Conversion to a Pawn Ending

Near the end of a game you want to trade the final piece on your own terms. Here are 4 examples from my recent games where I had the opportunity to trade down to a pawn ending. See what you think of each one, then check your answers at the end!

Trade the queens?

Should white play Qxe5?

Trade the rooks?

Should black play Rxf5?

Trade the bishops?

Should white play Bd3, "forcing" the trade of bishops because otherwise white will capture the pawn on h7?

Trade the knights?

Should white play Nxc3? (This is harder than the others!)

Answers

Trade the queens?

Yes, white should trade queens. Black has blundered in offering the trade in this way. White has the outside passed pawn. I took the trade in the game, and won.

Trade the rooks?

Yes, black should trade rooks. The key in this position is that black has the protected passed pawn on d4 that white can't capture, while white's only threat is the a-pawns which the black king can reach and capture. Black also has the g- and h-pawns against white's h-pawn, though this isn't necessary to win. I took the trade in the game, and won.

Trade the bishops?

Yes, white should trade bishops. White's g- and h-pawns create an outside passed pawn against black's h-pawn. I took the trade in the game, and won.

Trade the knights?

Trading the knights results in a draw with best play.
Black ends up with c- and e-pawns where the c-pawn is one square further advanced than the e-pawn. This means white can't capture the e-pawn. Black however can't force through these pawns without help from the king. For example if black plays c2, white plays Kd2, gobbles that pawn and has time to come back for the e-pawn too.
White needs to quickly convert the a- and b-pawns into a passed pawn and play that pawn to b5 before black gets a chance to capture the d4 pawn. This gives white the same formation as black.
The g- and h-pawns are irrelevant.
I took this trade in the game, knowing it was a draw with best play, but thinking it was all a bit complicated and black might mess it up, and not seeing good options for my knight to make any other move anyway. Black did act a bit confused with 48...Kc7 which allowed me to push my pawns one square further each. But other than that, they played it out correctly for the draw.