I'll post my response here since it seems more appropriate. This is basically a repost with some modifications and additions.>

I know I probably won't get a good answer, but why were you not willing to try in good faith on the other page, when doing so would've made it much easier to transfer the discussion here? Refusing and insulting there before even acting like here was the "right" place for the discussion simply <increased> the number of posts over there. If you simply tried even slightly there rather than acting so dismissively and insultingly you'd have been able to maintain a good faith assumption of a willingness to discuss things in an honest, adult fashion. Calling people trolls, kids, and saying they post drivel is obviously not an effective tactic.

Maybe the problem is that what looks like a valid argument to you doesn't to me and basically everyone but you on the previous page. I think you "trying to hide" by saying it's your opinion is pointless, because you clearly have specific conclusions on the value of a knight, the extent of possible Elo ratings and their usefulness, and indeed even the result of a Carlsen-engine or Carlsen-PP knight odds match. In that case there really ought to be something clearly in favor of your conclusion, not merely a hole it can fit into regardless of how much the reverse conclusion has in favor of it.

Anyway, if you fail to quote and/or adequately respond to something I say I take it that it's fair to assume that you're "losing" on that point, as that was your standard for me. Your standards should work both ways, so I'll try to do better to point out when you are apparently "losing". If you think I misunderstood or skipped something you said you can point it out to me, too, but I do recommend you avoid the insults you're prone to giving, as they only undermine you.

<If knight odds is on average worth about 600 points (in some cases maybe 800 in others 400, etc), a human player has absolutely no chance of beating a PP (perfect player). As mentioned before, modern engines already may be 3400-3500+ relative to humans; and they are obviously very far from perfect play. Since PP has to be way higher than engines with 3500 Elo, it follows that 600 Elo odds is definitely not enough to beat a PP.>

Evidence doesn't suggest 600 points (funny that you claimed sometimes 700, sometimes 500, but now it's even wider for no apparent reason), though. And we know that the value of the knight increases as the value of the player holding it increases (it in fact reaches infinity before the player with the knight is perfect, which means that the mode and quite possibly also median value for the knight is infinity, given a standard where all possible opponent values exist in equal proportion (for example simplified by having all possible integer ratings represented)). So the fact that the only plausible conclusion for the 2284 master is not merely 600 points makes it easy to see that it's very probably a quite extreme advantage for Carlsen.

Your estimates of engine strength are also not as solid as you seem to think they are, even if we (generously to you) assume that 3500 is in fact the appropriate number (rather than 3300 or 3100, for example). It was mentioned that engine ratings are calculated using a different formula from the formula used for humans. Engines are also more prone to the horizon effect than human players, because they don't mind entering into long "forced" lines full of only moves (which humans would avoid, knowing that it's unwise to play into a line that doesn't clearly end somewhere; a computer on the other hand will have no idea whether or not there may be more only moves, or, worse, simply no adequate moves, and would not care, either, having no concept of not trusting in its own evaluation ability 100%).

A human would also try to play more solidly, especially given that holding the extra knight simply radiates ever more advantage anyway (it gives constant extra pressure on squares on its own and maintains the plan to trade into victory, which gives constant pressure of its own; this outweighs mini-blunders (<by human and engine standards, to be clear now and in the future>) of handfuls of squares worth 0.2 pawns; they will simply be made up by default so long as Carlsen doesn't lose the clear extra knight advantage). Engines also have no concept of an overall plan for the game, so they'd not understand how to avoid trades. Even if they did understand that trading is tantamount to resigning, the only way to avoid trading against Carlsen (who need not push hard for trades, but merely try to get more and better squares as usual while preventing the same from his opponent; this naturally leads to trading) is to simply cede the board to him, which makes the position ever worse, not better. Carlsen would simply slowly build up his position until he broke through on his terms. The computer would cede any way to steer the position if it went into such a backwards setup.

<To simplify and make things a bit more primitive, lets take a rather conservative estimate for a PP of 4500+ Elo (a difference of 1000 points relative to the best engine seems reasonable). How is a 2900 human supposed to beat an entity which is some 1000+ Elo stronger with knight odds?>

There's no reason to believe that a perfect player would have such a rating (it's simply an assumption you've made until you can prove this somehow, which seems unlikely given that we have no idea how good a perfect player would be; we do however know that every ply deeper one looks into the position is less valuable (on average per move) than the last one; this naturally leads to an asymptotic progression given that perfect play is assumed to not be worth infinite Elo, which also has to be the case if a perfect player can not beat a "near" perfect player a full 100% of the time), especially under knight odds settings where the main factor is simply avoiding losing the material advantage that itself naturally pays constant dividends (I later explain this in more depth). As I said, the knight is simply not plausibly worth so little as you think even for the 2284 master, let alone Carlsen, who can not plausibly not gain considerably more value from the knight than the master did (there is a spectrum from negligible to infinite value for the knight that corresponds to terrible to "near" perfect skill for the knight-holding player; Carlsen is far higher on that skill spectrum than the master and thus should gain an even more extreme advantage from it than the master did).

<An accident? Well since the PP is defined as a perfect player, he does not make mistakes! So how exactly is human able to beat the PP? I don't see any possible way.>

Of course the PP will at least never lose (and I agree would virtually always win)...if this was an equal game. Carlsen has the knight, though. And your assumption regarding a perfect rating is just an assumption until you prove otherwise (which seems impossible given our lack of a perfect player to test the skill of, which is why I've mentioned the much easier avenue of evaluating the position and Carlsen's ability to exploit it). Your value for the knight is also implausibly low.

