Kevin Pacey wrote on Tue, Nov 7, 2017 11:09 PM UTC:
For what it's worth, I once tried to estimate how often a K was randomly able to stop a lone pawn, if the enemy king was out of the picture or otherwise preoccupied. A pawn is on rank 4 or 5 in the average case, I suppose, so there's a lot of cases where the king is in the square of the pawn, depending on the files involved. Moreover, a king might more often be in its own half of the board based on previous play from the start position, but I didn't know how to quantify this.
I did this sort of guesswork in trying to estimate how effective my own primitive formula for estimating what the value of a king might be, when it came to computing it for large boards. For a 12x12 board I came up with a very low value for a king/guard, and someone questioned it. All I could say is that a king takes a lot more moves to cross from one side to the opposite, compared to a knight. I could have added that in an average case, a king on a 12x12 board might have an impossible task on average in stopping two isolated passed pawns x files apart. That's when I began to try to estimate how often a king might be in the square of both, and it seemed surprisingly often, though as I wrote above I could only do guesswork.
For what it's worth, I once tried to estimate how often a K was randomly able to stop a lone pawn, if the enemy king was out of the picture or otherwise preoccupied. A pawn is on rank 4 or 5 in the average case, I suppose, so there's a lot of cases where the king is in the square of the pawn, depending on the files involved. Moreover, a king might more often be in its own half of the board based on previous play from the start position, but I didn't know how to quantify this.
I did this sort of guesswork in trying to estimate how effective my own primitive formula for estimating what the value of a king might be, when it came to computing it for large boards. For a 12x12 board I came up with a very low value for a king/guard, and someone questioned it. All I could say is that a king takes a lot more moves to cross from one side to the opposite, compared to a knight. I could have added that in an average case, a king on a 12x12 board might have an impossible task on average in stopping two isolated passed pawns x files apart. That's when I began to try to estimate how often a king might be in the square of both, and it seemed surprisingly often, though as I wrote above I could only do guesswork.