Bishop better than Rook?

I reached a position in a live game (10|5 time controls) in which I decided that my bishop was more powerful than the opponent's rook. I ended up winning the game, so I thought to myself "Gee, I sure am smart! I really evaluated the position well." I'd like to know what you all think.

It's clear that, from the position shown, I won the game due to sub-optimal play from my opponent. The question is this: given best play by both sides, was I correct in evaluating the White bishop as being stronger than the Black rook?

great game, great tactic. But usually if it is a standard endgame like this

Very nice! Yes, minor pieces can be superior to rooks in certain positions. I remember I got into a position almost exactly like yours in a tournament playing someone 200 points above me, and managed to draw. But I didn't have the great placement of your pieces or my opponent's unfortunate king position. Thanks for sharing.

I am thinking that the king move was probably to let his corner rook out. At any rate, I agree that the bishop has strong attacking chances while the rooks are getting almost no counterplay.

^ His point was that he could exchange bishop for rook, but he felt that, positionally, it was better not to make the trade and seems to have been correct.

@Sarthe: Earlier in the game I had gone up a minor piece, then my opponent traded off his light-squared bishop for one of my rooks, which led to the material imbalance in the position shown.

in some positions, bishop is better than rook, but the fact remains that you cannot force mate with B+K v K.

Bishop is better than 2 Rooks, I just finished this game...

CrypticC62

In that position, yes, I think you're right to say that the Bishop is stronger than the Rook simply because the it is trapped in the corner and not doing anything. Moreover, Black fixed all his pawns on the dark squares, leaving himself with tons of holes in his defense which your Bishop could exploit. If you had a dark Bishop, then it would have been very weak.

As a random aside, I do have a friend who enjoys attacking early above all else, so he prizes Knights and Bishops over Rooks. It takes a tournament player to appreciate the power of Rooks. Often time, they are of little to no use until the endgame, and even then, all they do is spend time quietly sitting on open files or supporting advancing pawns; they have a strong impact on the game, but it is a very subtle and boring strength.

I think kids hate Bishops in general because it's easier to think in vertical and horizontal lines versus diagonals.

@Rooperi 29...g5# the pawn is strongest of them all (nice finish anyway, though!)

Darn! Even my brilliancies are flawed.

But, as Tartakower said, some part of a mistake is always correct... :)

It's clear that, from the position shown, I won the game due to sub-optimal play from my opponent. The question is this: given best play by both sides, was I correct in evaluating the White bishop as being stronger than the Black rook?

You had a mating attack, so why exchange away a valuable attacker for a defender who's hardly involved? You clearly made the right decision. But in a position that commanding it's all good... even the "mistake" of taking his rook for your bishop leaves you a full piece up with all the play on your side.

I will say this. I think Bf3+?! was a genuine error. He should have responded to Bf3+ with d5 and he's got a fighting chance of regrouping. (Actually, he should have played d5 immediately instead of 1.Kg7 IMO... your bishop instantly goes from killer, to kitten.). You seem to think you'd have been better after d5... well, I don't think it's the pawn-munching laugher you seem to believe it would have been. After d5 what squares does your N have?  If Black gets in Qd7, pinning the N against your Q, you have a problem on your hands I think.

So, instead of the immediate Bf3+ you should have prepared for it with exd6. Then he can't shut your bishop out of the fight.

@rooperi "darn even my brilliancies are flawed" -- Not all that flawed,  Your variation is completely forcing... if you've already calculated a mate, why look for another?

Personally I would have just cashed in and took the rook, because although you certainly have an attack and are winning either way, although things look nice after 3 Nc6 if black had played ...Rdc8 The position seems closed enough where black's king could hold out for a while. Again, both ways should be completely winning, but I think taking the rook was a clearer win.

You would not have such a direct mating attack after taking the rook, but I don't think either continuation could mate that quickly and the win up a full piece would be absolute cake. I would just take a bunch of his pawns, and if he doesn't resign, make 3 queens (or knights).

Dynamically speaking, yes the white bishop is doing more than the rook. However, if this doesn't lead to a quick attack I think it's better to get rid of the rook, a potential defender of his pawns, while the white bishop can't really attack black's pawns, only the king. Still, the mindset you have is a pretty good one: to not always assume a rook must be better than a bishop in every circumstance, it just usually is and indeed in almost all endgames it is a much much better piece. But sometimes the clumsiness of the rook keeps it blocked in for a while, which can make exchange sacrifices make sense in a middlegame, but if an endgame can be reached and the rook gets an open file, absolutely everything changes about that pieces's strength.