<Of course, the story changes dramatically when the odds are increased: eg, Queen odds is so overwhelming that the Elo difference now is in favor of the human and even if he is playing the PP, he should still win (apart from any blunders).>

Without any arguments specific to the queen and not the knight I don't see why you magically divine that the queen is overwhelming in Carlsen's hands while the knight is not. As I've repeatedly mentioned, both scenarios give the same plan of trading into a won endgame. The queen simply gives stronger middlegame pressure (the knight still has a great deal of pressure, however, and in either case Carlsen starts the game with seven pieces to his opponent's six, and this by itself is a big factor when it comes to threatening and protecting squares), <slightly> more often won endgames (it's still overwhelmingly trivial to win the great majority of knight and pawns vs. pawns endgames even if you somehow screwed up the middlegame to the point where the enemy's pawns are more advanced than yours; something that isn't a safe assumption for Carlsen anyway, given that simply holding the clear extra knight gives him endless opportunities to make up the positional deficit throughout the middlegame given the combination of pressure from both the knight directly and the fact that trading is tantamount to resigning for the other player), and more margin for error (this is not highly relevant unless Carlsen materially blunders near or over a knight often; simply blundering a single pawn would not change the dynamics of the game very often). In the end you haven't explained why the queen is special and the knight isn't. I personally have stated the the knight is special relative to indeterminate numbers of pawns because of the unique pressure and strategy it gives as a piece. Pawns can not pressure and control the board at Carlsen's whim, unlike pieces, and the strategy of promoting pawns is actually quite non-trivial if pieces are equal between the players. So I don't really have a clear idea on how many pawns Carlsen would need. I suspect that four or more extra pawns has to be rather great for him, but I can't clearly establish that.

<Now, one issue here may be the Elo value of knight odds. Obviously it depends on the opponents, but relative to this discussion, an average of 600 seems reasonable. However, even if one is extremely generous and gives it 1000 Elo, it still doesn't change the conclusion relative to PP, since now the human is not 1000 Elo weaker but 600 Elo than PP with knight odds. Still a huge difference.>

Actually, it depends on the knight-holder most of all. As you've even admitted, knight odds is theoretically won, and we agree that queen odds is not something a PP can overcome against Carlsen. Without any clear reason for the knight being insufficient for Carlsen I have no reason to single it out as insufficient when the queen is not. Also, 1000 Elo is not extremely generous at all. In fact you already <exceed> 1000 Elo for the 2284 master if you value the Rybka that was whitewashed at a mere 2900 Elo. And Carlsen can not plausibly not get even more value out of the knight than the master did. These values for the knight for the mere master are based on 50% odds for the feat that 100% happened in reality. Assuming less is quite biased in your favor, while odds much higher than that are a mere matter of adding hundreds more points to the knight's value for the master. In fact there's no upper limit one can establish for the master (which is why performance ratings for perfect results are tricky), while a lower limit forces an assumption that the master was simply lucky. Using a 50% standard assumes that the master had average luck. This is the least biased assumption possible from this angle of reasoning. Another angle I invited you to explore was that of the nature of the position itself. This is highly relevant if you actually want to establish a clear distinction between knight and queen odds.

<Obviously none of our arguments are 100% conclusive, but the above gives my personal reasoning for my point of view on this matter.>

My problem is that you still make a lot of assumptions, or at least they appear to be assumptions given that you haven't truly supported them. These assumptions also tend to be very pessimistic regarding the value of the knight and Carlsen's ability relative to the information we have, and also pull large numbers in favor of engines or the PP from nowhere I've seen established so far. It just doesn't look like a perspective not tilted against the knight and humans in general.

<the PDP is perhaps 4500-5000+ Elo; though this is a bit artificial but still seems reasonable.>

It does to you, surely, but I can't really consider it a real piece of supporting evidence when the number is completely arbitrary and unsupported. This is why I think discussing the position's specific merits and what kind and strength of blunders are necessary to fail to win is a lot more relevant. It's really not the case that any "inaccuracies" that would "pile up" in normal games would simply do the same in knight odds games. The knight itself vastly alters middlegame pressure and gives a <really easy> plan to win (by Carlsen standards). It's not the case that mini-blunders of handfuls of squares worth 0.2 pawns (as a group) would just build up until the win is no longer there. It was mentioned that Stockfish considers the starting position to be -4.0. This is not a number that just sits there, only becoming less bad for the engine or PP, until it's too low and Carlsen fails to win. Unlike for "many" positions evaluated at 1.0 pawns off from equality, a -4.0 position will more or less continuously get worse over time unless there is a clear fortress constructed (or Carlsen foolishly trades off his last pawn without having mating material; I'm pretty sure he'd avoid that rather well, especially given how for his opponent it doesn't lend itself to overlapping with the fortress plan well in the least). Given that Carlsen knows this and has control of the game by merit of the clear extra knight he will not allow such a fortress to be constructed often at all. In essence, even if he blunders 0.2 pawns worth of squares away multiple times per game it doesn't particularly matter, because the extra knight has the ability to force square gains that will make it up. In engine play this factor effectively comes down to, on average, each move getting progressively more extremely better for black. For example, on move one Carlsen may only "gain" 0.1 pawns according to an engine, but by move 20, when the evaluation is -8.0, he may gain 0.3 pawns per move. It just accelerates that the game becomes more and more clearly terrible for white. So long as Carlsen maintains the clear extra knight by not blundering more than a pawn away, no fortress is constructed by white, and Carlsen abuses his extra knight's pressure in the middlegame to exploit the plan to trade off into a won endgame (which allows for more abuse, as trading is tantamount to losing for white), there is no way to fundamentally avoid the situation that starts well before -4.0 where the position just degrades ever faster, all else being equal. So unless Carlsen makes <large> material blunders often enough to throw the win away outright he'd have to <consistently> make serious positional errors every few moves to make up for the fact that he's gaining advantage in the rest of his moves. This really doesn't seem very plausible given that he's holding all the cards and needs only avoid fortresses and tactics he can't manage while abusing his <large> advantages. If it was an equal game then yes, he'd make "trivial" errors often enough to be screwed very often, because he can't make it up well on other moves. This is not the case when he's up a clear knight from move one. Essentially, the ability to out-boa-constrictor Carlsen ceases to exist when you are simply materially weaker in the first place. In that case it becomes a matter of whether Carlsen fails to use his material strength to constrict you even <somewhat> decently or not. If he does then you lose, no matter your level. The knight's Elo advantage is in the hands of the knight-holder, not the defending player who may only escape loss by the charity of the knight-holder making bad enough moves often enough.

