When I say 56.Qf6 is "quiet", I mean it's not as forcing compared to other candidates. My point was that 56.Qf6 is a good candidate to consider, but it's important to calculate far enough to see that the more forcing 56.Rxg7+ is indeed winning or at least the best move. Since it is winning, 56.Qf6 becomes a moot point. If 56.Qf6 or another similar strong move was not there, then 56.Rxg7+ can be played without much consideration since it's a "Do or die!" situation that gives white some hope.

In this case, it's clear that the pawn on g7 has to go. We have the rook right there able to eliminate it, and we have the positional benefit of a queen and bishop that can go to work on the now-exposed and cornered king.

Mackenzie vs Steinitz, 1883 (56.?)

White to play and win.

Material: B for N+2P. The Black Kh7 has 2 legal moves and is vulnerable to 56.Rxg7+, which leads to a forced mate.

Candidates (56.): Rxg7+

56.Rxg7+

(1) Black can accept the sacrifice:

56…Kxg7 57.Qf6+ Kg8 [Kh7 58.Qf7+ Kh8 59.Bf6#]

58.Qe6+

<[My variations were sloppy, because I missed the defense 58…Kg7. According to Toga, 58…Kg7 succumbs to a mate-in-15 after 59.Bf6, but requires b8=Q+ anyway, which I tried to avoid as an unecessary complication.]>

58…Kh8 [Kh7 59.Qf7+ Kh8 60.Bf6#] [Kf8 59.Bh6#]

59.Bf6+ Kh7 60.Qf7+ Kh6 Qg7#

(2) Black can refuse the sacrifice:

56...Kh8 59.Rh7+ Kxh7 [Kg8 Qf7#]

59.Qf7+ Kh8 60.Bf6#

Yes. To ensure the win, White needs a clear plan to stop the Black passers, e.g.,

59.b8=Q Qd4+ eventually [else, Black runs out of checks]

60.Qb3+ Kg7 61.Qb7+ Kg6 62.Qf3

Black cannot make progress, so White eventually wins the Ps, and then the game.

Unfortunately for Steinitz White (to move) mates first starting 56 Rxg7+. The main variation is 56 ...Kxg7 57 Qf6+ Kg8! 58 Qxd8+ Nf8! 59 b8=Q Qe8+ 60 Kh2 Qf1 61 Be7 d1=Q 62 Qxf8+ QXf8 63 Qxf8+ Kh7 64 Qf7+ fololowed by either Kh8 65 Bf6# or Kh6 65 Bg5#.
Variations are 56 Rxg7+ Kxg7 57 Qf6+ Kh7 58 Qf7+ Kh1 59 Bf6#; and 56 Rxg7+ Kh1 57 Rh7+ Kxh7 (or Kg8 58 Qf7#) 58 Qf7+ Kh1 59 Bf6#. Not difficult, but nice. It surprised me that the mate took 9 moves from the diagram: there may be a shorter mate involving 61 Qb3+ instead of 61 Be7. 57 Qf6? allows Rg8 58 b8=Q d1=Q+ 59 Kh2 Qxg2+ and Black is escaping - the penalty for messing around. Time to
check:
====
Much as expected except that Seinitz allowed the faster mate with 57...Kh7. There is an additional variation in my main line: after 56 ...Kxg7 57 Qf6+ Kg8! 58 Qxd8+ Nf8! 59 b8=Q Qe8+ 60 Kh2 Qf1 61 Be7 d1=Q 62 Qxf8+

click for larger view

<56.?>

Target: 1:25;000
Taken: 1:40;031
Bogey: +1s <> +1m

Material: Black up, 3♙

Candidates: <[Rxg7†]>

-ML-
The key move for this Tuesday puzzle is easy enough, the follow ups make it more difficult. White should be able to force a winning mating combination with:

<56.Rxg7†!> Black can either accept or move away. Moving away seems to hold with all the counter threats, but White just continues to sac away:

/A\
<56....Kh8 57.Rh7†!> effectively getting the Black King in the White Queen's grasp:

/AA\
<57....Kg8 58.Qf7‡ 1-0>

/AB\
<57....Kxh7 58.Qf7† Kh8 59.Bf6‡ 1-0> where the Bishop's role is critical. So it is also after the acceptance of the sac.

/B\
<56....Kxg7 57.Qf6†> now the Queen also enters, but Black has a sting in this variation. Moving to h7 results in variation AB. So, Black will move to g8, and seems safe there.

<57....Kg8 58.Qxd8†> although this nets the Rook back, it's the only move that allows White to check to avoid Black's promotion threats. Moving back to the seventh rank will mean the end for Black due to the b7-pawn promoting:

/BA\
<58....Kg7 59.Qd7†> there is a nice variation here:

/BAA\
<59....Kg8 60.b8=Q† Nf8 61.Qxf8†! Kxf8 62.Bh6† Kg8 63.Qg7‡ 1-0> showing that Black is helpless against two Queens.

/BAB\
<59....Ne7 60.Qxe7†> now back to the eight rank is mate in one with the pawn promotion, but:

<60....Kg6 61.Qf6† Kh7 62.Qf7† Kh8 63.b8=Q‡ 1-0> is still simple enough. Black should interpose the Knight on f8 immediately after the Rook capture.

/BB\
<58....Nf8> now this is where some people would get stuck, I guess. However, they should reevaluate this position. Especially the Black counter threats. With the Queen on d8, there isn't really threat from Black. White may play:

<59.b8=Q> and win. The only effective check Black has is:

Looks like it is the only winning line though. Steinitz' defense is weak, playing into the mate with 57....Kh7. I would've tried 57....Kg8. But alas, White played well.

Fellow kibitzers may care to try to win against Crafty, who finds an slightly different defence which also loses.

click for larger view

1: George Henry Mackenzie - Wilhelm Steinitz, match New York 1883

click for larger view

Analysis by Rybka 3 : <21-ply>

<1. (1.55): 17.Rf3> Kg8 18.Qxe6+ Kh8 19.Rh3 Qe8 20.Rd1 Qf7 21.Qxf7 Rxf7 22.Rh5 Kg8 23.Rd5 Re8 24.f5 Nb7 25.g4 Bd8 26.g5 Rff8 27.b4

Analysis by Stockfish 230120 64 BMI2:

1. -+ (-9.97): 54...Rb8 55.Qf6 Qe1+ 56.Kh2 Qxh4+ 57.Qxh4 Nxh4 58.Rd7 d2 59.Bxd2 cxd2 60.Rxd2 Rxb7 61.Rd5 Ng6 62.g3 Kh6 63.Kg2 Kg5 64.Kf2 Kf5 65.Ra5 Ne7 66.Ke2 Ng8 67.Kd3 Nf6 68.Kc3 Rd7 69.Kc2 Rd4 70.Ra7 g6 71.Ra1 Nd5 72.Rh1 e4 73.Rh4 Ke5 74.Rh1 Ke6 75.Rg1 Kf5 76.Kc1

< 56...Kh8 57.Rh7+ Kxh7 58.Qf7+ Kh8 59.Bf6# >