3

Assume such a situation: Both players (Black and White) only have two pieces, that is a King and a Pawn. They have the liberty of placing them according to their wishes on the first row of their side of board (White on row 1, Black on row 8) and then the game starts. (Yes, pawn start from the same row as kings).

Which starting positions guarantee a win to one side? Which will be drawn?

My intention: I wonder if such a chess variant would make sense. Since players have the liberty of placing their king and pawn on any column they please, are there any positions that are clearly best? Or (as I'd hope for) would it reduce to rock-paper-scissors, that is regardless of which position a player starts with their chances to win/lose/draw the game depend on which position their opponent starts with? Or would all games be necessarily drawn, which would make such a variant pointless?

So I guess I need a method of determining if any given position is drawn or won, or rather - general rules that govern this problem, so that I could grasp all possible positions without having to enumerate them.

  • Too broad perhaps? I’m not entirely sure. – Rewan Demontay Oct 9 at 15:58
  • @RewanDemontay why? – gaazkam Oct 9 at 15:59
  • There are hundrends and thousands of such postions that could be won or drawn. Maybe you could ask for a “a few examples of postions that will be won and drawn.” Or alternativly, ask for a method if determing if a given postion is drawn or won. Also, I presume you mean for the pawns to be on the second rank of each respective side, and the kings on the first? – Rewan Demontay Oct 9 at 16:01
  • @RewanDemontay No, pawns start from the the same row as the kings. My intention: I wonder if such a chess variant would make sense. (a) SInce players have the liberty of placing their king and pawn on any column they please, are there any positions that are clearly best? Or (as I'd hope for) would it reduce to rock-paper-scizzors, that is regardless of which position a player starts with their chances to win/loose/draw the game depend on which position their opponent starts with? So I guess I should ask for a method of determining if a position is drawn or won? – gaazkam Oct 9 at 16:06
  • 2
    Playing around here: k4it.de/?topic=egtb&lang=en I find that if you change to 2nd+7th ranks instead, and also allow 2-move first move (i.e. within regular chess rules), the only way white wins is if 1) the black king is 6 or 7 files (and the black pawn 2 or more files) away from the white pawn. And if the black king is exactly 6 files away, the white pawn must advance 2. All other configs seem to be draws. – Jeff Y Oct 10 at 17:17
6

As far as I can tell, in your proposed variant a player could always force a draw by placing the king in a reasonably centralized position, regardless of what the other side chooses. Even if he allows the opponent a seemingly superior king position, it still winds up as a draw with correct play.

Let's say Black chooses the king on the D file and the pawn on the C file. If the pawns start on the same file, Black could allow a position like this and still get a draw:

[FEN "3k4/8/8/2pK4/2P5/8/8/8 w - - 0 1"]

1.Kxc5 Kc7

With the pawns one file apart, it's a similar pattern:

[FEN "3k4/8/8/2p5/2KP4/8/8/8 w - - 0 1"]

1.Kxc5 Kc7

With the pawns two files apart, Black can take the diagonal opposition:

[FEN "3k4/8/8/2p5/3KP3/8/8/8 w - - 0 1"]

1.Kxc5 Ke7 Kd5 Kd7

Three or more files apart? No problem. White must abandon his pawn to eliminate Black's pawn.

[FEN "3k4/8/8/2p1K3/5P2/8/8/8 w - - 0 1"]

1.f5 c4 2.Kd4 Ke7

And, of course, Black can and probably will get his king to a better position than that. This is just to demonstrate that even if he doesn't, he can still draw.

As far as when a king and pawn can win against a king and pawn, there's one position that comes to my mind, outside of the obvious pawn race scenarios. This position is a loss for whoever has the move - they must abandon their pawn and will be out of position to block the opponent's pawn:

[FEN "8/8/8/1Kp5/2Pk4/8/8/8 w - - 0 1"]
  • 1
    I fully agree, the only way for this variant to not end in a draw is if a player doesn't know opposition or in some rare corner cases of really dumb placement. E.g., if Black places their king on a8 and White has their pawn on h1, White wins because Black cannot get inside the square of the pawn after 1. h3. But why would Black place their king in the corner in the first place? – Annatar Oct 10 at 6:42
  • 1
    It may still be an interesting pawn ending exercise for beginner learning groups, but unsuited for actual competitive play. – Annatar Oct 10 at 6:45
2

It would come down to raw calculation a lot of the time.

Which pawn would queen first? Can the opponent prevent the pawn from queening? ? If so, what happens after that? Also consider square of the pawn, opposition and zugzwang. There are also positions where one side queens first but still loses (for example queening with check). Who queens first is the most important factor but, like I said, there are a lot of variables. You might also look at Reti's position which in an ingenious proof that you just have to calculate a lot of this stuff out.

Those elements will tell you who wins but it would be difficult to boil it down to a simple formula.

Bottom line: Start with who queens first and go from there unless one side can force a zugzwang or push the opponent back with opposition.

  • I don't think this require much calculation. The draw is straightforward if you place your king on a central file. D M's answer explains it nicely. – Evargalo Oct 11 at 8:08
1

Other than special cases like with a rook pawn and the defending side getting to a8 or c8, or where the pawn can just queen, there is a simple rule that applies to most positions.

The rule is that you need to have your king in front of the pawn, and be able to get the opposition. So if you can win the pawn, and still meet this criteria, then it is a win.

1

I think this is winning for white -- if pawn can still move 2 squares on move 1.

[FEN "6pk/8/8/8/8/8/8/PK6 w - - 0 1"]
0

You could reference either Encyclopedia of Chess Endings, Volume 1, Pawn Ending by Aleksandar Matanovic (Editor),

or,

Endgame Tablebase: https://en.wikipedia.org/wiki/Endgame_tablebase.

  • 2
    His pawns start on the 1st rank... no existing books or tablebases are going to help. – RemcoGerlich Oct 10 at 11:24
  • 1
    once the pawns move off the back it should transpose into a tablebase – Ywapom Oct 10 at 17:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.