<Each move it chooses the "lease losing" move, and eventually, due to human inaccuracies, its position should improve.>

You don't improve too easily against Carlsen when even the second best move being made <every single move> (to avoid quibbling I'll specify that once Carlsen sees a mate he would surely mate you instead of making suboptimal moves) should be sufficient to beat you. In practice the top five moves would still remain trivial wins to Carlsen. The difference between them is mainly how quickly they win. Carlsen is good enough that he'll often happen to even select the best move, and keeping it in the top five almost every move is a given. Even moves outside of the top five would <still> be wins in many positions; there are often around or over 20 moves per position, and anything that doesn't give away material or allow a fortress to be constructed by white would remain winning.

<But as I said, it's not possible to say <totally winning> since the game starts from the start and not from some tablebase position that a human can play right to the end.>

The problem is that we know that search depth becomes less and less useful as you increase it more and more. Going from 4 to 8 plies is an amazing improvement, and 8 to 12 is also big, but 12 to 16 is not quite as big anymore, etc. Once you get to 20 plies how often is it that the position appears totally winning because you're still up that clear knight, but 30 or 100 plies would prove otherwise? I know that Carlsen would investigate more dangerous and complicated lines to something like 20 or more plies, and if he couldn't be rather sure he'd just avoid them. You can't really stop this well because at these types of depths he simply has too many options, too many options that are <all each winning>, that is. He just needs to avoid the fortress and excessive tactics situations, and avoid serious material blunders. If he does all of these things he will win very often, as his advantage is crushing. In a regular game of course Carlsen is fighting to hold the draw, but it's quite different when you simply always hold all the cards and small mistakes simply delay your victory rather than turning it even into a draw.

<And that is the principle point in which we differ: I think that the PDP will be able to prevent most of the simplifications (since it realizes that those would be beneficial for the human) and play those lines which would keep as many pieces on the board as possible until it is able to at least equalize the position (eg, win material by very complex tactics, gain some lasting positional advantage, etc), so that the human will not be able to reach the clearly winning endgame like K+N+3p vs K+3p.>

Carlsen will avoid playing into such tactics (i.e. he won't pick engine-like moves that are "dumb" in the sense of assuming that he'll play at least as well as his opponent when the resulting position is not clear) and will avoid allowing the PP to construct fortresses. The PP on the other hand can not avoid trading pieces without handing control over the board to Carlsen, which gives Carlsen the ability to reposition his pieces to his liking before opening the position somewhere on Carlsen's terms (while the PP's pieces simply can't reposition themselves to stop this, as the PP's pieces (not pawns) are constricted to effectively just its first two ranks).

<As I said above, PDP's evaluation need not extend all the way to bare kings (when it is minus infinity), PDP is sophisticated enough to evaluate all the possible positions (usually trillion of them) to +1 or so advantage for itself if the human makes inaccuracies, while play the best defensive move if the human plays the best possible move, which, considering the immense complexity of chess, will not be very often (although we can expect the best human to make many perfect moves).>

Well, this (the last part) seems like quite the problematic claim. If Carlsen in fact makes "many" perfect moves then, so long as he is in a winning position (and he would be so long as material is good and there is no fortress and no tactics coming; something he'd not have the greatest problem preventing given that he has control over the game by default, and need only pick a top five (if even that) move to remain winning), those moves by necessity must entail Carlsen making progress towards winning the game sooner. Since it's known that outside of fortresses and tactics which Carlsen can simply not allow, having the dominating position (obviously in an equal one he would simply fail at this) that even 0.2 pawn type "mistakes" will simply be made up for after a handful of good moves (let alone perfect ones) because his material advantage is doubly powerful (middlegame pressure and the trading plan), why would Carlsen fail to win many games in the match? Do you claim outright that Carlsen will simply hang a piece and/or two or more pawns at least near half the time? Remember, he really does have to lose material unless the PP can achieve other things that Carlsen will, from a position of great power, specifically work to disallow. Given that Carlsen has immense freedom because he keeps the win in hand so long as he stays a piece up and avoids both fortresses and tactics that <he can't calculate to be clearly at least still winning for him> (keep in mind that tactics can hardly be infinite in length; there would have to be lots of trading or sacrificing somewhere, which reduces the ability to continue making the situation one where Carlsen must remain in tactics so long he can't calculate any way to escape into a position still defaulting heavily to a win; he's also specifically avoiding heavy tactics from move one and starts and remains in control from move one, so it's not as if he'd just slip into them randomly given that he also has plans the PP <must> avoid to avoid losing; i.e. Carlsen has the initiative by default once he completes development) he should win a given game unless he makes a material blunder of at least two pawns (of course if we're already in an endgame blundering his last pawn away would be good enough in many cases, but since he knows this he merely has to avoid losing that last pawn; not too hard when he has been otherwise dominating materially from move one).

<The thing is that NOT all evaluations lead to minus infinity since a human will inevitably make inaccuracies which, if one looks far enough, will lead to + scores for the PDP.>

Assumption alert! In fact the burden is on you to show that Carlsen, who you claim would play "many" <perfect> moves anyway, would not have enough freedom among his <several> winning move options every move to avoid the specific situations in which he could let the win out of his grasp. And Carlsen has the initiative until he stumbles into <deep, continuous> tactics, blunders enough material, or blunders into allowing a fortress that comes largely down to pawn structure, itself not the hardest thing to keep in mind (he merely needs to ensure that he can trade a couple of pawns and he can then open the PP's backwards pseudo-fortress on his terms). If you can't establish the plausibility of this then the idea that a PP would achieve a + score often enough to win the match is low. If the plausibility is low then you should abandon your assumption.

