Something Hikaru Said

[bob]

We don't know if there is an upper bound. I'm not saying there is or there is not. I am saying we don't know. You seem to somehow have an ability to get some sort of divine communication that provides such a bound.

Obviously there is an upper bound. If with all the explanations that you have now been given you still cannot understand why that is so, then I can't help you any further.

No need for divine communication. Sufficient is a good brain.

Something I suppose you seem to lack. WHAT empirical data suggests that there is an upper bound on this? What specific theoretical proof suggests that there is an upper bound on this? All you have to go on is that computers can win with a pawn handicap, but have great trouble with a knight handicap. TODAY. But the question is not about "today". It is about the future, with no specific time-limit on how far, other than it is bounded by the time where 31 piece EGTBs are available, which I believe is "never" (in a practical sense based on the life of the sun, etc).

Nobody has given any "explanation". Just the nonsensical "a GM can play a knight-odds game perfectly. WHAT is that based on? Anyone taken the first move a GM plays in such a game and searched to the win to prove it was the perfectly best move?

No, you want to hand-wave as though you have any idea what you are talking about. Once again, you don't. And it is painfully obvious, too. As of today, we have NO IDEA what this bound might be. It might be a knight, it might actually be less than a knight. But it might also be that one day a computer wins with a rook or queen handicap. I do not believe a human can play such a complex game perfectly. Yes, for KR vs K. NO for 31 pieces with one knight, rook or queen missing. There is a HUGE potential tree below that starting position, a tree that might approach the size of the original tree using the original starting position. Until someone actually proves something, rather than either guessing, or doing as you are doing and saying "obviously there is an upper bound". Which I happen to agree with. I just don't agree that this bound is a knight, since we have absolutely zero data to support that.

[syzygy]

Something I suppose you seem to lack.

Since my track record shows differently, there might be something wrong with your perception.

What specific theoretical proof suggests that there is an upper bound on this? All you have to go on is that computers can win with a pawn handicap, but have great trouble with a knight handicap. TODAY. But the question is not about "today". It is about the future, with no specific time-limit on how far, other than it is bounded by the time where 31 piece EGTBs are available, which I believe is "never" (in a practical sense based on the life of the sun, etc).

As I have explained about a dozen times now, all that is needed is an advantage for the GM that allows him to play the game "perfectly" at least most of the time (Hikaru did not suggest the human would win 100% of the time). As I have said many times, whether knight odds is already sufficient is still a matter of opinion. I expect it to be enough.

You keep saying "a GM can't play perfectly from the start position, so he can't play perfectly with knight odds" (and even "a GM can't play perfectly", thereby covering KRK). That argument is simply wrong and misguided on all levels, but you will stick to it anyway, so this discussion is a waste of my time.

[bob]

Something I suppose you seem to lack.

Since my track record shows differently, there might be something wrong with your perception.

What specific theoretical proof suggests that there is an upper bound on this? All you have to go on is that computers can win with a pawn handicap, but have great trouble with a knight handicap. TODAY. But the question is not about "today". It is about the future, with no specific time-limit on how far, other than it is bounded by the time where 31 piece EGTBs are available, which I believe is "never" (in a practical sense based on the life of the sun, etc).

As I have explained about a dozen times now, all that is needed is an advantage for the GM that allows him to play the game "perfectly" at least most of the time (Hikaru did not suggest the human would win 100% of the time). As I have said many times, whether knight odds is already sufficient is still a matter of opinion. I expect it to be enough.

You keep saying "a GM can't play perfectly from the start position, so he can't play perfectly with knight odds" (and even "a GM can't play perfectly", thereby covering KRK). That argument is simply wrong and misguided on all levels, but you will stick to it anyway, so this discussion is a waste of my time.

Nice proof. "As aI have explained, all that is needed..." REALLY convincing. My argument does NOT cover KRK. It covers ONLY starting with a 1 piece handicap, 31 other pieces left on the board. In the case of the knight, if he trades perfectly, at best he can draw, since using your rather ridiculous analysis, KNK is a dead draw. And that assumes he makes NO mistake between the first move and the last. I don't buy it. You are offering no evidence rather than "I think". Which is very thin evidence indeed.

This discussion was a waste of time the minute you joined in. I've not even seen "the GM here" (larry) claim that a knight odds will stand for all time, just that it is clearly too much TODAY.

[syzygy]

In the case of the knight, if he trades perfectly, at best he can draw, since using your rather ridiculous analysis, KNK is a dead draw.

So you still have not grasped the rather simple argument. Or pretend not to.

If you want to look intelligent, at least show that you understand the other side's point. Then explain, if you don't agree with it, where the argument fails. Do not misrepresent the other side's position.

But what can we expect after all these years.

[bob]

In the case of the knight, if he trades perfectly, at best he can draw, since using your rather ridiculous analysis, KNK is a dead draw.

So you still have not grasped the rather simple argument. Or pretend not to.

If you want to look intelligent, at least show that you understand the other side's point. Then explain, if you don't agree with it, where the argument fails. Do not misrepresent the other side's position.

