5+1, if available, can be amusing too).

[guyhaw]

The URL you are looking for is, I think, not 'icg.org' but 'www.icga.org' ... and thence by 'Game-Specific Info' to 'Western Chess' and 'Chess Endgames'.

g

[crplr]

Recently the longest mate was known as in 524 moves

Now the page informs about 545 moves:
http://rybkaforum.net/cgi-bin/rybkaforu ... l?tid=8477

How all this may be verified?

[kronsteen]

Hmm… main line is clearly flawed as someone reported (wn can take br at move 142), and therefore DTM=545 claim (built upon it) might well also be.

Author also speaks of a “hard calculation taking almost 12 hours”. I would be absolutely astonished if such a result could be achieved so fast. krbnkqn has 718 G positions, and has to be probed more than 500 times (by standard methods) in order to dig out maximal position(s). Should this prove true, it would mean that one of the biggest issues for building 7-men TBs (needs in CPU time) is about to be solved.

I don’t trust these results for now, but let’s wait a little…

[crplr]

Author speaks about using very powerfull computer. He didn't generated all 6-men tables and directly went to 7-men. The paradox is that only a few persons in a World can check each other in 7-men generation. Other may beleive or not to beleive (except discovering evident flaws).

Let's look at the next steps.

[kronsteen]

Ok, main line has been fixed.

How can this be verified ? Here’s a paper about implementing formal verification techniques in TB building in order to be absolutely sure that results are flawless. Results are given for 3-4 men only, though, and this technique might not be suitable for handling much bigger TBs.

http://www.gilith.com/research/papers/chess.pdf

Apart from this, TBs built from different sources can be checked against each other in order to increase confidence. Author says it has generated the kqnkrbn TB in DTM format. If so, he can easily generate the same TB in DTC and check the result against Marc Bourzutschky & Yakov Konoval’s work back in 2006.

[guyhaw]

Joe Hurd and I contributed a paper on 'Data Assurance in Opaque Computations' to the ICGA ACG12 Conference this year in Pamplona. Proceedings are not yet out.

It was a second follow-up to Joe's paper on HOL and EGTs: our first follow-up was too long to limbo under the conference ration of 12pp

What I learned from writing the paper with Joe is that the future is to specify programs 'functionally' and then let some 'box of magic tricks' create an equivalent imperative program to run on parallel hardware where possible. Currently, we have to work too hard to specify the sequence of computational steps, a task which distracts from the core activity of making sure that the relationship between all the 'data stores' is defined and maintained correctly.

Guy