<While to deal with the <minus infinity> one can cut that infinity asymptotically, and look as many moves as required deeper than the human (yes that sounds like an super advanced computer 100= years into the future, but I thin that's enough). So PDP will always take advantage of those inaccuracies, reply with the "least losing" moves (or even winning moves in case of serious inaccuracies) which eventually, if the human makes enough of inaccuracies, can accumulate to an advantage for PDP.>

I see that Bureaucrat already mentioned most of what's in this paragraph, but: To a PP "inaccuracies" don't <truly> exist. Either you blunder from a win into a draw, a win into a loss, or a draw into a loss. Otherwise you maintain a loss, draw, or win (and Carlsen starts with a winning position). I think I've been assuming that your PP, or PDP as you like to call it now, has been optimizing for human unpleasantness, not true tablebase moves. This is because you <need> Carlsen to blunder the game state into changing somehow, and merely playing the moves that delay your loss (but that would not always be the moves that would most allow Carlsen to be confused) would not maximize your overall statistical result against Carlsen, who is not a tablebase.

The problem is that Carlsen has many winning moves to choose from among practically every move (the main exceptions being recaptures and excessive tactics that Carlsen would work to avoid, and his work is easy given that he has the initiative and middlegame pressure on top of a simple plan to win that is not possible to avoid without ceding control of the board to Carlsen, which also is still a loss, as explained earlier) so long as he maintains his material dominance. If Carlsen in fact doesn't make serious material blunders (even two pawns may not be enough much of the time, but this is a good lower limit if you must somewhere include the lower-odds cases of one pawn being a strong enough blunder occasionally) then he remains in the position of being able to choose from among several good options very often. And you said he'll even play "many" <perfect> moves. If that's really believable then him staying within the bounds of the top five or ten winning move choices that he'd often have to choose from among shouldn't be such a huge problem. And that is a <lot> of times where Carlsen can "randomly" escape both <excessive> tactics and fortresses. Everything Carlsen needs to focus on in general is much easier than usual for him (normally you need to do much harder things in an equal game), and he can do it at his leisure so long as he has the material superiority. All Carlsen has to do in a match is win more than he loses, so he'll have to blunder all the harder to end up with a loss instead of a draw. If he mostly blunders into draws then he must have to do so overwhelmingly often, or his >10% win rate will win him the match.

<<For very strong players, the sum of errors they make in a single game is less than the value of a Knight>

1. Not necessarily so since humans make blunders, whoever they are.

2. Their error rate must surely depend on their opposition; against a monster (any one which we have been discussing) any of top GM's rate must surely increase relative to what it is against other GM's of basically the same strength.>

3. Their <meaningful> error rate also surely depends on the dominance of their position and how many options (i.e. winning move options) such dominance affords them; the more dominance, the easier it is to <force> resulting positions that are both <at least> as dominant as before (wasting say ten moves without changing either the current game result state according to the PP or without blundering (for simplicity) two pawns or more worth of material (or blundering into allowing a fortress which is not possible to force without help; if it was chess would be quite drawish even between players of very different skill levels) is <not> a <real> blunder in any meaningful sense) while being <easier> for the human to both have and make progress on their plan while conversely making it so the opponent's plan is either purely defending due to lacking initiative (therefore no progress can be made in the PP's favor in the near future (~20 plies)), doesn't really exist (i.e. there is nothing in particular to strive for that would fundamentally help anymore), or is easily disrupted by the human.

Regarding (1), this is something I have <always> mentioned and invited you to make real claims about, but you have never established in the least that Carlsen blunders often enough, hard enough to end up not having a positive score in the match outside of other factors you could also (but haven't) disrupted (which I have also openly mentioned and invited you to talk about).

Regarding (2), of course, but you <totally> forgot about (3), which dwarfs and thus consumes (2) almost entirely depending on both the quality of the advantaged player (a knight from move one is worth infinity Elo to a "near" perfect player and worth very little to a "near" perfectly bad player (the "worst" player ever would be a practically minded PP that is constantly trying to get mated and avoid mating (and then avoid drawing) its opponent)) and the ease of the position (it takes less material and/or a less perfect player depending on the type and thus ease of the position).

(3) is crazy important because we're not talking about normal games here, where Carlsen is quite possibly blundering into a loss vs. a PP in the first ten moves. We're talking about games where Carlsen starts out with a crazy amount in his favor, something that affords him a <great> deal of choice per move without worsening his game state from won according to the PP.

<I'll be completely honest with you and say that your idea of the PDP having to choose an <optimal move for its specific human opponent> makes no sense to me at all, and I tried to think about it for a while. Chess is a purely mathematical game, specific tendencies of a given opponent play almost no role whatsoever when we're talking about mathematically precise calculations of a given position. For example, what does it matter to a tablebase whether of the two, say, 2900 players, one is a tactician while another a strategist? It just scans the tablebase in a completely cold and precise matter to arrive at the best moves.>

It makes sense to us because it's what "god" would do if "god" was otherwise not able to read Carlsen's mind. "God" would, according to the absolute best information about the world, humans, and Carlsen in particular, tailor everything specifically to work the best it could possibly be expected to (short of knowing the future/reading Carlsen's mind) against the Carlsen that exists at that moment in time.

You're right that it doesn't play a large role against players that are too weak relative to the ease of their position (which should include Carlsen vs. the PP in a <normal> game), but when it's an uphill battle for the PP and easy to Carlsen it can make a big difference, as Carlsen blundering is the only thing that will save you. Maximizing the chance of that, even if it turned a mate in 80 into a mate in 20, would generally be the best thing when it comes to expected score.

<Now, we know (or at least all of us agree) that the only possible strategy for the human is to exchange as many pieces as possible (again regardless of who this human is), with as little damage as possible. However, as I suggested before, programmers from advanced civilization may be able introduce functions which will be able to make sophisticated comparisons between the tablebase moves and the moves which prevent the exchanges of most pieces.>

