Pawn Majorities
The Four-to-Three Wing

Point Count Chess, NO.184A to NO.184B, p261-262
Kostic v. Gruenfeld, 1922

IMPORTANT: While H&M-S title this example as the "Four-to-Three Wing," it also seems they include instances where the ratio is higher, such as 5-v-4, which is what we see in both No.183 (after 11.c3xd4) No.184A (also after 11.c3xd4), for they say: "But when the wing grows to four-to-three and beyond..."

The "Wing" that H&M-S refer to, seems to be one large Pawn Island, with this Majority consisting of at minimum 4x Pawns. If it stretches to 5x Pawns (with the opposing side limited to 4x Pawns), the bulk of the "Wing" will be in one half of the board -- in both examples (No.183 & No.184A, after 11.c3xd4), White has a 5-v-4 Majority, with the bulk of it residing on the Kingside, and just the d4-Pawn over on the Queenside.

A more accurate title would have been "Four-to-Three (or more) Wing," but that doesn't roll off the tongue as easily. So, just remember that the Pawn Majority will contain four or more Pawns, while the Pawn Minority will be one less than the opposition's Pawn Majority.
Beneath the ChessFlash viewer, you'll find my analysis of the two positions featured in Point Count Chess:
1. PCC, p.261, No.184A, after 12...O-O
2. PCC, p.262, No.184B, after 28...Rc2
3. Result of the Four-to-Three Wing.
4. Summary of the Four-to-Three Wing.
5. PGN

The Four-to-Three Wing
My Analysis

Position #1, My Analysis
PCC, p.261, No.184A, after 12...O-O

After: 1.d4 Nf6 2.c4 g6 3.Nc3 d5 4.cxd5 Nxd5 5.e4 Nxc3 6.bxc3 Bg7 7.Nf3 c5 8.Bb5+ Bd7 9.Bxd7+ Qxd7 10.O-O cxd4 11.cxd4 Nc6 12.Be3 O-O

After: 12...O-O
H&M-S contrast this example (No.184A), with No.183, explaining how a Passed Pawn can often be forced through, with either a 2-v-1 or 3-v-2 Pawn Majority; but, that it's much more difficult to generate the Passed Pawn, with a 4-v-3 Pawn Majority.

In situations where a 4-v-3 Pawn Majority exists, H&M-S say that "Chances abound for the weaker party to bring about a pawn stalemate," and that it is often time-consuming to try and win the game when the weaker side has three Pawns against your four Pawn Majority, "even with the help of the king."

This appears to suggest that, for victory, it's vital to reduce the adverse Pawn ratio to either 2-v-1 or 3-v-2 Pawn Majority, prior to launching the attack with your Pawn Majority.

1. The First Four Exchanges (2x Pawn, 1x Knight, 1x light-Bishop)

At the end of the following four groups of exchanges, Black will have his Offside Pawn Majority, consisting of his a- & b-Pawns, and they'll be up against (what will be) White's Isolated a-Pawn.

White, meanwhile, will have his "Five-to-Four" Wing, not a Four-to-Three Wing, (as H&M-S titled this example), so I'll refer to the following example as either "Five-to-Four Wing" or "5-v-4 Wing," etc.

