King and Pawn versus King

I introduce the concept of opposition in stages in my courses.
Direct opposition is introduced here: lichess.org/study/mG0bCXXs
See chapter 1 and chapter 3.

Also see: lichess.org/study/iXh5F2y8

You can refer to the Wikipedia page in #10 for the definition of distant opposition (sometimes distinguished as vertical and horizontal opposition), and diagonal opposition. The page does not define oblique opposition; when the Kings are on corners of a square where all the corners are the same color.

A key square is a square such that if a player's King can occupy it, he can force some gain. The gain in KPk is either the promotion of a pawn, the capture of an opponent's pawn, or the gain of another key square.

The concept of key squares is introduced in my studies here:



We saw in lichess.org/forum/team-jomegas-tabia/king-and-pawn-versus-king#7 why White wants to gain d7.

Black wants to prevent White from obtaining d7. That leads us to this chapter in the same study.

The key square idea is so well known that even teachers that teach opposition teach it. They will point out that the real goal of having the opposition is to use it to gain a key square (or some other advantage). If taking the opposition does not give an advantage then don't take it!

In the first position above, White plays 1.e7 so that Black cannot take the direct vertical opposition at d8. White's King attacks e7 and d7, and the pawn attacks d8, hence they restrict Black from those squares. Black is forced to give up his attack on d7.

The ideas of square occupation, and attack of a square, are axiomatic in chess. The idea of restriction is a layered concept on top of attack of a square. I talk about these layered concepts in another thread.

In the second position above, Black plays 1...Kd8, taking the opposition. White can try 2.e7+ to get the opposition back. Black must give up the opposition, but after 2...Ke8, White finds that taking the opposition at e6 stalemates.

I find the explanation with key squares, based on the idea of escorting the pawn, much easier for people to understand.

I could probably spend a few years reading the chess programming wiki site! For example KPk has been solved in various ways with "knowledge" based programming.
www.chessprogramming.org/KPK

These things are at first a "gumption trap". For defn see: en.wikipedia.org/wiki/Gumption_trap

It didn't take long though to see that how they have solved KPk is not what I'm after.

The idea of a bitbase is a poor man's tablebase. 98,304 positions is beyond human memory.

The Perfect Heuristic method is based on an idea called "effective distance". Also on the idea that the problem can be partitioned into 6 subcases with from 6-11 attributes. In each of these 36-66 subcases you still have to know the procedure from those. Again, this is too much for a human.
The Imperfect Heuristic methods are no better.

Chess programmers have always been, rightly so, more interested in getting their programs to play chess well by any method. The have not been interested, for the most part, in having a program that can explain to a human a procedure or a theory for the human to use to understand what is going on.

See also: http://oro.open.ac.uk/56945/1/479863.pdf
A Ph.D. thesis by Bramer on chess knowledge representation.

Sigh. I started reading the above PDF. It is not surprising that Mr Bramer failed to predict the future of chess playing programs writing in 1977. I applaud his efforts at "knowledge representation". However, reading his description up to section 2.7, he describes a model that no human uses in practice, or could learn to use. The model is simply too complex for humans. This is for the endgame KRk, which I have taught to many people. There are multiple procedures that a human can remember to play this endgame. Some are more complex than others. None of them remotely approach the complexity of the model in Mr. Bramer's paper.

By his own first major criteria:
"..firstly, that algorithms constructed using the model should be natural from the viewpoint of a chessplayer and commensurate with his view of the complexity of the task..."
the model fails.

Continuing to read Bramer's Ph.D. thesis, he has 11 equivalence classes for KRk. There are 15 classes for KPk.
While interesting, it is too much for a human. Even if the computer plays this way it should not explain how a human should play using these equivalence classes.

The latest paper I've looked at is
Aligning Superhuman AI with Human Behavior:Chess as a Model System
arxiv.org/pdf/2006.01855.pdf

Extremely interesting. However, the techniques they are talking about to get a program to predict what a human would play in a position is *not* going to get any closer to explaining *why*! Nor can a human use those techniques themselves. Bramer's Ph.D thesis in #16 is much closer to the goal of having techniques a human could use to play chess; and he still missed.

What the above paper's research might lead to is a program that played more like a human and be at a level that would be fun and educational to play. But the education would be up to the human playing the game. For example, suppose you had the ability to play a computer that played around 1400 ELO and you could specify that the program should play in a certain style; maybe with certain openings in its repertoire, etc. Attempts have been made to create such a program; Chessmaster 10 and Fritz-12 both have this ability. However those attempts used tuning of parameters of an A/B engine; not a NN style program.

#15 - #18 got somewhat off topic. I should continue here with what I teach next in KPk.

Also look up stats for KPk taken from the tablebase.