Doomed Fortress

Sigh. No London Chess Classic videos today. The last 10 days had an extra motivation to get up and watch video coverage of chess on the internet with the St. Louis Chess Club coverage of the London Chess Classic round robin among the world's elite chess players. That all ended yesterday with Wesley So winning the tournament and the tour. The stories of the tournament were So's solid play (+3-0=6) taking advantage of the chances that 2800-rated players give you. Nakamura's up-and-down performance (+3-2=4) and Topalov's down-and-down performance (+1-6=2). Even though the Najdorf is too deep for me, it was fun to see the theoretical battles in Caruana-Nakamura, Nakamura-Vachier-Lagrave, Anand-Vachier-Lagrave, and Anand-Giri.

One topic that was prominent in the middle of the tournament was the concept of endgame fortresses. Anand had apparently saved some incredible draws in previous tournaments. One of the games that Topalov lost was with Nakamura. On the time control move 40, with about 1 minute left, Nakamura blundered away a winning position with Black to play:

White is under massive pressure with Black's heavy pieces on his second rank. However, White's rook and bishop are barely holding the castle doors. White needs one more man to turn the tide and it turns out that 40...e4! is just what he's looking for with a -3.4 evaluation. Instead, Nakamura chose to get initiative on the h2 weakness with 40...Qh6? Now Topalov had his whole second time control to find the defense 41.Rb4! The nasty, nasty point of it is not just to gain useful moves such as Rb4-e4, but if Black somehow gets greedy with 41...Qxh2?? 42.Rh4! Qxg3 43.Rg4+ turns the tables.

Instead, Topalov played 41.Kg2?? and this time Nakamura did not fail to find 41...e4!. Topalov recognized the danger to his position and only now moved his wayward rook 42.Rb3 Qe6 43.Re3 exf3+.

Topalov continued 44.Kxf3 Qh3 45.Rd1 Qh5+Nakamura used the open lines to win the h- and g-pawns and drove Topalov's king to d3 whereupon Topalov resigned. GM Alejandro Ramirez, analyzing the above position with the help of engines, implied that a fortress might have been available to Topalov. Topalov has to purposely lose his bishop with 44.Rxf3 Rxe2+ 45.Rxe2 Qxe2 46.Rf2:

Black's pawns on h2 and g3 should provide some shelter against Black's shattered h- and f-pawns. Since there are too many men for tablebases, I cannot say with certainty whether this is truly unwinnable by Black, but it has some potential.

Wikipedia has an article on chess fortresses. The weaker side has a material deficit which should be losing, but because of the way the pieces are situated, the stronger side has no decisive breakthrough. Wikipedia cites bishop plus wrong rook pawn against lone king in the corner as a fortress position. I wonder if the basic drawing positions of KPvK fall under a loose definition of fortress. I am more intrigued by chess fortresses that actually have walls. My most fundamental example would be, with White to move:

Again, my favorite online resource with positions under 7 pieces is the Shredder Endgame Database. Indeed, you can set up your own experiments and see that even with Black's rook in the least active spot and with White on move, this position is a draw with best play. Black will aim to put his rook on f6 to keep the White King away from g7 and then from behind the wall, with enough shuffling space between g8, h8, and h7, Black's king can taunt the enemy at the gates forever (or at least for 50 moves).

Back to Topalov-Nakamura, I tried to defend the above position against Fritz 8 and couldn't fend him off. Black has four resources that are difficult for White to avoid:

• If Black can win the rook and g-pawn for the queen, he should win. I was able to do this against Fritz simply by putting my Queen on e5, the pawn on f5, and bringing my king up to g5. White left his rook on f4 and let me trade.
• Black can advance his h-pawn to h4 and with the threat of h3, the shattered pawns provide little shelter for the king
• To hinder h5-h4, I tried h2-h4, trying to lock the pawns into a wall. This time Black broke through by placing his king at e6, keeping the white king at g2, and straight trading queen for rook on f4 and racing the king to a winning spot on d4
• The queen can be quite annoying. If Kg2, then Q occupying the a8-h1 diagonal presents a problem. If White walks into a pin with Rf3, the only way to unpin is Kf2 and rook moves. Black can then play Qh1 getting into White's weak h-pawn.

So probably Topalov's fortress after 44.Rxf3 would have been doomed. However, in the absence of a refutation, I think 41.Rb4 would have held. A fascinating exercise is to use the Shredder Database to try shifting the rook-and-pawn fortress closer to or further from the corner and seeing if the game is still drawn with best play. Usually the fortress falls if the queen can get into the back side of the fortress and drive the king out into the open, so too much space is bad for fortresses. But if the king doesn't have enough space to shuffle back and forth, the fortress can also fall. Goldilocks wants a fortress that is not too cozy and not too drafty, but just right.

As I understand history, fortresses protected the stationary farmers from being driven off their productive land by invaders, but once those invaders started using cannons, fortresses became obsolete.