11

If a situation containing only pawns and kings is displayed is there a simple set of rules for determining if the position is won/drawn/lost?

I know for single pawn and double pawn endgames this is true with rules like the opposition, rule of square, rook pawns etc. My question is, does this extend into multipawn games or are they simply too complex and varied?

Another way of putting the question might be: if you show two grandmasters a pawn only endgame; do they both immediately know the outcome, or are there some that they would need to play out?

  • 1
    A variation of your question is to ask if it is currently feasible to program a computer to properly categorize pawns-only endgames (in a reasonable amount of CPU time). I suspect that the answer is "yes" -- but the resulting algorithm is incapable of being summarized by a humanly-comprehesible rule. – John Coleman Jun 6 '18 at 21:52
18

Generally speaking, the side with the most pawns will win. The tempo provided by the extra pawn is usually enough to gain opposition and access to the key squares. Doubled pawns don't matter for this, unless they're blocked. The extra pawn can also limit the movement of the opponent's king, resulting in the possibility of a triangulation maneuver.

Another recurring theme/rule is the breakthrough. Grandmasters know the patterns for which a breakthrough is possible by heart.

But generally, multi-pawn endgames are just as complicated as other endgames. There is a Russian endgame study composer, Nikolai Grigoriev, who is famous for his pawn endgame studies. They truly show the rich possibilities of chess with just kings and pawns. With so many beautiful studies available, you know that there can be no general rule to determine the outcome.

15

While there are general rules, these rules have many exceptions and nuances.

In the following position with White to move, both sides have a passed pawn, but the fact that Black's passed pawn is so much better means White is dead lost:

[FEN "6k1/8/6p1/2p5/1pPpP3/pP6/2P3P1/2K5 w - - 0 1"]

But it's precarious. Remove Black's A-pawn from the starting position, and Black doesn't have a passed pawn, and doesn't win. Remove his B-pawn, and the passed pawn isn't connected, and Black doesn't win. Remove his C-pawn, and White has a second passed pawn, and Black doesn't win. Remove his G-pawn, and White again has a second passed pawn, and Black doesn't win. Remove his D-pawn, and Black does win - but not if White's king started at b1 instead of c1. There's no "rule" that can cover all these situations; you have to calculate them to at least some extent.

  • The pawn structure in the example is taken from one of my games (although there were still rooks on the board) and I was thrilled when my opponent offered a draw - I think he didn't understand how much more powerful his passed pawn was than mine. – D M Jun 6 '18 at 6:03
  • Looking at that position, it looks like the primary initial function of the black A pawn is to keep White's king from coming to the defense of its E pawn. Would I be correct in assuming that zugzwang plays a major role in Black's victory? Take away all the E and G pawns, and whichever side next moves a pawn will lose it.with no compensation, but White can't keep his king at C1 without moving a pawn. If White's king moves to D1 or D2, Black's A pawn runs to the finish line. If White's king moves to B1 when Black's king is at D1 or E2, Black's king can move to D2. – supercat Jun 6 '18 at 17:22
  • I guess maybe I'm over-complicating things given the presence of Black's G-pawn. I think that pawn is only needed with White to move, though. If Black were on move, White's E and G pawns would both be lunch. – supercat Jun 6 '18 at 17:34
  • @supercat Without the g6 pawn, Black can't win even with the move. White just plays g4, and Black can't safely attack either pawn without the other promoting (Kg5 is responded to with e5, so Kxg4 would allow the e-pawn to promote, for example.) But yeah, if you take out all the pawns on the D-H files, Black moves his king up and wins when zugzwang comes into play; the c2 pawn falls followed by the b3 pawn because White eventually has to move his king away from them. – D M Jun 6 '18 at 17:52
6

There is no general rule for multi-pawn endgames as they are much too complex.

However I believe that most of the pawn only endgames that appear in regular games are readily assessed correctly by grandmasters (or even just masters). Sure there are pawn endgame studies that might be tricky, but on average assessing a pawn endgame is much easier than an endgame with say rooks on the board.

In order to win a pawn endgame you have to promote a pawn (apart from rare situations where you mate with pawns only). So obviously one of the first thing to look for is the availability of passed pawns or the options for creating passed pawns. If there are, you would further assess the strength of those passed pawns: Can the king catch them? Are they protected? (This usually means that the king is bound to a certain part of the board and could be used for operations in another part of the board.) Do you perhaps have more than one passed pawn? If both players have passed pawns; whose pawn is quicker?, etc.

If there are no passed pawns, it means that (in order to win) you have to capture an enemy pawn with your king. Target pawns to be captured are often fairly clearly defined. Your opponent may defend passively, e.g. preventing you from getting close to the target pawn or he may actively try to capture one of your pawns and promote a pawn.

In situations like this, it is often essential to count correctly, make proper use of opposition and triangulation. Fortunately the number of possible moves is limited in pawn endgames, simplifying the calculation of long lines.

When assessing multi-pawn endgames, of course it helps if you know the rules of single pawn endgames (rule of square, rook-pawn,opposition, active king etc) since the multi-pawn endgame might turn into a single pawn endgame or effective single pawn endgames if pawn chains are blocked.

3

There are a bunch of helpful rules on pawn endgames, but even a grandmaster wouldn't be able to call every pawn endgame won/drawn/lost.

Some pawn endgames involve immense amounts of calculation, involving concepts such as pawn races, corresponding squares, and long-distance triangulation. Other pawn endgames are too complex, and are beyond the calculation abilities and evaluation skills of a grandmaster to objectively evaluate (for example, six pawns each arranged in weird structures).

That being said, grandmasters can probably evaluate 99% of pawn endgames that come up, since they're the simplest endgame and have many helpful rules. But in the remaining 1% of endgames, these rules are often broken and the situation becomes very counter-intuitive, even to a grandmaster.

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