There was no misunderstanding on my part here. I just said that such "big table base" would tell the PDP that it lost in all variations, so according to that, its best choice would be just to resign, wouldn't it?

And if not to resign, then how would it choose the best choice from its huge table-base, when all its options lead to losing the game? Here comes in <practical choices>, which are not in the scope of our PDP, hence I think that the best engine that is optimized for best practical choices vs humans, can do better than such PDP.

<So how exactly will a 2900 human be able to beat an entity which is some 2000 Elo stronger? Knight odds on average may be worth about 1000 Elo, so the PDP will still be another 1000Elo stronger (including knight odds)>

My point was that at some level, the Elo difference is irrelevant when one side has a totally winning position, since it would just be easy enough for him to defuse any chance from the other side.

Take for example K+N+3p vs K+3p when the pawns and kings are on the same side, without anything special for either side. In such a case an 1800 player should easily beat a machine rated 5000 elo despite being rated some 3200 points below it, even though the human can't foresee all the variations, and there is still theoretical room for blunders for that 1800 player. That player simply knows the principles good enough, and his practical capabilities are also good enough to convert such advantage.

So the 1000 elo points for knight odds doesn't hold in case of simplified lost positions.

My claim is that Carlsen is proficient enough to simplify starting position with knight odds, when playing against any type of opposition. The same way the 1800 player is proficient enough to simplify a (much) simpler position with knight odds vs any kind of opposition.

Certainly not, it "wants" to win, so it plays those lines which are beneficial for it.

<And if not to resign, then how would it choose the best choice from its huge table-base, when all its options lead to losing the game?>

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

<My point was that at some level, the Elo difference is irrelevant when one side has a totally winning position>

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 whole game is ahead and the human will have to contend against an entity which always makes the best possible moves (in the practical sense as well).

<Take for example K+N+3p vs K+3p>

But once again, we were not talking about an endgame (tablebase) position which every GM can play right to the winning end; but instead, we were talking about a game starting from beginning, with all the pieces (apart from one knight) still on the board. Considering the immense complexity of chess, this scenario is very different from the relatively simple K+N+3p vs K+3p.

<So the 1000 elo points for knight odds doesn't hold in case of simplified lost positions>

Of course.

<My claim is that Carlsen is proficient enough to simplify starting position with knight odds, when playing against any type of opposition>

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.

<I agree that it is only an opinion until proven otherwise>

Yes we agree there; and I also admit that I also express only my opinion, I can't prove it. But I believe that the complexity of chess is so immense that we haven't even scratched the surface yet. My opinion is that the best human will not be able to force all the exchanges which are beneficial for it since it's opponent (with all of it's superiority in tactics and strategy) will oppose it and will try to allow only those exchanges which are beneficial for it (tactically or in long term strategy which is not easy for humans to see).

<If Carlsen played 10 games match against the current strongest engine>

--

I will clarify some of my points despite the above:

<shach: Each move it [the PDP] chooses the "least losing" move>

My point was that you cannot define that in the scope of PDP.

Since PDP "sees" all the way to end, when can it be helpful? Only in the following case:

When it has a move that wins in all variations with <both> sides chosing the best moves, it will pick such a winning move. And if no such move exists, but there is a move that leads to a draw with perfect play from both sides, it will pick that move.

But if none of these options exist, then we are getting into practical area: what is "least losing" here? the guideline to avoid simplifications is certainly not clear enough. So how to decide about the move when all evaluations lead to minus-infinity ?

If we shorten the PDP horizon in order to get "better" evaluation than -inf, then we already leave the PDP domain, and get into known engines domain (i.e. machines that don't see all the variations till the end).

Hence I think you are talking about a combination of strong engine + PDP, when the PDP is very helpfull when there is a forcing winning/drawing variation: it would take control <from that point> on.

However, in case of knight odds vs Carlsen, most chances are that such point would never reach, and hence the PDP would never be used, and only the "engine part" will be practically active..

<But once again, we were not talking about an endgame (table base) position which every GM can play right to the winning end>

I wasn't talking about GM with table bases, but rather about 1800 player without any table bases knowledge. Simply a player with 1800 chess understanding. I'd say that you can through in another Bishop for each side, or even a rook, and the 1800 should still beat the 5000 rated player in such a case (a Queen would probably be too tough for him though..).

<That would be fantastic to see with knight odds; I think Houdini people would be willing to do it (they have nothing to lose) but will Carlsen (or any other top player)? I think not, and you also think that>

I think we still haven't agreed regarding the definition of PDP. From the start it wasn't some sort of "perfect machine", but explicitly of divine origin, Perfect divine player, (or if one is atheist, call it an advanced alien) which chooses the best moves in every position. It's not a computer program for which one has to work out the "minus infinity" concept. But more about that below...

<When it has a move that wins in all variations with <both> sides chosing the best moves, it will pick such a winning move. And if no such move exists, but there is a move that leads to a draw with perfect play from both sides, it will pick that move>

Here I will repeat that a human usually will not play perfect (the best moves) and will make many tactical, strategic inaccuracies (and if the game is long enough usually also blunders). All of these will be immediately taken advantage of by the PDP to reach a "less losing" position, and eventually by accumulation all these small advantages, the PDP will be able to reach a position with material or strategical advantage.