 Pawn Majorities,The Five-to-Four Wing, After 1.d4 to 3...d5 After 1.d4 to 3...d5, the position is identical to No.183, with White's c4-Pawn poised to be exchanged for Black's d5-Pawn.
 Pawn Majorities,The Five-to-Four Wing, After 4.cxd5 Nxd5 After 4.cxd5 Nxd5, the first of the exchanges is made, led by White's c4-Pawn, which captures Black's d5-Pawn (4.c4xd5). Black's King Knight completes the trade (4...Nf6xd5) and sets itself up to initiate the Knight exchange (against White's Nc3). This also happened in No.183, albeit three moves later.
 Pawn Majorities,The Five-to-Four Wing, After 5.e4 Nxc3 6.bxc3 After 5.e4 Nxc3 6.bxc3, the second of the exchanges is made, as White's e-Pawn advance (5.e3-e4) forces Black to relocate his Nd5 ... Black chooses lead straight into exchanging this Knight, for White's Nc3 (5...Nd5xc3). Just as happened in No.183, White's b-Pawn completes the trade (6.b2xc3) and, in the process leaves White's a-Pawn totally Isolated. This will be the Pawn Minority that will end up facing Black's Offside Pawn Majority (the a- & b-Pawns).
 Pawn Majorities,The Five-to-Four Wing, After 6...Bg7 7.Nf3 After 6...Bg7 7.Nf3, Black's dark-Bishop clears its back rank (6...Bf8-g7), ready for Kingside Castling. White also begins clearing his Kingside back rank, developing first his King Knight (7.Ng1-f3).
 Pawn Majorities,The Five-to-Four Wing, After 7...c5 After 7...c5, Black's c-Pawn gets into position (7...c7-c5), ready to be exchanged onto d4, to give Black the Queenside Pawn Majority (although it won't be the "Offside Pawn Majority", until both Kings have Castled Kingside).
 Pawn Majorities,The Five-to-Four Wing, After 8.Bb5+ Bd7 9.Bxd7+ Qxd7 After 8.Bb5+ Bd7 9.Bxd7+ Qxd7, the third of the exchanges is made, as White provokes the swap of the light-Bishops (8.Bf1-b5+). Black's light-Bishop blocks the attack on its King (8...Bc8-d7), enabling White's light-Bishop to capture (9.Bb5xd7). Black's Queen completes the trade (9...Qd8xd7).
 Pawn Majorities,The Five-to-Four Wing, After 10.O-O cxd4 After 10.O-O cxd4, the fourth of the first four exchanges is entered into, by Black. The Kingside Castling by White (10.O-O) prompts Black to enter into the Pawn exchange, on d4 (10...c5xd4). The completion of this exchange, by White, coincides with White gaining his "Five-to-Four" Wing ...

2. White gains his "Five-to-Four" Wing

 Pawn Majorities,The Five-to-Four Wing, After 11.cxd4 After 11.cxd4, White gains his "Five-to-Four" Wing, following White's completion of the Pawn exchange, onto d4 (11.c3xd4).
A Quick Comparison between No.183 & No.184A

The Differences

Center Pawns; Exchange of Bishops; & Castling
 (QUICK COMPARISON) Differences, No.183, After 11.cxd4 (QUICK COMPARISON) Differences, No.184A, After 11.cxd4

Difference 1. Center Pawns

Difference 2. Exchange of Bishops

Difference 3. Castling

• In No.183, Black has Castled, but White hasn't.

In No.184A, Black hasn't yet Castled, but White has.

The Similarities

Black gains the Offside Majority
 (QUICK COMPARISON) Similarities, No.183, After 15.O-O (QUICK COMPARISON) Similarities, No.184A, After 12...O-O

Similarity 1. Black gains the Offside Pawn Majority

• Black goes on to gain the Offside Pawn Majority, as both Kings Castle on the Kingside (No.183, after 15.O-O; No.184A, after 12...O-O).
White's Center Pawns both Occupy the Center
 (QUICK COMPARISON) Similarities, No.183, After 16.e3-e4 (QUICK COMPARISON) Similarities, No.184A, After 11.c3xd4

Similarity 2. White's 2-v-1 Center Pawns

An Early Conclusion ...

Regarding the different Bishop Exchanges: After comparing the two games, the Bishops stand out as one of the main differences between the two games. However, since White goes on to lose in both games, it would seem that the choice of Bishops isn't the source of White's loss.

3. Black gains the Offside Pawn Majority

 Pawn Majorities,The Five-to-Four Wing, After 11...Nc6 12.Be3 O-O After 11...Nc6 12.Be3 O-O, Black gains the Offside Pawn Majority. First, there are a couple more Minor Piece developments (11...Nb8-c6 12.Bc1-e3), and then Black gains the Offside Pawn Majority, in the process of Castling Kingside (12...O-O).

Now we'll look at the next phase of play, to see White's difficulties, despite him having that large "Five-to-Four Wing" ...