But what can we expect after all these years.

Already done. Multiple times. And I get exactly what I expect from you. Vacuous arguments. Is there a class in that in law school? I have asked quite clearly and distinctly, "cite ANY evidence that suggests that a knight is the max upper bound and a handicap that large is enough to guarantee a GM win no matter how strong programs get in the future." There is simply ZERO data to support that. There is a mathematical curve that suggests it is false. 50 years ago a GM could give a queen advantage. Today a computer can give a pawn advantage. The slope of that line is quite distinct, and positive.

Feel free to give some actual evidence to support such a claim. AGAIN, not even Larry claims that, except that for programs/hardware today a knight is too much. Barely.

[Uri Blass]

In the case of the knight, if he trades perfectly, at best he can draw, since using your rather ridiculous analysis, KNK is a dead draw.

So you still have not grasped the rather simple argument. Or pretend not to.

If you want to look intelligent, at least show that you understand the other side's point. Then explain, if you don't agree with it, where the argument fails. Do not misrepresent the other side's position.

But what can we expect after all these years.

Already done. Multiple times. And I get exactly what I expect from you. Vacuous arguments. Is there a class in that in law school? I have asked quite clearly and distinctly, "cite ANY evidence that suggests that a knight is the max upper bound and a handicap that large is enough to guarantee a GM win no matter how strong programs get in the future." There is simply ZERO data to support that. There is a mathematical curve that suggests it is false. 50 years ago a GM could give a queen advantage. Today a computer can give a pawn advantage. The slope of that line is quite distinct, and positive.

Feel free to give some actual evidence to support such a claim. AGAIN, not even Larry claims that, except that for programs/hardware today a knight is too much. Barely.

I do not agree that there is a mathematical curve that suggests that programs will be able to win against GM's without a knight.

All the matches with pawn handicap were faster time control than 120/40 so we even did not see that computers today can win against GM's with pawn handicap.
Maybe Komodo can do it but I have no proof for it.

[Laskos]

There is a mathematical curve that suggests it is false. 50 years ago a GM could give a queen advantage. Today a computer can give a pawn advantage. The slope of that line is quite distinct, and positive.

Well, if going with such speculations, I have stronger and more mathematical speculations that Knight odds is pretty much the limit, and very probably above the limit of the handicap to a good GM a perfect engine can give (32 men tablebases).

[bnemias]

I should know better than to jump into this... but I'm curious.

Doesn't an ELO difference of X indicate a particular chance of loss or draw regardless of the actual numbers? And if so, where is the breakdown of just comparing ELO for this handicap?

a) perhaps my understanding is off
b) perhaps ELO doesn't apply to handicap games, just regular chess
c) perhaps we lack ELO alignment between computers and humans

[syzygy]

Doesn't an ELO difference of X indicate a particular chance of loss or draw regardless of the actual numbers? And if so, where is the breakdown of just comparing ELO for this handicap?

At least one correct answer is

b) perhaps ELO doesn't apply to handicap games, just regular chess

The trivial example is KRK: no amount of Elo advantage is going to let black draw this, UNLESS white is not able to play it perfectly.

With only knight odds it is obviously considerably more difficult (compared to KRK) to not make a mistake that loses half a point or a full point, but it might well be within the abilities of a top GM to play it out perfectly most of the time. And once the GM can do that, no amount of Elo advantage (in normal chess) is going to help the computer draw the game.

So as already pointed out by quite a few others in this thread, knight odds is primarily a test of the side with the material advantage.

And why might the GM be able to avoid half point / full point mistakes when playing with knight odds? Because having that extra knight means he can use it to continuously improve his position without taking risks (i.e. allowing complications). And because Nakamura might just know what he is talking about. But even if knight odds would turn out to be insufficient, it is clear that queen odds is more than sufficient. So there is definitely an upper bound.

[hgm]

WHAT empirical data suggests that there is an upper bound on this? What specific theoretical proof suggests that there is an upper bound on this?

The mathematical proof is this:

With maximum odds (1 Queen, 2 Rooks, 2 Bishops, 2 Knights and 8 Pawns) the handicapped side just has a bare King against a full FIDE army. No way the handicapped side is going to score any points even when he defends perfectly even against a patzer, or in fact a novice, when the latter has had 10 min of instruction explaining him what stalemate is, and how you can checkmate with two Rooks. (He wouldn't even have to bother learning how Queens, Bishops or Knights move.)

So at maximum odds even perfect play is of no use against a patzer.
No computer, present or future, will be able to play better then perfect.
GMs will not perform worse than patzers.
=> At maximum odds, no computer will ever be able to beat a GM.

At zero odds GMs already lose badly to computers.

So the set of odds where any future computer will not be able to overcome the odds against a GM is non-empty, and the complement of that set also is non-empty.
In addition, the possible odds form a finite set.
=> the set of odds that can be overcome by a stronger player has an element in it where the odds is larger than any other odds in it, but still smaller than maximum odds.

Q.E.D.