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MatPlus.Net Forum Endgame studies New endgame study stipulations?

### New endgame study stipulations?

I was recently wondering about the following endgame study related stipulations:

1) help-win: black plays and helps white to win (from a lost or drawn position for white. may include h# by black)
2) help-draw: black plays and helps white to draw (from a lost position for white. may include h= by black)
3) self-win: white plays and forces black to win (from a lost or drawn position for black. may include s# by white)
4) self-draw: white plays and forces black to draw (from a lost position for black. may include s= by white)

Has anyone come across something like these?

Hi Shankar,

Thanks for this.

Is it sufficient to reach a position which is a book win or draw, when adversarial play resumes? Or is the endpoint a mate or pat, but the shortest path is no longer unique? Please explain your idea here. Also, I don't get what you mean by "may include h~ by black".

>1) help-win: black plays and helps white to win (from a lost or drawn position for white. may include h# by black)

This kind of analysis is implicitly already part of OTB chess. One-sided dead position means that the opponent cannot lose on time in FIDE rules; two-sided DP ends the game. I would offer this old retro by me as a candidate:

(= 8+9 )
R0093 StrateGems 18 04-06/2002 2. Lob
White to move. Last move?

> 4) self-draw: white plays and forces black to draw (from a lost position for black. may include s= by white)

This is already implicitly part of OTB chess studies where White self-stalemates to avoid loss.

Cheers,
Andrew

Help-draw is trivial: Just repeat the diagram position 3 times.

And self-win just sounds like selfmate without specified number of moves to me.
V. Röpke, version
(= 5+6 )

s-win 3
1. Sc2 bc2 2. a5 d3/d5 3. b3 s-win

Thanks for your replies, Andrew and Joost!

>>> Is it sufficient to reach a position which is a book win or draw, when adversarial play resumes?
>>> Or is the endpoint a mate or pat, but the shortest path is no longer unique?
Either of the above scenarios is possible.
In other words, the goal is to either reach a theoretically won or drawn position, or play a cooperative (h#, h=) or defensive (s#, and s=) sequence respectively in each of the 4 stipulations.
If the h#/h=/s#/s= shortest path is not unique, it may count as a defect!

>>> I don't get what you mean by "may include h~ by black".
Hope it's clear now!

>>> This is already implicitly part of OTB chess studies where White self-stalemates to avoid loss.
In a "self-draw" the position is already lost for black, so white has no need to avoid loss from his side. Instead, W and B play in opposition to reach a theoretically drawn position (which includes a stalemate of W or a stalemate of B). The "self-draw" stipulation needs to be modified as self-draw: white plays and forces black to draw (from a lost position for black. may include = or s= by white).
Similarly, the "help-draw" stipulation may include stalemate of white as one of the end positions: black plays and helps white to draw (from a lost position for white. may include h= by black or h= by white).

>>> One-sided dead position means that the opponent cannot lose on time in FIDE rules; two-sided DP ends the game.
Maybe DP rule needs to be excluded! A K+S+k+s position is a DP (is it?) but a h# is possible!

>>> Help-draw is trivial: Just repeat the diagram position 3 times.
If that is possible in any position, then the move-by-repetition rule may have to be excluded!

>>> And self-win just sounds like selfmate without specified number of moves to me.
See above. selfmate is one of the options. The other is forcing a theoretically won position for black.
I agree that the Ropke problem is a valid "self-win"!
I suppose, ideally these stipulations should include both theoretical won/drawn positions as well as h#/h=/s#/s= sequences.

Is the notion of "theoretically won/drawn" well-defined? Normally, precision here is not needed. But Black will be slipping from ally to adversary at this point, so you must be sure. Will it be defined by tablebase game value?

> Maybe DP rule needs to be excluded! A K+S+k+s position is a DP (is it?) but a h# is possible!

By Convention 17A, DP rule is already excluded except for retros. But that's not my point. I'm saying the concept of help-win is already explicit in the FIDE Laws. Miguel Ambronas' Chess Winnability Analyzer has gone through all the lichess games to assess whether the draw arbiter operated correctly.

Shankar, I am glad that DP is not yet so over-publicized that everyone understands it. I must publish more! :) A dead position is one which can *never* end in a checkmate. So KSvKS is generally living. KSvK is dead.

KS+ks i think is not a DP, since it is possible to mate with black help

>See above. selfmate is one of the options. The other is forcing a theoretically won position for black.

So black is trying to avoid a theoretically won position? In that case, please define 'theoretically won position', because it seems you want to change black's behaviour from trying to avoid winning to want to win halfway during the solution.

Don't start playing for a win until after it is certain you can't win... hmmm, where have I seen that before?

Oh yeah, I remember: it's the plot of every action movie ever made; the only difference is, the hero wins anyway.

If you can invent a stipulation for that scenario, Bollywood may take notice.

>>> So black is trying to avoid a theoretically won position? In that case, please define 'theoretically won position',
A position where Black could win by playing "normally"!

