human elite vs. top chess engine (tourny timecontrol): How many moves until engine has a winning adv

Super-GM [~2800] versus top chess engine on modern software [~3500]: live round at basic human tournament tmecontrols (e.g. 45|15 or 60|0), no matter for the computer but point is not correspondent and not blitz; standard chess; no piece- or pawn- odds; no predictable opening played by computer ('no book' goes without saying, since heuristics of that strength wouldn't benefit from confines of limited lines).

Naturally the player that dons White has the first-move advantage and a degree of luck may apply beyond that inasmuch as how 'booked' an opening line that the engine happens to play into the human's reportoire, but of course the engine will win every time ---save for perhaps 1/100 when the human squeezes a draw (maybe better---I haven't done recent research. I pose this here for the follow-up.)

And how much quicker would this be against a human GM [~2600] or IM [~2400?]?

As far as what qualifies a 'winning advantage': the point at which the leading side as played by top engine would secure a win against other side performed by same engine at that point.  Or more 'superlative' winning advantage could be defined in same way but with a human GM vs human GM. or perhaps a quantifiable assessment churned by said engine of a certain positive value (+1.5? +2.5? you tell me)

There are many recorded rounds between human grandmaster and chess-engines (playing for highest score achievable or most draws possible).  It would be simple enough to analyze those rounds.

perhaps with enough encouragement.  ]~}

Well, +2 should be sufficient as the winning advantage.

How precise !?! The little problem is that various engines and even the same engine at different depths will give different fluctuating evaluations.

Boris Spassky, when champion, did beat top computer in less than 20 moves.

What was the effective engine strength back then pre-1980, like 1700 Eli by human ratings? Probably more like 0900.

Agreed. David Levy, only an IM, posted a bet* that there wouldn't be a computer that could beat him in a match by 1978 and he won it comfortably. It would be just over another decade before computers became as strong as that. Naturally, computers pre-1972 were far too weak to bother Spassky.

*  The bet grew to more than £1250 before the match was undertaken. In 1970s terms this was serious beeswax and a fair indication of Levy's willingness to put his money where his mouth was.

And does not allow much margin for error against perfect play by opposition. While I question his assessment of '0.90' being the true evaluation by modern heuristics that is the cusp separating a theoretical guaranteed Draw into a theoretical forced Loss by one side & Win by the other {Can you see what my username references?}, I don't doubt it. He surely analyzes all of his competitive as well as slow practice rounds at depth.

What this would suggest, in align with reality's indication, is that two weak moves or several decent moves--- enough to shift the evaluation from say +0.2 to -0.8 against strongest possible responses--- followed by one more sub-optimal move (which at its surface may seem decent, but is not one of one or two accurate candidate moves that could maintain Draw, thus is by definition a blunder)--- is enough to lose the round.  Of course, that is defining terms of strength by relative candidate moves that the strongest engine would offer, which has not yet mastered the game, but close enough so as never to blunder against a human, rendering the difference moot. Only in terms of a stronger[e.g. 4100] engine (either by extended analysis or superior programming/hardware) might few of the lesser[e.g.3400] engine's 'strong' choice moves be considered sub-optimal 'decent' or secondary 'decent' move as 'weak' or even a positional blunder, even if the tactical weaknesses aren't realized by strategizing humans till five moves down.  

This also ties in with idea of 'equalizing' a disadvantage (such as the half-tempo Black is down from turn1), which in terms of calculating may have to do with number of valid candidate moves available to either side at depth in consideration of attack & defence/counter-attack (more being better, whereas risky lines may offer only one valid response for several moves if the opponent plays correctly punishing weakness without inducing own despite potentially more than flipping this status if the side with initiative makes a blunder not realized for several turns unavoidable).

Similarly, if +.85 to +0.95 is indeed the threshold for a winning advantage (at any stage

of round), then this means that if someone did edge ahead to say +1.05, a winning lead, then that evaluation should only further climb under perfect play until checkmate. If it drops below 1, even 0.97, then the move played by side with advantage that lowered it must have been an error (and likewise the disadvantaged side must have responded well, unless a better Moe that would have reduced the gap closer still to 0.00 based off of advantaged side's blunder. The only caveat I could see to this 'rule' is considering sinplucation toward winning endgame with a pawn-advancement or piece-exchange/capture: suppose the winning side has an evaluation of +3.00" predicated on a "best" move of Nh7 or Kh8 and assuming 'best' responses by other side (as is defaultmode for chess engines, playing as they would against another engine). Instead of doing the engine move, or any of several other legal moves that may raise evaluation to +3.01 or higher, the player opts for NxB to be followed by ..RxN, resulting in -2.76 for opponent (and +2.76 for winning side). Although in a case like that the evaluation may still indicate better (e.g. 3.05), the engine would not nominate that move unless it was measurably The best, I.e. strongest or guarantees mate the fastest--- 'guarantee' being operative, as until it finds a mate-within-nn moves line, the heuristic will continue playing with limitation of the horizon effect.

Today, human grandmasters aren't what they used to be in the past. 

Even so, keeping perspective, they[ GMs from and, even more so definitely *champions of* past decades] in total---, most professionals of this game would agree,--- all things considered comfortably over 1750elo by today's measurable relative performance standards, even without vastly accumulated openingtheory wisdom nor advent of sophisticated digital training tools et so-forth

Number of moves to win (or get a winning advantage) means close to nothing.

It depends on the opening for one thing.

Sure, a top GM would hold a QGD for forty moves or so vs stockfish. With a more tactical/less solid line, could have problems before move 30