No, no. Carlsen has all normal game plans he could have on top of this one, <really easy> plan he normally doesn't get to have for much of the game, let alone for the whole game! And you're still ignoring that you <can't> avoid trading pieces against a good enough player (which should include Carlsen, who fundamentally understands what to do in the won starting position and who even you admit makes "many" <perfect> moves (this when he need only stay in the top five or ten moves in a great number of his moves; he can pick the one that makes the position the easiest to him, regardless of it delaying the mate in PP vs. PP play)) without making real concessions. In the extreme case the PP could avoid trading everything except for pawns by constantly retreating its pieces and thus ceding the ability to place it's pieces (not pawns) on pretty much the entirety of Carlsen's first six ranks. Now, this would be just fine if the position was simply a fortress, but all Carlsen need do here is avoid having two (or often just one) pawns of his own get locked against the PP's pawns. He can then maneuver at his leisure until he gets an easy position after opening up part or all of the board entirely on his terms (because anything the PP could do to stop it would involve either placing pieces where they could be traded and/or allowing enough pawn trades to make a fortress impossible due to the position being open enough, which again makes it impossible to avoid piece trades, as you can only cede so much of the board before your pieces have nowhere to go, especially nowhere favorable!). Anything else presumes that Carlsen will either lose the material advantage significantly enough or that Carlsen will magically not be able to use his 7 vs. 6 piece advantage to gain (and if necessary regain) squares in the middlegame and endgame. If Carlsen indeed allowed the PP to always have non-retreating squares to move all of its pieces away to in order to avoid trades then the 50-move rule could possibly be reached (which still doesn't win the PP the match by itself, mind you), but that is simply implausible in the extreme given the limited number of squares on the chessboard and Carlsen's knowledge of how to play for square advantages without ceding tons of squares to the PP on top of the fact that Carlsen has the initiative by default by way of force after the opening.

Given that your "opinions" and "may happens" on PPs or similar and possible extreme ratings are in fact based on nothing you can establish, all you are really saying is that you don't see how there's a way out, but perhaps there is. Well, I've always agreed that I haven't proved that Carlsen would surely win such a match, but there is no way to prove anything completely if one is particular enough about every last detail and its foundation, as you eventually run into axioms. "Carlsen would lose" is a very poor axiom by my standards, though. As I've stated, I'm operating under a preponderance of reasoning standard. If you can't fundamentally upset Carlsen's advantage and/or Carlsen's plan and there's nothing else to really suggest that the limits of chess in fact <must> be "way out there" or whatever in a sense that <strictly means something> then your possibility is backed up by nothing at all, while the other makes sense in various ways, which makes it seem more likely and thus the conclusion to operate under (which is not a conclusion believed perfectly proven, of course). I kept trying to get you to establish anything wrong with these things or to bring up any sort of <non-vague>, <explicitly suggestive> evidence-conclusion chain, but you haven't. However, you still believe that Carlsen not only may lose, but <probably would lose> such a match. It just doesn't make a lot of sense. Being agnostic about this would be fine, but that's not your position at all.

<Regarding PDP, my opinion (since concerning PDP that's all we can have really) still remains that if it uses a tablebase and its "judgement", it should still win. Chess is 100% mathematical, a tablebase analyzed by PDP should be enough to win.>

You still haven't explained why you believe this probable for the knight but not the queen. It's just intuition, then? You have to understand when the knight actually looks good it is enough for a working conclusion for others. In fact pretty much everyone on both pages didn't consider your conclusion very plausible. Since you don't really ever give a basis in favor of its actual existence rather than its possibility it's a hard thing to find probable for most.

<How it will do it? Well, maybe we better ask it; but perhaps it can choose those lines which pose more difficulty to an average human (avoid exchanges, complicate positions, etc).>

How can you judge when you don't even understand the argument. You're the real lightweight here. If you have any comments on the actual issues, you're welcome to make them and I will refute every one of them. Otherwise, you'll remain just a featherweight ;)>

Typical shach matov: "You disagree so you must not understand, and no, <you> suck!" No possibility whatsoever you're even slightly wrong anywhere, right? You could just ignore it because it's obviously not supporting any arguments (and is thus not a refutation rather than a conclusion of your already having been refuted; the conclusion is not itself a refutation and can thus be ignored, after all).

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<metatron2: But until the machine recognizes such position, it doesn't use its tablebase <at all>, since that has no practical use, and so it uses its evaluation engine mechanism.

In other words, the evaluation engine and the tablebases are two mutually exclusive mechanisms.>

If you mean reach in the sense of evaluating a single position at the end of a line or in the sense of a position on the board that's already in a tablebase, then yes. Otherwise I believe that engines can evaluate various lines simultaneously, some that have enough captures to resolve into tablebase positions, and others that it still has to calculate normally. In those cases it's actually using both parts together in a useful manner. If it sees a tablebase loss in one line would it normally do <anything> else? If so, that of course may (per instance) actually be worse for its chances against a human (or even other engines).

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<Bureaucrat: In a starting position with Knight odds, the win should be a matter of technique for a very strong player. The tablebase computer would say something like "1. e4 (mate in 80)", if 1.e4 happened to be the best opening move for White and 80 moves happened to be the minimum needed to force checkmate. Now, every time the human deviated from the optimal line, mate would be delayed. Blunders or a series of inaccuracies might even turn the position into a draw or loss. Surely, if won by the human the game would last longer than the minimum number of moves, but the threshold for squandering such a crushing advantage is very high. The human's plan would simply be to trade off pieces and simplify the position without making positional concessions.

For very strong players, the sum of errors they make in a single game is less than the value of a Knight. Furthermore, with a winning material advantage from the start, it would be even easier to avoid mistakes, because it is much more difficult for the side with a material disadvantage to put real pressure on the opponent. There is very little the tablebase computer would be able to do about that, because it cannot force the human player to make mistakes.>

First, lets make sure that my argument with ratings was not supposed to be a proof but merely the reasoning behind my point of view on this matter (as I explicitly stated).

Now, the 600 value is certainly not much less then your estimate of 800! Come on! However, I did mention that it is merely an approximation and gave a possible value of 1000 (or more). However, if my estimate of PDP around 4500 Elo is accepted, then even 1200 Elo for a knight odds is not enough to beat a PDP. I think it's very reasonable to assign a 4500+ Elo to PDP since it's only some 1000 points above our best engines operated on best hardwear. Afterall, PDP is defined as the entity which has solved chess completely (plus "divine" judgment ability make it even more powerful than a tabelbase). We know that we're very far away from solving chess, so 1000 Elo over our engines seems very reasonable.

