# Is the following position a fortress?

[FEN "8/4k2p/p1b1p1pP/Pp1p2K1/1PpP1P2/2P1R3/8/8 b - - 0 1"]


Houdini6.02 eval flatlines at 1.37, but I reached d= 54 , and , although the eval continued to flatline, the main line indicated White pushed the f4 pawn in f5 toward the end. I started a trial with the pawn already in f5 , Black to move, and White won. Still I am not sure because Houdini 6.02 could have missed a possible defense against the f5 push. Can Black defend against the f5 push without deteriorating the position ( maybe allowing the White rook to penetrate its position)? Or the position is a win for White , albeit slowly? Just for curiosity , if the verdict is draw , can White win in absence of the 50 move rule?

• Is it White to move? If so, looks like it is too late to defend and immediate f5 wins. Oct 15, 2020 at 13:40

The key to tackling these kind of positions in a game is to imagine where you would like to put your pieces and then see how you could achieve that.

In this position for white the first aim would be to get the king to e5 to attack the e6 weakness and at the same time threaten to infiltrate on either f6 or d6. The problem is that black will have no problem defending the e6 weakness and defending the infiltration by keeping the king on e7 meanwhile shuffling the bishop.

Another weakness will be required to make progress. As it happens there is also no way of getting the king to e5 while the f pawn is on f4 so any plan will have to start with sacrificing the f4 pawn.

If it were white to move then the immediate f5 would force open the g file, a second weakness. Black would have to accept the sacrifice and ef would expose the black king to check from the rook so gf is forced. Then there is no way for black to both prevent the rook penetrating on the g file and prevent the king from infiltrating via f6 or d6. One line could go like this:

[fen "8/4k2p/p1b1p1pP/Pp1p2K1/1PpP1P2/2P1R3/8/8 w - - 0 1"]

1. f5 gxf5 2. Kf4 Be8 (2...Kf6 3. Rg3 {and black can't prevent the rook coming to g7 next move}) 3. Rg3 Bg6 4. Ke5 {Black is in zugzwang. Either the white rook is going to penetrate on the g file or the king is going to infiltrate on f6 or d6}


So, black's first task is to stop this simple plan. The only way to do that is with Kf7 which unpins the e pawn and allows the recapture ef. The problem for white with this is that it gets rid of the weak e6 pawn and replaces it with a weak d5 pawn.

The now open e file is nothing like as good as the open g file because of the white pawn on h6. The only way for black to defend an open g file is to block the file with the bishop on g6 but for the open e file all black needs to do is to cover the entry squares of e6, e7, e8 which can be done either by the king on f7 or a combination of the king on f6 and the bishop on c6. The weak d5 pawn can be protected by the bishop on either c6 or b7 and the white king can be prevented from infiltrating via e5 by the black king on f6.

If white could both threaten to infiltrate with the king to e5 and threaten to take the d5 pawn with the rook then a zugzwang could be possible but unfortunately the only way for the rook to threaten the d5 pawn is from e5 and if the rook is on e5 then the white king can't go to e5. Hence this position is a fortress.

This is what the lines would look like:

[fen "8/4k2p/p1b1p1pP/Pp1p2K1/1PpP1P2/2P1R3/8/8 b - - 0 1"]

1...Kf7 2. f5 exf5 3. Re5 Bb7 4. Kf4 (4. Re1 Bc6 5. Re2 Bd7 6. Kf4 Kf6) Bc6 5. Re1 Kf6 6. Re2 Bd7 7. Re5 Bc6


Going back to the initial position is there anything white can do to prepare the f5 push to make it work? Or, to put it another way, what must black do to stop f5 from working. The answer is that black must keep the king on f7, ready to both defend the e file if it opens and to play kf6 if white threatens to play Ke5. At the same time black's bishop must defend the d5 pawn from either c6 or b7 whenever the white rook is on e5 and it must defend the e8 entry square from d7 or c6 whenever the rook is not on e5.

• In your line White can just play 4.Rxg6 and the h-pawn queens Oct 15, 2020 at 17:02
• Again , in the second try at d= 53 White managed to push the f4 pawn in f5. In the follow up both sides promote, but White promotes first and managed to win the Queen endgame. At this point , if a hidden defense actually do exist, it should be found by a much more powerful engine than I have. I suspect this is a White win , albeit slow. Oct 15, 2020 at 17:52
• @Stefano : I think your software plays f4-f5 just before move 50 just to prevent a 50-move draw. Anyway, the key to this position is not engine power and depth, but the possibility to build a constructive plan for WHite to invade. I reckon it's Black's move at the beginning (can you be clear about it in the question?) and then I agree with BrianTowers : it does looks like a fortress. Oct 26, 2023 at 6:50

I tried again with Houdini 6.02 Pro for One hour ( depth 58/97) and again , starting from a criticala point , one quarter of and hour again ( depth 55/92). On the thitd iteration the win was evidentv, although in some defensive lines slightly more than 50 moves were necessari. The questione however was not Is the position above a draw with perfect play under FIDE rules , but Is the position above a fortress , which clearly Is not , since Black position can be broken even with perfect defence.

• With no accompanying analysis this answer qualifies as a comment at best. It is not a worthwhile answer. Oct 26, 2023 at 21:43

Definitely not a draw. Use zugzwang to invade with your king on the dark squares(since the bishop can only guard light squares)All you have to do is use the following sequence.


[FEN "8/4k2p/p1b1p1pP/Pp1p2K1/1PpP1P2/2P1R3/8/8 w - - 0 1"]

1. f5 gxf5 2. Re5 Bd7 3. Re1 Be8 4. Kf4 Bh5 5. Ke5 Bf3 6. Rg1 Bg4 7. Rg3 Kf7 8.
Kd6 Kf6 9. Kc6 e5 10. dxe5+ Kxe5 11. Re3+ Kf6 12. Kxd5 f4 13. Re8 f3 14. Kd4 Kf7
15. Re4 Bh5 16. Rf4+ Ke7 17. Kc5 Kd7 18. Kb6 Kd6 19. Kxa6 Ke5 20. Rf8 Bg4 21.
Rxf3! Bxf3 22. Kxb5 Ke4 23. Kxc4 Ke5 24. Kc5 Ke4 25. c4 Ke5 26. b5 Ke6 27. Kb6
Bd1 28. a6 Bf3 29. a7 Ke5 30. c5 Ba8 31. Kc7 Kd4 32. Kb8 Bh1 33. b6 Kxc5 34. b7
Kd4 35. a8=Q Bf3 36. Kc8 Be2 37. Qa5 Bg4+ 38. Kd8 Kd3 39. b8=Q Ke4 40. Qb7+ Kf4
41. Qxh7 Bd7 42. Qg7 Bb5 43. h7 Ke4 44. h8=Q Kf4 45. Qh4+ Ke3 46. Qgg3+ Ke2 47.
Qxb5+ Kd1 48. Qb1+ Ke2 49. Qhe4+ Kd2 50. Qgd3# 1-0

All you have to do is use the following sequence.


 
• Hello, it doesn't seem that this answer adds anything to @BrianTowers answer above. Also, you assumed that it was White to move (with a trivial win indeed) but I strongly suspect it is actually Black's move judging from OP's diagram with Black at the bottom. I agree that this should be more explicit in the question. Oct 26, 2023 at 6:53