hgm wrote:But move 7-10 were nearly free.
So my calculation was indeed not entirely correct: cutting on move 11 would need a full-depth search on 1-6 and 11, and reduced searches on 7-11. That is 7 times full depth and 5 times reduced, or 7.5 total (under the stated assumption). On average (1+7.5)/2 = 4.25 rather than 3.75.
Still smaller than 6, though.
Probably too late for me, rather than your writing something unclear, but I don't see the issue here.
if you fail high only on move 6, you are going to average searching 6 moves normally, no issues. If you sometimes fail high on 11, that's a full-search also. So are you assuming that the program always fails high on move 6, never anything less? That seems like a poor assumption. From my numbers, at least 90% of the time the fail high happens on move 1 if it happens at all, so we are only talking about that remaining 10% of the time.
Basic assumptions.
(1) you have to search move 1 with no fail high. then you continue searching until you do get a fail high, whether it is at 6 or 11 is only relevant to efficiency.
(2) if you have to get to 11, and assuming you don't reduce the first 6 and do reduce the second 6, there is little difference between 7 through 11 and just going directly to 11 since the first 5 would be reduced. But 11 still hurts since it will be a full search.
(3) The additional danger is that you fail to fail high on move 11 because it was reduced and you couldn't see the tactics needed to flag it as better...