Houdini3 has a rating of about 3300 or so. Most of us can probably agree that Carlsen+3200Engine would be significantly better than Houdini3, while Carlsen+2000Engine would be inferior to Houdini3. A little thought shows that there must be an intermediate strength between 2000 and 3200 where Carlsen+Engine is about equal to Houdini3.
What do people guess the strength of that engine would be? And what strength of an engine do you think is needed for Carlsen to be significantly better?
I think the break-even point is probably roughly intermediate between 2000 and 3200 myself, as a tactical beast with mediocre positional understanding would complement the human perfectly but wouldn't actually be that successful against the best human players (e.g., GMs) alone.
A very interesting question. But wouldn't a 2000 computer be pretty weak? I mean, Carlsen's tactics are probably superior to an engine of that strength. Maybe Magnus could do quite well with a 2700-2800 machine, to blunder-check.
For Magnus to be better, maybe 3000.
Magnus' positional chess is about as good as it gets ~ 3000 elo probably, but his tactics are probably a bit lower, id say add a 2900 houdini/rybka with magnus would easily draw/beat houdini 3.
Yeah, an engine of strength 2000 would be almost no help to Carlsen. The point is that there is some strength between engine-2000 and engine-3200 where Carlsen+engine matches Houdini3, and some higher point where Carlsen+engine is better.
I think it's an interesting idea because it gives a quantifiable answer to the question of how much a human's superior strategic knowledge is worth. There will probably come a point though that the engine's strategic knowledge surpasses that of the best human chess players, and at that point, it will not be true that human+engine can beat engine. Until then, the decreasing gap between the strongest engine's rating and the rating of the minimum engine that would allow Carlsen (or human #1) to be equal (or better, if you prefer that measure) gives a way of tracking the progress of the engines and how strong they are positionally and strategically.
Computer strategic knowledge will never surpass human's... because computer strategic knowledge will always be zero.
Now it's strategic performance may become higher. It just has to be able to calculate farther than our foresight aids us... e.g. to the end of the game.
On topic, it's an interesting question. I have no idea.
I should have said "positional knowledge" rather than "strategic knowledge". And I would definitely argue that computers do have positional knowledge. The evaluation function that a computer uses to decide how to value each node in the tree of moves it examines includes material considerations as well as positional considerations. When they compare thousands of quiet positions, with little or no tactics, positional knowledge is all they have to distinguish between the positions.
I think you're right though that computers don't yet have any strategic knowledge. Positional knowledge for sure (else their evaluation function would be worthless in quiet positions rather than just hugely inferior to the evaluation function that (e.g.) Carlsen uses), but they don't use strategy at all.