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Kmoch's definition of a backward pawn or straggler: A half-free pawn on the second or third rank whose stop square lacks pawn protection but is controlled by a sentry. The definition of a backward pawn seems a bit ambiguous. May an isolated pawn also be a backward one? Or an pawn on a closed file? What about a backward ram or faked candidates or even levers?

Backward

We may use a more general definition of backwardness, to consider certain subsets independently. All pawns, which stop is not member of own front-attackspans but controlled by a sentry are backward:
U64 wBackward(U64 wpawns, U64 bpawns) {
   U64 stops = wpawns << 8;
   U64 wAttackSpans = wEastAttackFrontSpans(wpawns)
                    | wWestAttackFrontSpans(wpawns);
   U64 bAttacks     = bPawnEastAttacks(bpawns)
                    | bPawnWestAttacks(bpawns);
   return (stops & bAttacks & ~wAttackSpans) >> 8;
}

Straggler

Stragglers are the intersection of backward with open pawns and the second or third rank:
U64 wStraggler(U64 wpawns, U64 bpawns) {
   return wBackward (wpawns, bpawns)
        & wOpenPawns(wpawns, bpawns)
        & 0xffff00; // rank 2,3
}
In the strict sense, we still need to exclude levers. On the other hand, levers are subject of quiescence search anyway.

Telestop Weakness

As pointed out by Sam Hamilton [1] considering stop squares might be insufficient for pawns which may actually push, but have a permanent weakened telestop, f.i.:
  • 8/5p2/6p1/p1p3P1/P1P5/7P/1P6/8 w - -
    8/5p2/6p1/p1p3P1/P1P5/7P/1P6/8 w - -

On the other hand, such a backward prospective pawn has a vital tempo, which is often decisive in certain pawn endings, so one should be careful to don't make the penalty too worse. Anyway, one may either apply the above wBackward algorithm with so far movable pawns shifted one rank up, or alternatively determine a backward square area, which is the black attack span of all black attacks which are outside the white front attack spans:

white pawns         black pawns
. . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . 1 . .
. . . . . . . .     . . . . . . 1 .
. . . . . . 1 .     1 . 1 . . . . .
1 . 1 . . . . .     . . . . . . . .
. . . . . . . 1     . . . . . . . .
. 1 . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .
 
~white front     &  black attacks    -> stop squares
attackspans                             dominated by black 
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . 1 . 1 .     . . . . 1 . . .
. . . . 1 1 . 1     . . . . . 1 . 1     . . . . . 1 . 1
. 1 . 1 1 1 . 1  &  . 1 . 1 . . . .     . 1 . 1 . . . .
. 1 . 1 1 1 1 1     . . . . . . . .     . . . . . . . .
1 1 1 1 1 1 1 1     . . . . . . . .     . . . . . . . .
1 1 1 1 1 1 1 1     . . . . . . . .     . . . . . . . .
stop squares
dominated by black
filled down
-> white         &  white pawns      -> backward pawns
backward area
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . . 1 1 . 1     . . . . . . 1 .     . . . . . . . .
. 1 . 1 1 1 . 1  &  1 . 1 . . . . .     . . . . . . . .
. 1 . 1 1 1 . 1     . . . . . . . 1     . . . . . . . 1
. 1 . 1 1 1 . 1     . 1 . . . . . .     . 1 . . . . . .
. 1 . 1 1 1 . 1     . . . . . . . .     . . . . . . . .

Dynamic Backwardness

A further Pass

Another issue is that some pawns or their stop squares are statically member of their own attack spans, but those spans could not be realized, since their pawns are either backward or rammed (or both). Those pawns (f.i. white pawn c4, and mutually black pawn a4 in the diagram) may determined in a second pass, only considering attack spans of movable pawns.
  • 8/8/1p6/8/p1P1p3/3pP3/1P1P4/8 w - -
    8/8/1p6/8/p1P1p3/3pP3/1P1P4/8 w - -

Stops with negative SEE

A more sophisticated definition of backwardness was given by Vincent Diepeveen [2], even a member of a pawn duo may be backward, if its stop square has a negative SEE score, also considering pieces. Here b7 is considered backward, no matter whether the other friendly pawn is on c7 or c6, since it's stop square b6 has a negative SEE in both cases.
  • 8/1pp5/8/2P5/8/8/8/1R6 w - -
    8/1pp5/8/2P5/8/8/8/1R6 w - -

See also


Publications

  • Hans Kmoch (1959, 1990). Pawn Power in Chess. New York: Dover, 1990. Previous ed.: New York: McKay, 1959. ISBN 0-486-26486-6

Forum Posts


External Links


References

  1. ^ Re: Doubled and Backward Pawn Engine "Definitions" by Sam Hamilton, CCC, September 13, 2009
  2. ^ Re: WHAT is the definition of a backward pawn? by Vincent Diepeveen, CCC, December 24, 2002

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