How could it be less?syzygy wrote: ↑Sat Oct 26, 2019 11:01 pmBut they don't take into account the 50-move rule. Whenever they show a mate in more than 50 moves, you can't really be sure about the number of moves it would take under the 50-move rule (it could be more, it could be less).Dann Corbit wrote: ↑Thu Oct 24, 2019 10:22 pmI think to do this accurately, you must have the complete Lomonosov files.
They have distance to mate.
If the winning side can force mate in N moves under the 50 move rule, there must exist a proof tree demonstrating that win.
In this proof tree all terminal nodes are at most N moves away from the root and have a score that is "mate" for the winning side.
A (correct) draw claim by the 50 move rule would correspond to a terminal node with a none-mate score, so there can be no draw claims in the proof tree.
In a game without the 50 move rule, the proof tree is a valid game tree since it does not contain any draw claims by the 50 move rule.
In a game without the 50 move rule, this game tree contains all valid moves for the losing side in all positions, since in the game without the 50 move rule, the set of legal moves is always the same or one less than the set of legal moves in the game with the 50 move rule (depending on if the "claim draw" move is valid or not in the game with the 50 move rule).
Therefore the game tree is a proof tree also for the game without the 50 move rule and since all terminal moves are at most N moves away from the root, this proves that it is possible to force mate in at most N moves.
A shorter but maybe less formal proof goes like this:
Assume there is a forced mate in N moves under the 50 move rule. If you remove the 50 move rule, two things happen:
1. The losing side loses the ability to claim a draw in some positions. Taking away options for the losing side cannot give him the ability to defend better. (compare relaxation in mathematical optimization)
2. The winning side loses the ability to claim a draw in some positions, but claiming a draw never wins the game, so losing the ability to claim a draw does not hurt the winning side.