I don't have a problem. You present two alternatives. I just point out that one of the alternatives seems very bad. What remains is trying the null move at any depth, in nodes where you would do null move at high depth.Sven Schüle wrote:which solves your problem.
Agreed. The null move would be just another move.There is at least one downside but that one already decides the battle: trying the null move at d=1 can simply be proven to be wasted effort if at least one null move search fails low (and that will definitely happen). At a d=1 node all moves (subtrees) are searched with d=0 = QS (ignoring extensions here) until we get a cutoff. If you start by searching the null move with d=0 and you get a cutoff then the effort (in terms of tree size) is about the same as if you had searched one regular move to d=0 until getting a cutoff.
Of course you can save nodes. If you search 19 real moves that fail low before you find the cut move, under conditions where the null move would have failed high, doing the null move would have been 20 times faster.But if the null move fails low then searching the null move simply adds nodes to the whole tree without any benefit. So you never save nodes this way but in general you search more nodes.
As mentioned above, the null move at d=1 is just like any other move. So your reasoning here would actually apply to any move. "Can you play Nf3 in the node? Better not search it, because if it fails low once, the nodes of its search just add to the total you burn up to find the cut move. Better not search any moves at all, at d=1!".
In reality you want to try the moves that have the best chance to provide a cutoff first, if they take equal effort. The point I argue is that the null move has a better chance to fail high than most non-captures. Because a large fraction of the non-captures actually do something stupid that the null move can never do. To find a cut move amongst the non-captures you would have to search many.
Note that playing a capture often complicates things: you create a new tactical exchange on top of the existing ones. (It would probably be useful to distinguish 'simplifying captures' from 'complicating captures' here.) In alpha-beta you don't want to start with the best move, but with the simplest sufficient move.
[/quote]Why would anyone do this? Trying the null move with a reduction of zero is useless, that is known for decades already.[/quote]