Chessy
Queen vs Bishop
Queen versus a lone bishop is a win for the side with the queen, and a more straightforward one than queen versus knight — a bishop is tied to one color of square for its entire life, which limits how well it can shield its own king.
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Qe8+ Kf4 Ke2 Bd4 Qa4 Ke5
Bring the king up, then get to work
As with most queen endings, start by improving your king toward the center or toward the action, as in this position's Qe8+ followed by centralizing the king with Ke2. A queen alone can win material or force mate, but having your king nearby speeds everything up and removes any need to calculate precisely.
Exploit the bishop's color-bound weakness
Because the bishop only ever controls squares of one color, the queen can often maneuver to threaten the king and the bishop at once by picking a square of the other color relative to the bishop, where the bishop simply has no way to interfere. Chasing the defending king toward the edge of the board while keeping an eye on the bishop's diagonal usually wins the bishop outright within a handful of moves.
Mating the lone king
Once the bishop is gone (or has been reduced to uselessness by being driven from its king), it's a standard king-and-queen-vs-king mate: box the lone king in with the queen a knight's-move away to avoid stalemate, herd it to the edge or a corner, and bring your own king up to deliver the final mate.
Frequently asked questions
Is queen vs bishop always a win?
Yes, with no other pawns on the board, the side with the queen wins with correct technique. The bishop's inability to cover both colors makes this an easier conversion than queen vs knight.
How do you win the bishop with just a queen?
Maneuver the queen to threaten the king and the bishop at the same time, choosing squares of the color the bishop can't control — the bishop frequently has no way to both defend the king and stay safe.
What's the danger to watch for in this ending?
The usual stalemate risk of any king-and-queen mate — keep the lone king with at least one legal move until your own king is close enough to help deliver the final blow.
Is this ending easier than queen vs knight?
Generally yes. The bishop's fixed color makes it easier to trap or win than a knight, which can hop to squares the queen doesn't immediately cover.