>>> because it seems you want to change black's behaviour from trying to avoid winning to want to win halfway during the solution.
This kind of "change of behaviour" already exists in stipulations like hs#, where Black cooperates, but on the last move he has to be forced to #1. Or in semi-r#, where he opposes, but the last two plies are a h#1 by white.

Here's an attempt: WKb1, WBa2, WPb3, BKa3, BPc5; is a theoretically won position for White (1.Ka1, Kb4 2.Kb2, etc.). He can turn it into a theoretically won position for Black by playing 1.Kc1. It may be argued that Black will refuse to win after 1.Kc1 by playing 1...c4, etc. But the goal of reaching a theoretically won position for Black has already been reached. In this position, it's only by a single move of white. In more complicated positions, white may need more moves to turn a won/drawn position into a lost one.

Let's focus on help-win study.

In adversarial chess problems that are not too large, an engine can prune the search space to find all solutions. However, if one relaxes the adversarial constraint, the search space becomes much larger, particular if one also switches off the clock limiting the number of moves. So you essentially ask for all positions that can be derived from the diagram position in which White has a win. This requires at the least that one is operating within a tablebase, and even then one would need the kind of reporting available with some engines to filter all positions in which White has a win. But in the help play we might choose to capture *all* units except minimum mating material. So it's very hard to see how such a problem might have an even approximately unique solution.

The nature of hs# proves the point: in order to get uniqueness there is very limited adversarial play allowed after the end of co-operation.

Without an indexed tablebase, e.g. if there's more than 8 pieces on the board, we can't know who would "normally" win in all accessible positions.

The FIDE Laws just ask for an existence proof that at least one help-win exists, which is a much more limited goal, and even that is known to be computationally challenging in general.

I'm on the fence...

Andrew makes a compelling case:
An open-ended Help-Win (or Help-Draw) stipulation is dead on arrival (except in VERY RARE cases, where the problem terminates quickly, failure to achieve a unique solution is virtually certain).

That said, I think this stipulation can be of interest if the number of helping moves is limited (the resulting win/draw can -- and should -- be open-ended).

I do not believe a tablebase will resolve this matter (and I bristle at the suggestion that a tablebase is necessary -- in fact, it's probably counter-productive to finding those very rare cases where a unique solution is possible with this stipulation).
The trouble is: I don't expect those rare cases to be of interest (they are almost certain to be a trivial conversion to a standard win/draw study, unless the number of help moves are limited).

In general, we shouldn't be too quick to dismiss novel stipulations/conditions (even bad ideas can yield interesting problems), but at least some of these proposed study stipulations do raise doubts.

An absence of evidence is not evidence of absence.
In general, we should be patient with novel ideas -- wait for some composers to take up the challenge -- but I very much doubt that will happen in this case (even if the idea has merit, unfortunately, there is already very little interest in fairy studies).

That said, Andrew makes a strong case against the viability of at least two of these stipulations proposed.

I think those would work much better if you limited the number of help-moves, but even there, I doubt it will generate much interest for composers (at least in the short-term).

If some composer proves me wrong, I'd be happy to consider their work.
But, in all honesty, I'd much rather see them apply the standard study stipulations to positions with fairy elements (too few study composers are willing to use fairy elements).

Not to get on my soap box, but ... LOL ...

If you recognize that one valid stipulation can be the goal of another stipulation, that stipulations can be iterative (as I've been advocating for years), you'll appreciate that there is little novelty in these "new" stipulations.

A help-(win)-2 is essentially as valid as a help-(#)-2.
A self-(draw)-3 is essentially as valid as a self-(=)-3.
The only difference is that the goal has changed (from # to win, and from = to draw).

What is new here, or what tries to be new anyway, is that you might have an open-ended help-(goal) problem, or an open-ended self-(goal) problem -- that is, a problem which doesn't specify how many moves are required.

Personally, I doubt these will yield interesting results (there's a reason these problems work better with a limited number of moves).
Can you compose an interesting h# (or s#) problem that is open-ended? Maybe it's possible, in some limited cases; but even if you can, ask yourself this question: is it really beneficial to deny the number of moves?

Maybe there are benefits.
Is it possible to compose an open-ended proofgame of high quality?
Let's be real: a proofgame in 10.0 moves is just a help-(diagram)-10, where white starts from the initial game array.

OK, let's say it is possible to make an open-ended proofgame, or a help-(diagram) without any move limitation.
Or let's say it is possible to make any open-ended help-(goal) problem.
If so, it begs the question: would such a problem really be diminished by informing the solver of how many moves are involved?

I would assert that an open ended proofgame has inherent value (doesn't matter whether the problem is of high quality as a proofgame -- it would be sufficiently interesting to see that a problem, proofgame or otherwise, can be stipulated in an open-ended form).
Compositionally speaking, the achievement of such a stipulation, by itself, would be a very interesting achievement (particularly if it's achieved by non-trivial means).

