Defended Pawns (Bitboards)

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Each pawn, member of the own pawn attack set is obviously defended by a pawn, thus likely not a winning capture target for opponent pieces (except pawns). If a defended pawn is open, opponent rooks on half-open files bang one's head against a brick wall.

Working in the bitboard centric world to determine pawn related pattern set-wise.

Defended

Again, it is advantageous to keep disjoint east-west attack sets for a unique 1:1 source-target relationship. On demand we can use the union or intersection on the fly. Note that attack direction is related to the target square. East attack is from south/north-west to north/south-east

white pawns         defended            defended
                    from west ->        from east <-
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . 1 . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . 1 .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

U64 wPawnDefendedFromWest(U64 wpawns) {
   return wpawns & wPawnEastAttacks(wpawns);
}

U64 wPawnDefendedFromEast(U64 wpawns) {
   return wpawns & wPawnWestAttacks(wpawns);
}

Defenders

To get the set of defenders on the fly, we use the intersection of white pawns with it's "black" attacks:

white pawns         defenders           defenders
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . . .
. . 1 . . . . 1     . . 1 . . . . .     . . . . . . . 1
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

U64 wPawnDefendersFromWest(U64 wpawns) {
   return wpawns & bPawnWestAttacks(wpawns);
}

U64 wPawnDefendersFromEast(U64 wpawns) {
   return wpawns & bPawnEastAttacks(wpawns);
}

Otherwise, if the set of defenders was already determined (or vice versa), we can already take advantage of the unique target/source relation ship:

wPawnDefendersFromWest = wPawnDefendedFromWest >> 9;
wPawnDefendersFromEast = wPawnDefendedFromEast >> 7;

Defended Defenders

Defended defenders already are the inner pawns of a at least triple-chain, the d5 pawn for instance:

white pawns         defended            defended
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . 1 . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . 1 .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

white pawns         defenders           defenders
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . . .
. . 1 . . . . 1     . . 1 . . . . .     . . . . . . . 1
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

                    defenders and       defenders and
white pawns         defended            defended
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . . .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

Not Defended Defenders

Not defended defenders are the base of a chain - target of opponent attacks:

                    not defended        not defended
white pawns         defenders           defenders
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . . . . . .     . . . . . . . .
. . 1 . . . . 1     . . 1 . . . . .     . . . . . . . 1
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

Not Defending Defended

Defended pawns not defending other pawns are likely the peak of a chain.

                    not defending       not defending
white pawns         defended            defended
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . 1 . . .     . . . . . . . .
. . . 1 . . 1 .     . . . . . . . .     . . . . . . 1 .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

Forum Posts

• pattern coding in bitboards by Pawel Koziol, CCC, February 26, 2015 » Pawn Chain

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