White has 2 rooks and makes random moves. Black only has a king. We’ll ignore the white king for now, but I’m pretty sure it makes things worse for White.
Each rook has 14 possible moves, for a total of 28 rook moves. One of those 28 progresses towards a winning state, one regresses it, and 3 blunder a rook.
The Markov Chain for this converges at a rook blunder being ~435x more likely than a checkmate. If black tries to hunt down the rooks, this gets even worse.
Thus, an impossibly big advantage against Stockfish is still extremely unlikely to convert into a win.
I don’t think the other endgames are massively different—the number of possible moves and blunder-moves are roughly the same, although progression is more likely to be completely lost to a random move.
My question is: does this imply that a double-rook endgame is more likely to checkmate after losing a rook than before?
Turns out, the answer to my question is a clear “no”. The white King has up to 7 moves, and the rook 14. In about half of the positions, the black King is in diagonal contact with the white Rook. This means that 4⁄14 rook moves and all but 2 King moves blunder the rook. In addition, white requires up to 16 moves to get to checkmate. The only positive factor is the slightly lower number of moves (~20 vs ~32), but a much higher proportion of moves for the single rook endgame is a blunder for white, and that more than cancels out any upside.
Consider the relatively simple 2 rooks endgame.
White has 2 rooks and makes random moves. Black only has a king. We’ll ignore the white king for now, but I’m pretty sure it makes things worse for White.
Each rook has 14 possible moves, for a total of 28 rook moves. One of those 28 progresses towards a winning state, one regresses it, and 3 blunder a rook.
The Markov Chain for this converges at a rook blunder being ~435x more likely than a checkmate. If black tries to hunt down the rooks, this gets even worse.
Thus, an impossibly big advantage against Stockfish is still extremely unlikely to convert into a win.
I don’t think the other endgames are massively different—the number of possible moves and blunder-moves are roughly the same, although progression is more likely to be completely lost to a random move.
My question is: does this imply that a double-rook endgame is more likely to checkmate after losing a rook than before?
Turns out, the answer to my question is a clear “no”. The white King has up to 7 moves, and the rook 14. In about half of the positions, the black King is in diagonal contact with the white Rook. This means that 4⁄14 rook moves and all but 2 King moves blunder the rook. In addition, white requires up to 16 moves to get to checkmate. The only positive factor is the slightly lower number of moves (~20 vs ~32), but a much higher proportion of moves for the single rook endgame is a blunder for white, and that more than cancels out any upside.