Crippled Majority Wing:
Part of the Advanced Beginner's Chess Guide (Section 1)

Crippled Majority Wing
Point Count Chess: [-]

The "Majority Wing" refers to one army having a greater number of Pawns on either of the Flanks (a,b,c on the Queenside; f,g,h on the Kingside), but excluding the central, King & Queen Pawns (files d & e, respectively). This could be, say, a 4-v-3, 4-v-2, 3-v-1 inequality. In Diagram 1, below, Black has a 3-v-2 Queenside Majority Wing, while White enjoys a 2-v-1 Kingside Majority Wing,

Crippled Majority Wing, Image 1, Advanced Beginners Chess Guide
Diagram 1: Black's Queenside Majority Wing;
White's Kingside Majority Wing.
In stark contrast, a Crippled Majority Wing is one where an army has more Pawns on one of the Flanks, but those Pawns contain some sort of crippling weakness, such as Doubled Pawns or Isolated Pawns, which prevents the Majority Wing from forcing a Passed Pawn against the Minority Wing facing it.

Diagram 2, below, shows Black's 3 Queenside Pawns v. White's 2 is the Majority Wing, but the "Crippled" weakness also applies to Black's Pawns, due to the Doubled Pawn formation of the b4 & b5 Pawns.
Crippled Majority Wing, Image 2, Advanced Beginners Chess Guide
Diagram 2: Black's Crippled Majority Wing.
If it is Black's turn, either 1. ... a3 2. b3, or 1. ... b3 2. a3 means Black cannot force a passed pawn, even though he has a majority, and so it is "Crippled".

Another example is shown in Diagram 3, below, where White's 2 Queenside Pawns v. Black's 1 is the Majority Wing (though, on the Kingside, Black has the Majority Wing, albeit NOT Crippled). As for White's Queenside Pawns, they're "Crippled" because they're BOTH Isolated, with Black's solitary Pawn able to attack either, then leave the remainder to be got by the Black King. So, neither White Queenside Pawns can advance, even though they're both "Passed Pawns", without being captured, which is paraphrasing the reason they're the "Crippled Majority Wing".
Crippled Majority Wing, Image 3, Advanced Beginners Chess Guide
Diagram 3: White's Crippled Majority Wing.
Black must keep his King about where it is, and it would indeed be a Crippled Pawn Wing. White's King needs to get to the b-file.

If White is to have any chance in this position (Diagram 3, above), he will need to move his c-pawn to be taken by Black's pawn (not King), while keeping his King on the b- to d-files (turning this into an Outside Passed Pawn situation, as above).

If he moves the a-pawn, to be taken by the b-pawn (not King), then White should try to push the c-pawn for Promotion, as it is easier to Queen a c-pawn than an a-pawn (Black's King can get in front of the a pawn, and it would be a draw). This might be a good option if it weren't for Black's 4-v-3 Majority on the Kingside. Because of that, the Outside Passed Pawn strategy is definitely better, I feel, for White. Black needs to be careful moving his 4-v-3 Majority, as the King cannot assist.

Further Reading

Point Count Chess (Horowitz & Mott-Smith, 1960)
  • The Crippled Majority, (p252)

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Studying the Pawns (Weak Pawns)
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