Position #2, My Analysis
PCC, p.262, No.184B, after 19...Rc5

After: 13.Rb1 Na5 14.d5 Rfc8 15.Bd4 Bxd4 16.Qxd4 b6 17.Ne5 Qd6 18.Ng4 Qf4 19.Ne3 Rc5 20.Rbc1 Rac8 21.Rxc5 Rxc5 22.f3 h5 23.g3 Qc7 24.e5 Nc4 25.Nxc4 Rxc4 26.Qe3 Rc3 27.Qd4 Rc4 28.Qe3 Rc2

After: 28...Rc2

4. Mobilization of the Five-to-Four Wing

 Pawn Majorities,The Five-to-Four Wing, After 13.Rb1 Na5 After 13.Rb1 Na5, with the impending advance of White's d4-Pawn, White's Queen Rook is taken off the dark-diagonal, where it would otherwise come under fire from Black's Bg7, and is put onto the first available light-square, on the b-file (13.Ra1-b1). Black's Queen Knight moves across to defend its b-Pawn (13...Nc6-a5), so that Black's Queen can focus on her current task, applying frontal pressure to White's d-Pawn.
 Pawn Majorities,The Five-to-Four Wing, After 14.d5 Rfc8 After 14.d5 Rfc8, the first of White's 5-v-4 Pawn Majority is mobilized, as White's d-Pawn is pushed into an Advanced position (14.d4-d5), onto a light-square, putting it out of the line of fire from Black's Bg7. The other intended safety advantage, so White hopes, is for his d-Pawn to be better protected while in the Advanced Chain formation with White's e4-Pawn (d5,e4).

Black, meanwhile, develops his King Rook to the base of the Open c-file (14...Rf8-c8). Seven moves later, and this Black Rook will be sacrificed to trade White's Queen Rook off the board -- this will improve the odds of Black's Offside Pawn Majority (the a- & b-Pawns) surviving long enough to generate a Passed Pawn.*

* Only, in this game, unlike in examples No.182 & No.183, Black's surviving Queenside Passed Pawn won't be used as a Decoy, but will actually be in touching distance of Promotion -- at which point, White resigns. See 60...b3-b2 » 61...Rh2-h3+.
 Pawn Majorities,The Five-to-Four Wing, After 15.Bd4 Bxd4 16.Qxd4 After 15.Bd4 Bxd4 16.Qxd4, the dark-Bishops are exchanged off the board. White needs to advance his e-Pawn through the dark-square of e5, which would make it a target for Black's dark-Bishop. Therefore, White elects to make the exchange (15.Be3-d4); Black accepts the proffered swap (15...Bg7xd4); and White's Queen completes the trade (16.Qd1xd4).

If White can force Black's King away from the h8-square, White's Queen can win the game with a Back Rank Mate. That this was never realized, reinforces how the weaker side, whether in a Three-to-Four Wing, or a Five-to-Four Wing, such as it is here, is more than capable of overturning the Majority Wing.

 Pawn Majorities,The Five-to-Four Wing, After 17.Ne5 to 19.Ne3 After 17.Ne5 to 19.Ne3, White does try to get his Knight into a more offensive position, possibly up to h6, to bring about the aforementioned Back Rank Mate opportunity, but Black's Queen is on hand, to repel White's, which is chased all the way back to the third rank (17.Nf3-e5 » 18.Ne5-g4 » 19.Ng4-e3).
 Pawn Majorities,The Five-to-Four Wing, After 19...Rc5 to Rxc5 After 19...Rc5 to 21...Rxc5, the first pair of Rooks are exchanged. It would appear the advance of Black's Rook, on the Open File (19...Rc8-c5), and its threat to White's d5-Pawn (if/when White advances his e-Pawn), was too much for White to allow ... White moves his Queen Rook to the Open c-file (20.Rb1-c1) and, after Black forms a Rook Battery on the Open c-file (20...Ra8-c8), White launches into the Rook swap (21.Rc1xc5).

Black's Rook completes the trade (21...Rc8xc5), and once more has a Rook attacking White's d5-Pawn (the nearest Pawn in White's 5-v-4 Majority Wing).

