what is the current slope of the curve

[CRoberson]

History has shown that one gets 200 elo for each ply (all else the same)
and an initial rating below 2200. This is a linear progression and many
claimed that it wouldn't continue. It was thought that the slope would
change toward diminishing returns.

Does anybody have data or know of a reference that states what the
curve looks like with a rating above 2200?

[Pradu]

History has shown that one gets 200 elo for each ply (all else the same)
and an initial rating below 2200. This is a linear progression and many
claimed that it wouldn't continue. It was thought that the slope would
change toward diminishing returns.

Does anybody have data or know of a reference that states what the
curve looks like with a rating above 2200?

I guess this depends on how much pruning an engine is doing. If there's more pruning done, the rate of change of ELO with respect to depth will become less.

[hgm]

But in such engines the slope would also be less if you set them to a search depth that would make them play below 2200 ELO. And there is no engine yet that has 2200 ELO at 1 ply, so one can lbring all existing engines in the region.

I think the question is how for one and the same engine the ELO per ply behaves as a function of total depth at maximum depth vs low depth.

[CRoberson]

Reviewing the CCRL date, I see that each doubling of processors is
worth 50 rating points if the single proc version is rated >= 2800.

Lots of good data there. The web pages are very well organized.

[bob]

But in such engines the slope would also be less if you set them to a search depth that would make them play below 2200 ELO. And there is no engine yet that has 2200 ELO at 1 ply, so one can lbring all existing engines in the region.

I think the question is how for one and the same engine the ELO per ply behaves as a function of total depth at maximum depth vs low depth.

All someone needs to do is set this up on ICC and let it run for a few months. Start at depth=1 for 2 weeks and see where the rating stabilizes, then sd=2, 3, ...,

[mjlef]

The "sahpe of the curve" is a lot harder to judge now. Programs using Late Move Reductions, Null Move Reductions and other pruning typically have a branching factor of about 2 versus something like 6 for a traditional program. Of course these reductions mean the length of the tree varies a lot, and so they miss things. Programs are much more selective now. Testing results suggest an extra ply is worth around 50 ELO. A more accurate curve would not use depth at all, but some sort of time units. How much is each doubleing of time worth, for example.