Endgame Explorations 7 (ACJ Extra)

Endgame Explorations 7: Underpromotion (Part 2)

Noam Elkies

Knight promotions, which we've seen in the previous column, occur with some regularity in actual play. An obligatory rook promotion is already out of the ordinary. But rarest of all is the forced bishop promotion, which has occurred only a handful of times in all of tournament practice. The most recent example known is the following endgame. [Thanks to Ron Birnbaum of Chestnut Hill, MA, for locating the reference.]

(diagram)

Play continued:

1 ... g2! 2 Rxd3
2 Kh2 d2! snares the rook -- a useful tactic. Now the expected 2 ... g1/Q? would run into 3 Rd7+ Ke8 4 Rd8+! with perpetual check or stalemate. Black cannot wriggle out with 3 ... Kg8 4 Rd8+ Kh7 (5 Rd7+? Qg7!) because 5 Rh8+! draws all the same, and 2 ... g1/R 3 Rxe3 or 2 ... g1/N+ 3 Kh2 get Black nowhere, so...
2 ... g1/B!!
And Black won after
3 Rd7+ Ke8 4 Rh7 Nd5
With this knight on its ideal square the new bishop can't be stopped from gobbling white's weak pawns.
5 Rh8+
Hastens the end, but the immediate 5 Kg3 Be3 6 Rxh5 Bxf4+ wouldn't take long either.
5 ... Kf7 6 Kg3 Be3 7 Rxh5 Bxf4+ 8 Kf3 Kg7!
Oops! Now the rook is trapped.
9 Kf2 Bh6 0-1

Now it's not hard to construct a position where a bishop promotion is required either offensively to avoid stalemate (as in Chan-Depasquale above) or defensively to force it, as in this 1909 study by K. Traxler and F. Dedrle (#1204 in Sutherland and Lommer's 1234 Modern End-Game Studies):

(diagram)

Together with the advanced pawn at g7, White's two pieces would ordinarily balance the Black queen, but here they are both threatened and White's rook is loose too in such lines as 1 Kh7 fxg6 2 Rh1+ Kb2 3 g8/Q Re7+ 4 Kh6 Qf4+ 5 Kxg6 Qg3+ 6 Kf6 Qxg8 7 Kxe7 Qg7+ 8 Ke8 Qe5+ and 9 ... Qd5+. Hence the drawing combination:

1 Ra2+! Kxa2 2 Bxf7+ Qxf7
And now the startling...
3 g8/B!!
... forces 3 ... Rxf8, stalemate!

Multiple promotions are naturally much more challenging. Here's a modern setting in which the theme of Diagram 2 is multiplied, White having to promote two bishops to extract a draw:

(diagram)

This study earned Y. Afek a Commendation in the 1981 Guanabara Jubilee Tourney. The natural stalemate try 1 c8/Q?! Rxc8 2 dxc8/Q Rxc8 3 Rb6+ fails to 3 ... Kc4!, but contains the germ of the solution:

1 Rb6+! Kxb6!
Forced here since after 1 ... Kc4?? 2 Rxb8 Black even loses; but with the White rook now gone the stalemate tries 2 c8/Q or 2 d8/Q fail to 2 ... B(x)c7! Thus:
2 d8/B!! Ba7!
White has his way after 2 ... Bxc7 or 2 ... Rxd8 3 cxd8/Q+ Rxd8, with stalemate in either case, as well as the tricky 2 ... Kb5!? 3 c8/Q Rxd8 (or B-any) 4 Qa6+!. Now 3 c8/Q+? Rxd8 wins, so of course White continues
3 c8/B+!!
Again!
3 ... Kb5 4 Ba6+! Kxa6
And despite all of Black's squirming, it's stalemate after all!

We turn back to offensive underpromotions in the next example, showing all three underpromotions by the same pawn in three variations:

(diagram)

This is Herbstmann's second-prize study in Tyovaen Skakki (1934). A similar position, with six more pieces but showing all four promotions (the Allumwandlung task-- German for "omnipromotion") by the same pawn, was published by Lommer a year earlier. The key is

1 Bh7+!
Not 1 Rg1+? Bg6! =. But now 1 ... Kxh7 loses to 2 exf8/N+! Kg7 3 Nxd7 (not 3 Rxd7? Kxf8 4 h6 Kg8 5 h7+ Kh8! =). Black has the stalemate tries 1 ... Kh8(g7)!? (hoping for 2 exf8/Q+? Kxh7!, when White must either give stalemate with 3 Rxd7, allow perpetual check, or else drop the rook), but they fail respectively to 2 exf8/R(B)+! K-any 3 Rxd7, winning.

And finally a comical orgy of knight promotions by Korolkov (1937):

(diagram)

Black threatens to win with his own knighting: 1 ... c1/N+! 2 Kc1 Ndb3# or 2 ... Bd4#. Thus White must start checking.

1 Nf4+ Kh6
Here and subsequently, 1 ... Kg5(h4)? allows 2 d8/Q+; that's why White did not check on f6.
2 g8/N+ Kh7 3 Ngf6+ Kh6
Not 3 ... Kh8 4 Nxg6#!
4 Nxg4+ Kh7 5 Nef6+
Now the eighth rank is off limits.
5 ... Kg7 6 Ne6+ Kf7 7 d8/N+! Ke7 8 c8/N#!
A "model mate" (each of the king's escape squares is guarded just once) administered by five knights!

This concludes our exposition of underpromotions; the next column will feature more slapstick along the lines of Diagram 5.

Noam Elkies is now Professor of Mathematics at Harvard University and is the author of "Chess Art in the Computer Age," published in ACJ 2 (1993). This article originally appeared in Chess Horizons.

Next column: White Minimals.