The other benefit to Black is there's one less White Rook to hassle and threaten the existence of his Offside Pawn Majority.

 Pawn Majorities,The Five-to-Four Wing, After 22.f3 h5 23.g3 Qc7 After 22.f3 h5 23.g3 Qc7, there's renewed activity among the 5-v-4 Majority Wing, as White develops his f-Pawn (22.f2-f3), though primarily to reinforce support for the attacked e4-Pawn. The advance of the g-Pawn (23.g2-g3) drives Black's Queen away (23...Qf4-c7).

Black's development of his h-Pawn (22...h7-h5) accomplishes two objectives:

1. It puts an end to White's hope of winning with a Back Rank Mate, as White's Knight can no longer get over to h6, to drive Black's King onto f8, because Black's h5-Pawn now guards the g4-square, which White's Knight would have to pass through.

2. It makes it awkward for White to advance his g- & h-Pawns, beyond their third and fourth ranks, respectively.

It would appear that this sort of restrictive activity is, in part, how the weaker force of Pawns can put up sufficient resistance, and take a lot of effort for the Majority Wing, to triumph over (and that's assuming they 'can' win against such a sizeable, but weaker opposing force of Pawns -- in this game, White ends up losing, despite initially holding the greater force of Pawns: 5-v-4).
 Pawn Majorities,The Five-to-Four Wing, After 24.e5 After 24.e5, White gets in another advance of his 5-v-4 Majority Wing. Having threatened for a while, White finally advances his e-Pawn (24.e4-e5), into an Advanced position, and also into Phalanx formation, alongside the d5-Pawn. White's ambition is to trade Pawns onto e6, with, what I assume is the hope that he'll, at some point, be able to remove Black's blocking e7-Pawn, and escort his then Passed Pawn, the shorter distance up to gain Promotion.
 Pawn Majorities,The Five-to-Four Wing, After 24...Nc4 25.Nxc4 Rxc4 After 24...Nc4 25.Nxc4 Rxc4, Black forces the exchange of Knights, as he brings his own Knight to c4 (24...Na5-c4), threatening to capture White's e5-Pawn, which would then give Black a Four-to-Three Majority Wing on the Kingside. White's Knight captures Black's Knight (25.Ne3xc4), and Black's Rook, supported by his Qc7, completes the trade (25...Rc5xc4); White's Qd4 is helpless, unable to intervene, and now finds herself under attack ...
 Pawn Majorities,The Five-to-Four Wing, After 26.Qe3 to 28...Rc2 After 26.Qe3 to 28...Rc2, White's Queen flees from persistent attacks by Black's Rook, while trying to maintain her support for the two Center Pawns (26.Qd4-e3 » 27.Qe3-d4 » 28.Qd4-e3). Black avoids Stalemate (via Three-time Repetition of Position), and instead puts his Rook on the Seventh Rank (28...Rc4-c2), which H&M-S describe as "murderous."

5. The End of White's "Five-to-Four" Wing

 Pawn Majorities,The Five-to-Four Wing, After 29.e6 After 29.e6, White's e-Pawn advances (29.e5-e6), to provoke the Pawn exchange.
 Pawn Majorities,The Five-to-Four Wing, After 29...Qc5 30.Qxc5 Rxc5 After 29...Qc5 30.Qxc5 Rxc5, Black delays entering into the impending Pawn exchange, by instead provoking an exchange of Queens, to further Simplify the Position. Black's Queen applies an Absolute Pin (29...Qc7-c5), against White's Queen. Combined with the location of Black's Rook on the 7th Rank (Rc2), White's Queen is compelled to capture Black's Queen (30.Qe3xc5), and Black's Rook quite happily leaves the 7th Rank, to complete the trade (30...Rc2xc5).

This exchange has served to enhance the threat of Black's Offside Pawn Majority, and its intention to generate a Passed Pawn on the Queenside.

