Rook Vs Queen endgame -drew a lost game

Congratulations on the half point and the nice stalemate trick! This endgame is very hard for the attacker; even grandmasters have failed to checkmate here. I believe that the defense wasn't completely optimal; the best defense seems to be to keep the rook on the third rank for as long as you can to cut off the enemy king and have your king on the back rank, and when that breaks keep your rook on the second rank. 

The winning idea is to get into the Philidor position with black to move. Note that black is in zugzwang and must move his king away from the rook (note that Kh8 fails to Qf6, pinning the rook and winning it next turn).

If it's white to move, the idea is to make it black to move in the same position using triangulation.

If you have an extra pawn from b to g and are the defender, then the best place to have the pawn is it's starting position. Then you can guarantee a draw, even against a person who knows how to win the queen vs rook endgame (which again is really hard, much harder than the bishop and knight checkmate).

The basic idea is that you want your pawn guarding the rook on the third rank and king guarding the pawn, and shuffle the rook in the 2 squares that the pawn protects. The rook on the third rank cuts off the attacking king from making progress. If you ever get in check, then just move to any square that defends your pawn, in which there will always be one available.

Note that if the pawn is not on the second rank, then there exists enough space from behind the king for the queen to attack and force the king away from the pawn. In that case I believe you need 2 connected pawns to form a fortress, with one guarding another, the more advanced pawn guarding the rook, which  cuts the enemy king off, and the king mostly shuffles in the back of the board but has to be careful to avoid getting put in zugzwang and defend the pawn in case a tempo move of the rook is necessary. Like this:

These situations rarely occur, but when you cover a lot of situations that rarely occur, the probability of getting one such situation no longer is rare.

I believe that you are allowed to study endgames, just not use the tablebase or engine for your particular position, unless it's a well known one. I don't know what would count as breaking the rules or not, but since I'm a diamond member, whenever I get into a endgame in one of my daily games I'm planning to take lessons on that endgame.

Yeah in general if the enemy has only few pieces that could move left (eg the rest are all blocked pawns), then you don't want to put the enemy king in a stalemate position. In a queen vs rook endgame, never put the enemy king in a stalemate position (and try to keep the queen not on the same file/rank as your rook).

If you have an extra pawn from b to g and are the defender, then the best place to have the pawn is it's starting position. Then you can guarantee a draw, even against a person who knows how to win the queen vs rook endgame (which again is really hard, much harder than the bishop and knight checkmate).

The basic idea is that you want your pawn guarding the rook on the third rank and king guarding the pawn, and shuffle the rook in the 2 squares that the pawn protects. The rook on the third rank cuts off the attacking king from making progress. If you ever get in check, then just move to any square that defends your pawn, in which there will always be one available.

Note that if the pawn is not on the second rank, then there exists enough space from behind the king for the queen to attack and force the king away from the pawn. In that case I believe you need 2 connected pawns to form a fortress, with one guarding another, the more advanced pawn guarding the rook, which cuts the enemy king off, and the king mostly shuffles in the back of the board but has to be careful to avoid getting put in zugzwang and defend the pawn in case a tempo move of the rook is necessary. Like this:

These situations rarely occur, but when you cover a lot of situations that rarely occur, the probability of getting one such situation no longer is rare.

I believe that you are allowed to study endgames, just not use the tablebase or engine for your particular position, unless it's a well known one. I don't know what would count as breaking the rules or not, but since I'm a diamond member, whenever I get into a endgame in one of my daily games I'm planning to take lessons on that endgame.

Yeah in general if the enemy has only few pieces that could move left (eg the rest are all blocked pawns), then you don't want to put the enemy king in a stalemate position. In a queen vs rook endgame, never put the enemy king in a stalemate position (and try to keep the queen not on the same file/rank as your rook).