This position didn't occur in my game but could have - I'm white here. My opponent has accidentally entombed their rook, so I'm feeling like I'm cruising to an easy win with essentially a rook against nothing. However, the computer pointed out a potential fortress that would have occurred after a forced series of moves, the last of which is black playing e7-e6 leading to this position:



Is there any way for white to break through and win?

My first thought was sacrificing on g5 with the rook but the White king still can't penetrate to win the remaining e and g pawns.

So that seems to leave b4 as a break - White will be able to place his king much better but I have no idea if it can be winning or not.

Curious position indeed. I think it is actually winning, by combining several different threats.

So the only conceivable plan I think would be the b4 break, but for that you need to bring the King to a3 (to protect a4). If black does nothing, then b4 will just win the rook basically, so he has to react. The only reaction is to play e4, so that after b4 black would have an e5 square for the rook.

So now the question is how to prepare and react for that e4 - I now think both playing f3 and not playing f3 likely wins for white.

If you start with f3 (black is just shuffling with the king and our rook's position does not matter at this point yet) and then continue with Kd3, Kc2, Kb2, Ka3, at some point black plays e4 and forces us to take fxe4. Now the idea of white is simple - bring the king back and play e5 to break it open. And if black plays e5 himself to stop white from playing e5, he has again taken the e5 square from his rook - so we can march with our king all the way back to a3 and push b4.

If you don't start with f3, I think it is likely still winning. You bring the king to the queenside again, black plays e4 at some point. Now we bring the king right back to the center again to attack e4 - black can at some point play e3 (essentially merging with the first line above), or leave the e4 pawn undefended, or try to defend it with f5. If he plays e3, the winning method is e4-->e5. If he leaves the e4 pawn undefended, then the method is Kxe4 and f4. And if he tries to defend it with f5, now the black king is too far and white should be able to gobble up the pawns.

I don't see a way for black. Anyone?

I think you've cracked it. The idea of just walking over to a3 and playing b4 seems so simple but it's kind of unstoppable. Because black has to play e4 before b4 happens, white gets the chance to not open up lines for black's rook.

As soon as black plays e4, the fortress is busto and white wins easily.

White has the advantage which is obvious when you look at the Kings.
White's King is able to roam the board and able to participate in the plan of playing b4 by trekking to a3.
Black's King on the other hand is jailed by White's rook on the back rank and won't be getting out anytime soon.