 Pawn Majorities,The Five-to-Four Wing, After 31.Rd1 After 31.Rd1, with the d-file about to become fully Open, White moves his remaining Rook there (31.Rf1-d1).
 Pawn Majorities,The Five-to-Four Wing, After 31...fxe6 32.dxe6 After 31...fxe6 32.dxe6, White's Five-to-Four Wing is dissolved; it ends as the Pawns are exchanged (31...f7xe6), with White's d-Pawn completing the trade (32.d5xe6), becoming immobilized by Black's e7-Pawn.

The Result of the Four-to-Three Wing...

 (RESULT) Pawn Majorities,The Five-to-Four Wing, After 32.dxe6 After 32.dxe6. NOTE: While White has 4x Pawns on the Kingside, versus Black's total of 3x Pawns, it's not considered a "Four-to-Three Wing," since the e-Pawns are immobilized and so cannot threaten or attack. From what I understand, the "Wing" must consist of Pawns connected on adjacent files, otherwise there's no reason not to include every single Pawn across the board, as being part of the Wing ...

Therefore, White now has the benefit of a "Three-to-Two Wing," which, according to H&M-S, is better for trying to force through a Passed Pawn, which is precisely what White manages to achieve (after 34.f2-f4 » 35...g5 36.fxg5+ Kf6xg5 » 43.Rb5xh5).

 (RESULT) Pawn Majorities,The Five-to-Four Wing, After 43.Rxh5 After 43.Rxh5, both sides have two connected Passed Pawn, on opposite flanks, after White's Rook completes the capture of Black's h-Pawn (43.Rb5xh5).
Question: Whose Passed Pawn will win the race for Promotion?

H&M-S point to a quick way to answer this, and it's to assess which side the Kings are, in relation to the opposing Passed Pawn(s) ...

Black has the better chance, because his Passed Pawns are on the "offside," (they're on the opposite flank to the Kings).

White's Passed Pawns will have to negotiate their way beyond the close proximity of Black's King, which can get across to, at the very least, slow down White's attempt to convert one of them to a Queen, through Promotion.

At first, you may point to White's Rook, that it's in place to chase away Black's King, thus enabling the swifter Promotion of one of the White Passed Pawns.

BUT, if you play through the remainder of the game, you'll see that White's Rook is forced over to deal with Black's own Passed Pawns, which begin closing in FAST on their very own Promotion squares.

And, while Black's Passed Pawns are entertaining White's Rook; Black's King is able to nip in behind the cover of its e7-Pawn, and prevent White's Passed Pawns from gaining Promotion.
 (RESULT) Pawn Majorities,The Five-to-Four Wing, After 61...Rh3+ After 61...Rh3+, White resigns, as he will be forced to move his King out of check, while Black is able to Promote his b2-Pawn to a Queen, for the game-winning advantage. Over on the Kingside, we see White was never able to get either of his two Passed Pawns up to their Promotion squares.

This example proves how time-consuming it is for the owner of the greater force of Pawns (be it 4-v-3, 5-v-4, or greater), to try and succeed against the opposition's numerically weaker force of Pawns.

And, conversely, one should keep in mind that not all is lost, if you're the owner of the smaller force of Pawns, facing an opponent's Majority Wing (again, be it 4-v-3, 5-v-4, or greater).

A caveat: It would appear that the owner of the smaller force of Pawns, if he is to be successful, requires being in possession of the Offside Pawn Majority, and the subsequent ability to generate, from it, a Passed Pawn.

Summary of the Four-to-Three Wing...

1. In this example, White gained the "Five-to-Four" Wing, following the completion of the first series of four exchanges, when White's b-Pawn captured its way up to d5 (6.b2xc3 » 11.c3xd4).

2. White gets the greater force of Pawns, in the "Five-to-Four" Wing; Black gets the Offside Pawn Majority, which occurs when both sides have Castled Kingside (10.O-O » 12...O-O).

3. Both sides seek to Simplify the Position (trade Pieces off the board), to enhance the potential to generate a Passed Pawn, from their core advantage: White's 5-v-4 Majority Wing; Black's Offside Pawn Majority. With the first four trades already done, White's focus is primarily on trading dark-Bishops; Black's focus appears to be on trading all Rooks, the remaining Knights, and the Queens, off the board.