I doubt it's possible to achieve an open ended proofgame in orthodox chess (maybe I'm missing something), but I'm sure this would be possible in some fairy conditions (or, more to the point, I'm sure we can invent some fairy condition where at least one sound open-ended-proofgame would be trivially possible).

Once you realize that it this open-ended aspect which is the real novelty here, you immediately realize that it transcends the study aspect (turning the study into the goal of an iterative stipulation is hardly the point of this idea; the real novelty here is to present some stipulations as open-ended).

So, if that's the novelty you want to investigate, it makes little sense to impose a limitation upon yourself by making study the goal in an iterative problem.
Instead, focus on any open-ended problem.
Open-ended problems with study as the goal might be interesting; but, it would be far more productive to focus open-ended problems, regardless of the goal -- whether help-(goal), self-(goal), helpself-(goal), etc.

If the composer is limited to study as the goal, this exploration is likely to be much more challenging.
Any hope of computer verification goes out the window (except within the confines of an EGTB -- which already imposes a severe constraint).

On the other hand, if you chose a goal that a computer can more easily verify (#, =, diagram, etc), a computer could weakly-verify such a problem.
I say weakly-verify, because, obviously, computers may not strongly-verify a problem with unlimited moves (they can with an EGTB, for adverse stipulations).

But, if you compose what you believe is a sound open-ended help-(goal) problem, and the computer finds your intent in 3 moves, but finds no solution in 4, 5, 6, ... 25 moves, you might have a good argument that it's weakly-verified.

So, my advice to anyone who wants to explore this novel idea: if you don't have luck with stipulations where win/draw is the goal of an iterative stipulation, consider alternative goals in conjunction with carefully selected fairy conditions (which might help).

And I wish you luck in this endeavor, because it's already quite a challenge just to achieve a sound, non-trivial, open-ended help-goal problem.

I think EGTB's can be usable for s-win: Black avoids moves that give white the opportunity to play a move that leads to a position where the evaluation is 'won for black', white tries to reach it.

Example:
(= 2+2 )

s-win

1. Kb3 and now the tablebases show us that after every black move, 2. Ka4 leads to a position that's theoretically won for black.

Joost,

As I understand self-win (open-ended), white should make a move (or white should begin a series of alternating moves -- any length -- since the stipulation is open-ended) which forces black to play into a win for black. In other words, black should avoid any position which is a theoretical win for black, until a theoretical win for black is achieved (at which point black should play for the win).
I don't see this here. What am I missing?

And even if I am missing something, or even if you manage to alter it, it is (slightly) more involved to prove there is no other path to force black to play into a theoretical win for black.

But, even if you achieve such an open-ended stipulation with a unique solution, I never disputed that EGTB could be used to weakly-verify such a problem; my only claim is that the need to rely upon EGTB makes this more challenging for the composer (as the EGTB will constrain the number of units a composer may use, whereas there is no such constraint if you seek to compose, and weakly-verify, a problem with an open-ended stipulation using a goal other than win/draw).

Furthermore, when you do achieve such a problem, I would still want to ask some key questions:
1) Is there really a benefit to the open-ended nature of the stipulation (versus specifying a limited number of moves to achieve a won position for black)?
and
2) Does this open-ended self-goal stipulation have any real merit, beyond achieving a sound version of this unusual stipulation?
I am willing to concede that such a problem has some inherent value (the achievement of such a problem would be of interest), but I doubt it has much interest beyond that.
I would suggest that a self-win (or self-draw) problem has far greater potential if you limit the number of moves (for the self-phase).
Not only does an explicit limitation on moves facilitate broader verification, it also affords the composer greater space to craft something of value.

As a matter of fact, I would suggest there is much greater potential here if you add a "series" condition -- white makes a series of moves, and black is compelled to play a single move which results in a winning position for black (after which the win is played out).

The funny thing is, if black's winning move is compelled, the goal (win for black) was actually met before black moved, which begs the question: is this a self-win (in a standard self-goal problem, the goal is not reached until black is compelled to play a move which achieves it), or is it an auto-lose for white?

Iterative stipulations can be tricky like that, because some goals describe an aspect of the move (e.g., +, x, ep, oo, ++, etc) and other goals describe a state of the position (e.g., #, =, ==, diagram, win).

It would be nice if we had a clear and consistent standard spanning all iterative-stipulations (which resolves cases where the goal may be reached prematurely).

Today, various genres have various standards, because nobody recognized the benefit of establishing a standard that it consistent across a broader set of iterative stipulations.
And we keep creating new elements without giving any effort invested in a simplified, formal categorization system.
It may have made sense waiting, when the range of stipulation possibilities was unclear, but we are at least two decades beyond that point, and it's becoming increasingly clear that we have no mechanism to improve our formal expression of problems (even if we demonstrated a desire to improve upon our antiquated forms of problem expression).

And, for the record, I'm not suggesting I have the optimal answer.
I'm only putting forward a convention that covers a greater range of stipulation forms.

Iterative stipulations is simply the best methodology I know to formally describe a broader set of problem stipulations (both invented, and yet to be invented), but even that could benefit from enhancements.