However, even if I make a major concession, say 4000 for PDP and 1000 for a knight, we still have the human behind by 100 points. But I am simply not willing to accept the idea that PDP is only some 500 points stronger than our engines, as explained above. So 4500 seems very reasonable to me.

Wrong, you did not read my reply to Bureaucrat and now want me to repeat it. His (and your) idea of error rate comparison with knight odds is clearly incorrect because quite obviously human vs human rate is much lower than human vs engine. So we can't use human vs human to make a judgement about knight odds against an engine some 500+ points stronger.

First let me say that initially my idea was a match against any human, past or present, not Carlsen in particular.>

This doesn't matter much to me as Carlsen is about as good as anyone's ever been, and regarding playing against engines he's quite possibly the best ever; I recall the matches Kasparov and Kramnik had against computers, and Kasparov didn't really outperform Kramnik there in spite of being the better player (against humans); I attribute this to his tactical style which is not so useful against computers. Carlsen is luckily even better positionally than Kramnik.

<Now, above you're making a mistake since the error rate against Calsen's usual opponents will definitely be much lower than against a monster like one of the best computers today (operated on the best and most powerful hard-wear). So those statistics will not give us any definite answers as far as the match Carlsen vs Computer.>

As I (and Bureaucrat as well) have mentioned, you are making the mistake of ignoring that a normal game and a knight odds game are fundamentally different. In a normal game any ground you give up is just gone forever if your opponent is good enough to keep it. Your conclusion of PP crushing Carlsen thus makes perfect sense if we're talking about normal games. In a knight odds game not only do you get to play with seven pieces against your opponent's six (making attacking and defending single squares and groups of squares much easier), and not only do you get the benefit of trading heavily favoring you (trading is something that happens all the time in chess, something impossible to avoid without making <more> concessions when you're already down the knight), but you also get to roll that pressure into whatever other plans you attempt to accomplish (besides just trading pieces). If you happen to slip up and lose some squares, no problem! Just use your <more powerful army> to force the PP to either cede the squares back or trade with you. Either way is fine, since you can even leave those squares to the PP in most cases if you traded enough, as the relative piece advantage will increase the more you trade! 7:6 is already bad, but 6:5 is worse, 4:3 is ridiculous, and, as we know, 1:0 (really 2:1 in the endgame as the king counts then) is quite easy to win with.

<<With an extra piece one can trade off pieces to get to a probably won endgame, on top of the extra middlegame pressure (and thus an even better endgame) one gets for having an extra piece>

The problem with such a scenario is that you're concentrating exclusively on the possible advantages of the human side while completely ignoring that he is playing against a chess monster, which relative to us virtually makes no tactical mistakes whatsoever!>

Carlsen is a monster in his own right, you know. Enough of a monster to understand <everything> I've outlined <plus> lots more. And, as I've stated, the plans he has to accomplish and prevent in order to hold and convert the win are simply <easy> compared to his struggles in normal games, even many games against players not quite on his level. Unless you can break the reasoning that small positional setbacks simply aren't permanent if your army is stronger and can thus gain the squares back (and then some) there's no need to care how good the PP is. You can't establish anything specific regarding its actual level of play, anyway, so it may as well not be considered particularly heavily.

<1. Trading off pieces is not so primitively easy as you make it look! It certainly may be possible sometimes, but other times the comp may trade off and refute the human idea by very deep tactics, which no human can see; in other words, because of our tactical shortsightedness, the trade may be beneficial to the comp, and sometimes dramatically so, leading to a lost game for us humans, through major loss of material or major positional concessions. And even if it's only a small mistake by the human, many such small mistakes can eventually add up a sizable advantage for the comp or at least an improved position.>

Chess has many pieces that are easy to trade off for each other. 2 queens, 4 rooks, 8 minor pieces (7 for our purposes, though). Minor pieces aren't generally equal but this matters less given that increasing the piece ratio in Carlsen's favor from 7:6 to 4:3 (only heavy pieces and Carlsen's extra knight left) is worth more. In chess you try to put pieces onto good squares, which often means more aggressive squares. Carlsen would understand that he can get rid of advanced or other well-positioned enemy pieces by trading, while the opposite favors him due to the piece ratio going up for him. There just isn't infinite space to retreat to in chess. There aren't infinite useful files for rooks, infinite good diagonals for bishops, infinite outposts for knights, and the queen can in fact be hard to position in some cases because any lesser piece whatsoever that threatens it makes it move. If you add the enemy queen doing the same, lest you increase Carlsen's piece ratio, it's all the harder.

Anyway, an "improved position" isn't as meaningful as you seem to think it is. To Carlsen increasing the piece ratio is an improvement, because he'll play better after that than before. It's not actually one you can do anything about unless <Carlsen> screws up. You assume that he would, but his margin for error is quite wide given that he has so many <winning> move choices. He will pick the moves that make his position easier and/or <more> advantaged to play (in the former case you still have a real problem because he's all the less likely to blunder away the win now...), and slight mistakes along the way don't really matter when he can simply make them up because he can push the position around by virtue of his extra piece...it simply delays winning, but a win is still a win. The PP is effectively also a tablebase in addition to whatever else, so from its perspective Carlsen merely wasted some time without changing the only result that matters for the match, but even that is fine if the position is easier for him to play now...

<2. Middlegame pressure works both ways: again, lets not forget that we're playing against a monster which tactically sees tens of moves deeper than us; any slight miscalculation by the human will inevitably lead to the worsening of his position and the worse endgame.>

Again, this is true in equal games. Carlsen having an extra piece is like a boxer having an extra arm. All the skill in the world isn't going to save you very often against a skilled enough boxer when you have two arms and they have three. All arms are equally functional for the purposes of this comparison. Another comparison is like two people lifting weights. One can lift up to 700 pounds and the other can lift up to 600 pounds. Now, factors such as health, morale, psychology, and even skill at balancing the weight you're lifting come into effect here, but in general you are just going to be outlifted if you're the 600-limit person. You admit that a queen is enough, so unless there's a special reason regarding the knight there's just no reason to be remotely confident regarding the knight not being enough. In fact we know that the knight is pretty amazing even for those much worse than Carlsen. Carlsen would enjoy it all the more.