4. During the Simplification process, White begins to mobilize his 5-v-4 Wing. The initial focus is to advance the two Center Pawns up the board (14.d4-d5 » 24.e4-e5), so White can trade Pawns (his e-Pawn, for Black's f-Pawn) onto e6. This will serve to partially break-down Black's Pawn Guard, surrounding their King (Kg8).

5. Black's weaker force of Pawns (part of the "Four" in the Five-to-Four Wing), restrict the mobilization of White's Five-Pawn Wing). Black's deployment of his Kingside Pawns, into Chain formation, with the lead Pawn pushed down to h5, serves to halt the progress of a portion of White's majority force (White's g- & h-Pawns find their advancement is halted, blunting the overall threat posed by the greater force of White Pawns).

6. The "Five-to-Four" Wing is dissolved, as White's e-Pawn and Black's f-Pawn are exchanged on e6 (29.e5-e6 » 31...f7xe6), with White's d-Pawn completing the trade (32.d5xe6). White now has a 3-v-2 "Onside" Pawn Majority (onside, meaning they're on the same side as the two Kings).

7. Both sides generate Passed Pawns, but on opposite flanks. White's Passed Pawns are "Onside"; Black's are "Offside" (they're on the opposite side as the two Kings).

8. Black's "Offside" Passed Pawns have the better chance of Promoting a Pawn, as White's "Onside" Passed Pawns must negotiate Black's King, which won't have to contend with White's Rook, as it will have to leave for the Queenside, to halt the swift march of Black's Passed Pawns, as they close in on their own respective Promotion squares.

9. This example shows how the side with the Four-to-Three Wing (or "Five-to-Four" Wing, as it was in this game), can find it a struggle to break through the numerically weaker force of Pawns. However, it would appear that the side with the fewer Pawns in their portion of the "Wing," requires not only the Offside Pawn Majority, but the ability to safely advance them, to generate a Passed Pawn, which must then have a realistic chance of gaining Promotion.

PGN

[Event "11, Teplitz-Schonau it GER"]
[Site "11, Teplitz-Schonau it GER"]
[Date "1922"]
[EventDate "?"]
[Round "?"]
[Result "0-1"]
[White "Borislav Kostic"]
[Black "Ernst Gruenfeld"]
[ECO "D85"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "122"]

1. d4 Nf6 2. c4 g6 3. Nc3 d5 4. cxd5 Nxd5 5. e4 Nxc3 6. bxc3 Bg7 7. Nf3 c5 8. Bb5+ Bd7 9. Bxd7+ Qxd7 10. O-O cxd4 11. cxd4 Nc6 12. Be3 O-O {PCC p.261 No.184A} 13. Rb1 Na5 14. d5 Rfc8 15. Bd4 Bxd4 16. Qxd4 b6 17. Ne5 Qd6 18. Ng4 Qf4 19. Ne3 Rc5 20. Rbc1 Rac8 21. Rxc5 Rxc5 22. f3 h5 23. g3 Qc7 24. e5 Nc4 25. Nxc4 Rxc4 26. Qe3 Rc3 27. Qd4 Rc4 28. Qe3 Rc2 {PCC p.262 No.184B} 29. e6 Qc5 30. Qxc5 Rxc5 31. Rd1 fxe6 32. dxe6 Ra5 33. Rd2 Kg7 34. f4 Kf6 35. Re2 g5 36. fxg5+ Kxg5 37. Kg2 Kf5 38. Kf3 Ra3+ 39. Kg2 Ra5 40. Kh3 Ra4 41. Rb2 Kxe6 42. Rb5 Rxa2 43. Rxh5 Rb2 44. Rh8 a5 45. Kg4 a4 46. Ra8 Rb4+ 47. Kf3 b5 48. h4 Kf6 49. g4 Rb3+ 50. Ke4 a3 51. Ra6+ Kg7 52. Kf5 b4 53. Ra7 Rf3+ 54. Ke4 Rf2 55. Ke3 Rb2 56. Rxe7+ Kf8 57. Ra7 a2 58. h5 b3 59. h6 Rh2 60. g5 b2 61. Rxa2 Rh3+ 0-1

End.