Pawns against pawns

One of the things I want to do in life is to study the following position. White to move.

Position 1

It's a position I thought of, although it's possible it has been examined before.

[Edit: I found out that it's in fact a study of Tattersall 1916, he says white wins and gives the following line. 1.b4! (1.a4? a5 2.d4 (2.c3 c6) 2...d5) (1.a3? b5 2.b4 (2.d4 d5) 2...d6) 1...d5 (1...b5 2.d3 d6 3.c4 bxc4 (3...a6 4.c5) 4.dxc4 c6 5.a4 d5 6.b5) (1...c6 2.c4) 2.b5 d4 3.a4 c5 (3...a5 4.bxa6 bxa6 5.a5 c5 6.d3) 4.bxc6 bxc6 5.a5 c5 6.c4 dxc3 7.dxc3 c4 8.a6 1-0]

It's clear that any king move loses immediately, and this is true for both colors.  Therefore all the action happens on the queenside.

I think I have not yet figured out everything but just to explain the difficulties let me set up a much easier position.

Position 2

Here I think white wins with 1.a4! or 1.d4! They are both good by the symmetry of the position. Instead, 1.b4 and 1.c4 lose. Before looking at the winning lines let's see why 1.b4 loses. We have 1.b4? b5! 2.c4 c5! 3.bxc5 dxc5 4.cxb5 axb5. There are no tricky pawn breaks in this line because here things are pretty simple: in a promotion race the more advanced pawn simply wins.

White needs to put black in Zugzwang.

Let's examine 1.a4. Black has four possible replies.

a) 1...a5 2.b4. Now 2...b5 loses because white will promote first, 2...c5 loses to 3.bxa5 bxa5 4.c4, and 2...d5 loses to 3.bxa5 bxa5 4.d4.

b) 1...b5 2.axb5 axb5 (2...cxb5 3.b4 d5 4.d4) 3.d4 c5 4.d5! c4 4.b4.

c) 1...c5 2.b4 b5 (2...d5 3.bxc5 bxc5 4.a5) 3.a5 c4 4.dxc4 bxc4 5.b5.

d) 1...d5 2.b4 c5 3.bxc5 bxc5 4.a5 c4 5.d4.

I want to show another "simple" position to try to understand the problem better.

Position 3

Here white has the move, and I believe this is a win for black. The strategy of black is to reply to the moves with central symmetry, meaning for example that to 1.a3 he should reply with 1...c6 (axial symmetry would be 1...a6), to 1.c4 he should reply with 1...a5, while any move of the b pawn will make central and axial symmetry coincide, so for example to 1.b3 black will reply with 1...b6. The idea is to keep doing this until a situation where two pawns are attacking each other. Then black should stop and think, because that will unbalance the position. So for example

1.a4 c5 2.c3 a6 3.b4

Here the "symmetric" move 3...b5 would lose, instead, black plays 3...cxb4 4.cxb4 b6! and wins. Note that this final position suggests to look at the even simpler position that follows.

Position 4

Here the situation is almost trivial: white is in Zugzwang, we see that. But trying to verbalize the principle we realize that it sounds as follows: copy white's moves according to axial symmetry until two pawns attack each other, then stop and think. So with three pawns we had central symmetry, with two, we have axial symmetry (with one pawn the two symmetries collapse to one symmetry so there is no point in examining that concept). This fact suggests that if there is an odd number of pawns then central symmetry will work, if instead there is an even number of pawns then axial symmetry will work. So in our 4 vs 4 situation (position 1) we might want to try axial symmetry. Of course if axial symmetry works there, it only works to some extent (remember that Position 2 is strangely a win for white).

I believe this gives a lot of importance to the strategy of looking at simpler problems when facing a big problem. It gives you ideas, your brain starts working well :)

So far what I know for sure is that in position 1 axial symmetry should be a good thing to try. I will need some more time to formalize the concept.

In the meantime I suggest a possible field of research. Consider the following game: place the pieces in the initial position and remove all the pieces that are not pawns.

Then play with the usual rules of chess. The aim of this game is to achieve one of the following two things:

a) promotion of a pawn;
b) the opponent is out of moves.

The general strategy should be to try to keep some kind of symmetry, and since only black can do this (because any white move now will break any imaginable symmetry), black probably has a forced win.

But is this known? Not by me :-)