Unless I'm much mistaken, there's no zugzwang here. I couldn't see what to do after 1. c4 c5 2. a3. My analysis went:

2. ... a6
3. b4 b6
4. b5 axb5
4. cxb5

Superficially it might look like we've forced the c-pawn through and it's happy days. The problem is that white's king covers that pawn and that white is going to be able to force his a- or b-pawn through in the same amount of time it's going to take us to queen the g-pawn.

So I fired up Stockfish and it confirmed this analysis. The engine line runs: 1.c4 c5 2.a3 a6 3.b4 b6 4.b5 axb5 5.cxb5 c4 6.Ke4 Kxg4 7.a4 c3 8.Kd3 Kf5 9.a5 g4 10.axb6 g3 11.b7 g2 12.b8=Q g1=Q with a drawn position. Am I missing something?

You are right- I don't have any engine- but the reason that this is a draw is because white's K is closer to the queenside.

What does stockfish say if you make white play a3 or a4 first (could be still draw idk)?

The idea is to maintain a zugzwang with 3 pawns vs 3 pawns- you should mirror moves both vertically and horizontally. i.e. meeting a3 with ...c6, and c3 with ...a6 and so on.

What about if we have black's K on f4 and white's K on h5?

Anything other than c4 loses horribly (as does anything other than c5 in response).

With the black K on f4 instead, it's a win for Black - but again, if it's Black to move, the position is drawn.

(Edit: oops, I thought you meant 8 pawns on each side, i.e. K+8P vs K+8P. Also, I assumed that the objective is to checkmate, not just to queen first, which, I reckon, would be even easier for White.)

(Edit 2: and of course I had forgotten to install the relevant 6-man Syzygy tablebases beforehand, so the effort is wasted )

I'm not sure what exactly position you mean, but the thing is that either the position with the kings on e1 and e8 or the one with the kings on d1 and e8 (all the pawns being at their initial places) isn't won by Black; if one of them is won by Black, then the other is necessarily won by White. That's because, in the former, White can play 1. Kd1 and mirror Black's winning strategy for the latter (if it exists; with the files being flipped as well), and analogously, in the latter, White can play 1. Ke1 and mirror Black's winning strategy for the former if it exists.

Hence, when playing one starting game from each of these two positions ideally, White scores at least one point.

I've just launched 6 classical games (90+30) of Stockfish 6 against itself from the former position, let's see how well White does (I know that engines play the endgame poorly, so it will hardly give an ultimate answer.) I think that both positions are drawn.

Yeah I meant a kingless endgame c00n. Also the point of my post wasn't really to find out the exact winning continuation for the position- but to know how to maintain a zugzwang with 3 pawns each at the starting position.

Actually, you can emulate the kingless endgame (with up to 5 active pawns on each side) by starting from the following legal chess position, where queening automatically checkmates and the only way to draw is to deliver mutual stalemate (with pawns going head-to-head with each other).



The game of Stockfish 6 vs itself from this position always lasts for only 9 moves and ends in mutual stalemate. (The way of achieving the draw may depend on the contempt factor or other configuration parameters, but it's still a draw; in real chess positions like above, it means that Black wins if his king is more centralised because White can't pass the move on to him; if White's king is more centralised, it's drawn as shown above.)

With 3 pawns on each side, the result is a draw in 6 moves.

However, with 4 pawns on each side, White queens / mates in 12; but with 2 pawns on each side, Black queens / mates in 7. With 1 pawn on each side, the game is trivially drawn. So the game seems to be drawn when the number of pawns on each side is odd and decisive when it's even.

Interesting results. Though black still wins the zugzwang war with 1 or 3 pawns each (just that it's a stalemate rather than with white being forced to lose a pawn).