Digression: Second Thoughts: Random Ain't Chess

All these numbers, and probabilities, and lots of decimal places.

They all depend on the idea that if you scatter the pieces randomly around the board, there is a certain probability that a Rook will be able to make a long-distance move of seven squares.

The probability is low, because half of the time there simply isn't such a move to be found; for example when the Rook is on e2, it can't move seven squares because the board isn't big enough.

The probability is low, because most of the time the Rook can't move that far without running into some other piece, and the orther piece blocks its path.

So how come so many games end with Re1-e8 mate?

It's because random ain't Chess.

It's because Rooks start the game on the first rank, so naturally they have a long move "on the board" until the game has lasted long enough for them to have moved more than once.

It's because the chessplayer is smart enough to move the Rook to a place where the Rook can run and run and never bump into anything.

The other side of the argument is that you had to spend a tempo to get the Rook on the right file, and if the Rook hadn't needed to be moved there, you would have had some other use for it; that is, you improved the position of the Rook but could have used that move to improve the position of some other piece; and the "random" values tell us a lot about how often you have to improve each piece before it becomes strong.

In addition, the argument against random would have us believe that making long Rook moves must be much more common in real games than the random values show.

So, over a period of 17 moves, with 4 Rooks on the board most of the time, there might be 60 "opportunities" to move a Rook, that is, there might be 13 moves where White has two Rooks, that's 26 opportunities, plus 15 moves where Black had two Rooks, that's 30 more, plus 4 more where White had one Rook, and so on.

Our "random" says that there should be 3 legal Rook moves of maximum length available to be made.

In Morphy-Brunswick, there was only one such legal move in the whole game, the move was played, it was mate, and we remember it; 17.Rd1-d8 mate.

However, random says that there should have been 3 legal long-Rook moves but there was only one, the one we remember.

Okay, okay, I'm exaggerating to make a point. This is one small sample of actual positions, and because it was early in the game, the board was too crowded for long moves; so of course the Rook performed worse than random.

Even so, it was a game that featured a long Rook move, and despite the fact that we remember the move, it was in all the game the only time that it was legal to move a Rook that far.

Perhaps the random numbers are not such a bad guide after all.

It would be quite a task to go over all the positions of all the games in a huge database and count up what percentage of the time it was able to move 7 squares, and what percentage 6 squares, and so on; and I doubt that the results would be very meaningful.

Perhaps if a piece has a big difference between its average crowded-board mobility and its best-position empty-board mobility, it means that the piece profits more than most from being used well.

Bishops have a higher ratio than Rooks have a higher ratio than Knights which are higher than Kings (commoners)....

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