Newsgroups: rec.games.chess
Subject: Re: pawn promotion
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Date: 20 Nov 92 12:22:46 EST
Organization: Harvard Math Department

In article <19413@ucdavis.ucdavis.edu>
lim@toadflax.cs.ucdavis.edu (Lloyd Lim) writes:
>There are situations where you might want to promote to a knight.
>Are there any reasons why you'd promote to a bishop or rook?
>The obvious answer is no, but I wanted to check to make sure.

The correct answer is yes, to avoid (or, much more rarely, to induce)
stalemate.  Time for a repost of my Liburkin article from 25 Oct 1991:

jpk2581 [Joe], in article <1991Oct24.143601.1@tesla.njit.edu>:
>Everybody has seen positions where the correct
>move is to promote a pawn to a queen, and it's
>also pretty common to need to promote to a knight, 
>but can you come up with two positions, in the 
>first the ONLY winning move being to promote to
>a rook and the second the ONLY winning move being
>to promote to a bishop. The rook problem is easy
>and the bishop problem is moderately difficult.

The key in both cases is stalemate --- the only circumstance
where one might prefer to have less power (B or R as opposed to Q).
This can be either to get the underpromoter stalemated (by bottling
up or pinning the promoted piece) or, more commonly, to avoid giving
stalemate.

For Rook promotions the canonical example is the justly famous
Saavedra position, which concludes thus: White King on c2 and pawn
on c7; Black King on a1 and Rook on d4.  White to move must avoid
promoting a Queen because then Rc4+! forces 2.Qxc4 stalemate!  Further-
more, 1.Kc3 Rd1! 2.Kc2 Rd4 and 1.Kb3 Rd3+ 2.Kc2 Rd4! only repeat the
position.  But the miraculous 1.c8=R!! works: Black no longer has
the stalemate resource, and despite the material equality soon
succumbs to White's threats: 1...Ra4 (against 2.Ra8 mate) 2.Kb3!
and if Black saves his Rook White mates with 3.Rc1.

An example of a Bishop promotion is: White King d3, Knight c1, pawn c7;
Black King a1, Rook b8.  White to move must capture on b8 and promote,
but either Queen or Rook will produce stalemate, and a second Knight
will not suffice to mate.  So 1.cxb8=B!! and the Bishop and Knight
barely prevail against Black's lone King.

And now the punchline: remarkably, both the Rook and the Bishop
promotions above arise in the analysis of the same position!  
This is Liburkin's classic 1931 endgame: White Kd1, Na2, pawns b5,c6;
Black Ka1, Rc5.  White (to win) plays 1.Nc1! and now if Rxb5 2.c7 Black
cannot stop the pawn with Rc5? (3.Nb3+) nor Rb8?! (3.Nb3+! again,
breaking the stalemate --- White does not need to underpromote yet).
So, 2...Rd5+ anticipating 3.Ke1 Re5+ and Re8, or 3.Kc2 Rc5+, but
instead 3.Nd3! Rxd3+ 4.Kc2! and Black must try Rd4! producing
the Saavedra position, which White wins with 5.c8=R!!  Alternatively
after 1.Nc1 Black could try the immediate Rd5+ 2.Kc2 (Ke1? R:b5
and Re5+) Rc5+ and now 3.Kd2? permits the new stalemate resource
Rxb5 4.c7 Rb2+ 5.Kd1 Rc2!! drawing, so 3.Kd3! follows, and after
Rxb5 4.c7 Rb8! (Rd5+ 5.Ke4 Rc5 6.Nb3+) White no longer has 5.Nb3+?
(Rxb3 is check!) but still wins with 5.cxb8=B!!

Bonus question: find a credible *middlegame* position showing
a beneficial Knight promotion --- *without check*.

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Department of Mathematics, Harvard University
Newsgroups: rec.games.chess