<<Carlsen would be able to offer many piece exchanges with the computer, and it would accept many of them, not seeing anything better>

Possibly. And possibly it would see better things (how do you know that it would not??) and refuse the exchanges.>

Yes, this is possible...per move. Do you honestly think that in a game that could go 60-80 moves Carlsen will seriously never manage to see a way to trade pieces? If so then Carlsen surely has the better piece placement. If the PP had it then Carlsen would simply threaten to trade with it, and it would lose that position for that piece one way or another. <Carlsen> is the one with lots of choices, all winning, every move that doesn't involved forced things, usually recaptures. The PP really doesn't have a lot of options, and the option of fleeing is rather bad when it comes to having a chance at not losing the game...

<<If the computer is set to refuse to trade pieces then all Carlsen needs to do is to threaten to trade pieces, and it will have to run away and crowd all its pieces in an ever more backwards position as Carlsen takes more and more squares by occupying and threatening them with his pieces>

Again, you have to be very careful not to express such scenarios as though you have already seen a match Carlsen-Computer and now are telling the rest of us about what transpired in that match. Such a match never happened so we can't make such blatantly bold statements about what will happen therein.>

Yes, I know there isn't ultimate proof, but that's really not the point. You've expressed a belief that the knight is <not> enough for Carlsen. There is nothing whatsoever that you've said that makes your working conclusion (i.e. conclusion of most likely scenario) more attractive than mine that the knight is enough. You simply insist that there will always be a way for the PP. But why? Even you admit that the queen is enough, so there is a limit there. Well, just establish <why> the knight is not enough, because it really is very like the queen in all key ways. That it's not as good of an extra piece is besides the point so long as Carlsen doesn't <materially> blunder enough to approach the knight (but not the queen). He still reaps all the benefits of 7 vs. 6 pieces.

<You can't say that <all Carlsen needs to do is to threaten to trade pieces, and it will have to run away and crowd all its pieces in an ever more backwards position> because Calsen will not be playing against a 2500 player or even a 2900 player, but a monster that sees many many moves deeper than any of our best players. We have to remember that at the beginning of the game, the computer still has seven pieces and all the pawns, all this material will not be simply sitting and waiting for the human to force trades or force it into backward positions. The best modern engines have various modes, including aggressive, attacking ones, which will be able to cause major problems for the human, piece up or not. It's not far fetched to assume that the human will find himself in many positions where he will have to defend for long periods of time, and every move will have to be very precise indeed, otherwise the comp will immediately punish it with cold precision, leading to either a won position for the comp or an improved one. Even many small mistakes by the human can eventually add up to a considerable advantage for the computer.>

Again, everything you say makes sense if it was an equal game. It very much is not. The PP can't even attack like a normal player could because Carlsen would just eagerly trade off all the pieces he could. Carlsen has the initiative by default once he's developed his pieces. Everything on the board is simply far easier for Carlsen and far harder for the PP. The PP <relies> on Carlsen <really> blowing it for the PP to get anything but a loss. As stated, minor setbacks don't mean anything because the PP lacks the <force> to effectively hold those extra squares. It will lose them back to Carlsen (and then some) so long as the material is so lopsidedly in Carlsen's favor. <Where is your basis for Carlsen being deeply troubled by an attack of six against seven, much less partial attacks involving fewer pieces?> (Carlsen of course will react to any such attacks, so it's not like he's sitting there and suddenly four pieces blow up his king, which was defended by only one piece. And in the end Carlsen can make it himself with more pieces in the theater if he sees fit, and that is a serious problem for the PP or engine's attack.) Anyway, why would every move have to be precise? Just piling enough pieces in there (by Carlsen's standards; obviously it wouldn't work for me since I'd place them too poorly) would do wonders. Are you imagining that the PP, down a full piece, just decides to sacrifice even more? And Carlsen unwittingly has no response? The initiative and thus ability to force plans on the opponent is Carlsen's once he's developed his pieces. So when is this dangerous attack supposed to occur? In the first ten moves?

<So clearly it's not as one sided as you made it look.>

I dunno, your whole premise is just "but Carlsen's opponent is just too strong". And it's a great one...if it was a normal match. When it's not and you have no real way to establish that the opponent is <enough> stronger as well as no stated way to defuse Carlsen's numerous <extreme> advantages it's just hard for the Chessgames community to see how "obvious" it is that the greater "monster" would win in spite of the knight.

<Another interesting point is that the engine may be set to play in anti-human mode, as mentioned, more aggressively, and constantly looking to complicate the position (perhaps also through avoiding trades when it is not detrimental to itself). We know that our top players are almost completely helpless against the best engines precisely because humans almost always make mistakes against engines. Because of that, I think that by increasing the level of complexity of a position, the computer will have even more advantage against a human.>

Sure, but again, when are these tactics happening, and how? Generally you need to grab the initiative to attack well, no? If you didn't then you're obviously not attacking well enough anyway. Regarding the initiative, you can get it by making smaller positional threats (including trading a knight for a bishop)...that really don't matter as much to Carlsen anymore. Carlsen has a whole extra piece with which to defend, attack, or just control various squares that help offensively and defensively. Where is the actual <pressure> from the PP (much less a "lowly" engine) coming from? Is it developing faster than Carlsen and just going crazy in the first ten moves? Unless that <seriously> works out, and it shouldn't, given Carlsen's ability to survive the first ten moves even with equal material, we're just back to the computer having to trade or sacrifice at least some pieces to squeeze an attack out of nothing. Sacrificing just makes the problem worse. It really still just all comes down to whether Carlsen, up a knight, can manage to blunt an attack that he'll see coming and work to defuse. He's not going to be ambushed very well when he doesn't need to make any suboptimal moves to avoid preparation or draws. Anywhere the computer attacks can be overdefended if Carlsen is trying, and your ideas on "attacks" beyond the scope of Carlsen's search depth when Carlsen is simply trying to play really solidly don't really make a lot of sense given that Carlsen is also the one squeezing "until" the attack starts existing enough for Carlsen to even notice (again, doesn't sounds like much of an attack to me). The more he squeezes, the more impossible attacking him in any relevant fashion becomes. So the attack needs to start during or directly after development to have the best chances.

