Jeremy Lennert wrote on Mon, Apr 18, 2011 06:50 AM UTC:
Adding the null move to your King is certainly very helpful in a number of endgames...but so is having virtually any extra piece. For example, I suspect a Wazir added to either the K+R vs. K0 or K+P vs. K0 endgames would easily turn them back into wins (probably even if you crippled it by, say, removing its sideways capture; though I have not worked it out). Based on Betza's theory, a Wazir should be worth around 1.5 Pawns at most (probably less).
And those endgames show the null move at its strongest; averaged over the course of the whole game, is it worth even a quarter that much? A tenth?
On the reverse side, adding a null move to your King is obviously more than enough compensation for having your ENTIRE ARMY saddled with the 'cannot lose a tempo' weakness due to switching. That's regardless of the size of your army, which shows that giving the weakness to multiple pieces can't possibly be linear, but still, on a single piece it has to be worth only a tiny fraction of the null move.
So at a wild guess, we're talking about maybe a one centipawn penalty for the switching weakness, or even less? That's noise.
And those endgames show the null move at its strongest; averaged over the course of the whole game, is it worth even a quarter that much? A tenth?
On the reverse side, adding a null move to your King is obviously more than enough compensation for having your ENTIRE ARMY saddled with the 'cannot lose a tempo' weakness due to switching. That's regardless of the size of your army, which shows that giving the weakness to multiple pieces can't possibly be linear, but still, on a single piece it has to be worth only a tiny fraction of the null move.
So at a wild guess, we're talking about maybe a one centipawn penalty for the switching weakness, or even less? That's noise.