<Another very important advantage for the engine in a standard match of 15 or so games is the factor of fatigue! We can expect some average length games and some very long games (100+). This will be a major strain on any human being, especially against a engine which relative to us almost never makes any tactical mistakes. Even after one 100+ games (lasting 8+ hours perhaps), the human will be drained completely! And he will have to play another game (perhaps of the same length) tomorrow or the day after tomorrow! Certainly he will start to make many mistakes and blunders, which as we know against an engine are usually deadly. And not to speak just keeping your attention sharp during one 100 long game! Now imagine that the human has to do this for a few weeks or longer. At the end he will have to be taken out on stretchers probably. Since from the start I specified that it will be a match (hopefully at least long enough to make conclusions), the fatigue will be a major factor in such a match.>

Obviously if you add enough fatigue Carlsen loses. It's generally not a major problem for him in normal-length classical matches or tournaments as long or longer, so you'd really have to work with a normal blunder rate for him unless we're just handing the trophy to the engine, no matter how much we have to arbitrarily disadvantage Carlsen to do so. I'm sorry, but I doubt many would consider fatigue under normal conditions to really destroy Carlsen when it's not like he'd default to being under a lot of pressure, given that he's up the knight, initiative, and more. I'd be more concerned about his lack of interest and motivation in the match. And indeed, that could well destroy his chances at least somewhat. However, to be fair it's unreasonable to assume that he was coerced into playing, as that's an abnormal condition for him. So we have to assume that he's fully motivated even if he may personally never really have the motivation to do something like this in real life.

<So we have to look at both sides of the picture before making up our opinion.

Now clearly we can't say anything with 100% certainly until the match actually happens. We can express our opinions, and there is nothing wrong with that>

Like I'm saying, it's a working conclusion. Not an opinion, because those are for subjective things like "ice cream is tasty" or "I love the color green". There is no way to totally prove it, but this the case for things in general. My question has always been why you take the reverse of the position <actually> supported by lots of chess games and chess reasoning? Why the knight but not the queen? Why <must> the PP be enough better to win in spite of the knight? It's just arbitrary. I admit that it could be wrong somehow, but at least I'm taking what appears to make sense as my working conclusion.

<<<Daisuki: Your value for the knight is also implausibly low>

First, lets make sure that my argument with ratings was not supposed to be a proof but merely the reasoning behind my point of view on this matter (as I explicitly stated).>

How can it be reasoning when you think it's much too small? Isn't it just wrong? And thus unable to be behind any point?

<Now, the 600 value is certainly not much less then your estimate of 800! Come on! However, I did mention that it is merely an approximation and gave a possible value of 1000 (or more). However, if my estimate of PDP around 4500 Elo is accepted, then even 1200 Elo for a knight odds is not enough to beat a PDP. I think it's very reasonable to assign a 4500+ Elo to PDP since it's only some 1000 points above our best engines operated on best hardwear. Afterall, PDP is defined as the entity which has solved chess completely (plus "divine" judgment ability make it even more powerful than a tabelbase). We know that we're very far away from solving chess, so 1000 Elo over our engines seems very reasonable.>

800 works if the Rykba is about 2700, or less. I'm very generous, because I wonder why you say things that <still> don't work even when tilted wildly in your favor. Your 4500 Elo is meaningless...based on nothing. So it's just <null> Elo. Even 4500 Elo only requires ~1600 points for the knight in Carlsen's hands...a number that's quite possible. Of course you can demand that 10000 Elo be accepted instead, but it just means nothing because it comes from nowhere.

<However, even if I make a major concession, say 4000 for PDP and 1000 for a knight, we still have the human behind by 100 points. But I am simply not willing to accept the idea that PDP is only some 500 points stronger than our engines, as explained above. So 4500 seems very reasonable to me.>

1000 isn't even a concession if we're talking about Carlsen. Let's say the Rybka was 3200, so the knight was 1300 for the crappy 2284 player. Carlsen, being much better and knowing how to squeeze his huge advantage far better, gets 2000 for it, if you want to make a moderate concession. So he beats a 4000 and even a 4500 Elo fantasy opponent. If you go linearly then the knight is worth 0 for a 1200 player. Except we know that it accelerates as the player quality increases, so perhaps this isn't even a real concession on your part, either. It could be worth well over 2000 Elo, especially if the master was only unlucky in the sense of the match being too short to drive the number up to a more realistic number. Even if the Rybka wasn't quite that good, after all.

<<Daisuki: Both of us seemed to understand this and not in the least see where shach matov fundamentally disrupted it>

Wrong, you did not read my reply to Bureaucrat and now want me to repeat it. His (and your) idea of error rate comparison with knight odds is clearly incorrect because quite obviously human vs human rate is much lower than human vs engine. So we can't use human vs human to make a judgement about knight odds against an engine some 500+ points stronger.

And I must emphasize! You have to be very careful on this thread since the idea of PDP and just a strong engine has been confused here (as I mentioned before), so we have to make sure we're talking about the same opponent vs human!!>

It doesn't matter, really. I've explained how most of these errors truly don't accumulate in any sense other than delaying the win. Carlsen is not a huge blunderer of material, so he's likely to keep his knight advantage.

<<And you're still ignoring that you <can't> avoid trading pieces against a good enough player>

Nope, I explained a few times that when your opponent is much much better than you, that is, 2900 vs PDP, it's not at all a simple matter to force exchanges. I go into much detail regarding this on the WCC page (the latest long posts), but what makes it even more convincing to me is that there I talk about an engine but here a PDP which is many times stronger than an engine. Feel free to reply to that post here.>

You say it isn't simple but you don't explain how. Carlsen isn't a flunky; he knows where good squares for pieces are. If you have yours on good squares he'll try to trade with you. If not then all the better; he could then do whatever he wants. Your ideas on strength come from nowhere in particular, since you lack this player. What we can discuss is what's actually possible, and you still haven't explained why queen, but not knight.