<So how to decide about the move when all evaluations lead to minus-infinity ?>

I think that all that PDP will require is analyzing to a +1 advantage for itself, it doesn't have to look all the way to bare kings. In other words, it can see all the possible lines and it will take advantage of any (however small) inaccuracies of the human player to accumulate a larger advantage. In other words, we know that not all the moves which look good for us humans are indeed good (even if it's exchanging pieces) since we can't really see as deep as the PDP; so any of our inaccurate moves (say such that reduce the human advantage by as little as 0.05) may eventually lead to PDP's position gradually improving.

<If we shorten the PDP horizon in order to get "better" evaluation than -inf, then we already leave the PDP domain, and get into known engines domain>

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). Every inaccuracy by human (however small) will be immediately taken advantage by PDP, so I think the human will have a very difficult time.

I have to emphasize: the PDP's evaluation to +1 is absolutely not the same as engines evaluation to +1 since the PDP looks at all possible lines that give him a small (say +1) advantage while the engine looks at only a small fraction of all such moves.

So I think the "problem" with the minus infinity is artificial because the human will make many small inaccuracies, leading to + evaluation for PDP. It doesn't have to be all the way to bare kings, but, say, 60 moves deep, and no human can usually see that deep.

Also, the problem of the "practical" chess doesn't exist since it exists only as far as human shortsightedness is concerned. Eg, Tal was a fantastic practical player, with his ability to complicate, but we know that objectively many of his moves were wrong, a computer will refute them, but other humans were not able to usually. The same applies to human vs PDP, for PDP many of human's moves will be just like Tal's to an engine.

<Actually I think Carlsen might agree for such a match in case he would be offered a high fee>

Maybe this needs a bit more attention.

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. 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.

Despite this claim, the PDP you described here operates as a powerful engine that needs to take <practical decisions> rather than playing perfect chess (unless you add it mind-reading capabilities as well..).

The "PDP" you suggest, takes advantage of human inaccuracies by scanning all the variations, and picking the "least losing" move, while considering inaccurate options from the human as well.

I already addressed that option in my second post (above): The problem here is that there is no "mathematical" way to chose that best option.

So <there is no single truth> about the best option when you take into account human errors, because <different humans make different errors>.

You want the PDP to scan all the variations deeper than any human can do, and pick the move that gave the best evaluations. But in 60 ply the evaluations with range between [-inf, +inf], and so the PDP will need to take some <practical decision> in order to pick its next move:

Unless it <can predict> the kind of inaccuracy/error its human opponent is going to make, it cannot know for sure, which move is perfect vs its <current opponent>. One move can be difficult for Carlsen to meet but easy for Kramnik to meet, and vice versa. So unless it can read its opponent's mind, it cannot make such best decision <by definition>, and hence such "perfect machine" <cannot exist> (I assume you didn't give your PDP mind reading powers..).

Moreover, by using the term "evaluation", you already contradict your "perfect play" assumption, because eval is not perfect <by definition>. Such PDP cannot perfectly eval its position, since that eval is based on general chess principles (material, control, pieces positions and coordination, etc), and its analysis within its scanning horizon (60 plys in your case). That's very far from "perfect truth". And BTW, super GMs normally have better evals than engines, in case they don't miss hidden tactical lines.

--

In one of your previous posts you wrote: <I additionally define PDP as the entity for which chess has been solved, the whole of chess is like one big tablebase for it> and you talked about PDP that sees all the way "to the end" there, So I still claim that your PDP is a combination of: Highly powerful chess engine + 32-man tablebase.

While that is exponentially stronger than today's strongest engine (with its 6-man tablebase), I still think that Carlsen will be the favorite with knight odds vs that theoretical chess monster.

Moreover, as I mentioned before, I think the "problem" of <infinities> is artificial. For example, engines play the 6-man tablebase positions perfectly and able to assign different values to their moves of their opponents and they don't face any problems with infinities. PDP may work in exactly the same way only with 32-man tablebase.

<So I still claim that your PDP is a combination of: Highly powerful chess engine + 32-man tablebase.>

Maybe that's what will be required, though as we know our opinions on who will be the winner differ. Although this doesn't mean that one has to get rid of the idea of "perfect truth". I think PDP could work as a 6-man tablebase engines: they play 6-man tablebase positions perfectly if the opponent plays perfect, but otherwise they have to have some to give the opponent's imperfect move a particular value. How this works I don't know exactly (not being a chess programmer) but why not do it in terms of the number of moves needed to the end of the game? That is, if the human makes a slightly imprecise move at the beginning of the game (still knight odds), it can win by longer lines on average relative to perfect play. This (the length of lines) can be the criterion for PDP's assignment of values to different moves. So the <negative infinity> problem disappears. If the human makes many such imprecise moves, the accumulated effect may be that the position becomes favorable for PDP.

So I don't think one has to limit PDP to only some particular number of ply. Engines are able to analyze tablebase positions and "evaluate" the imprecise moves of the humans and give those moves different values (eventhough the game may still be winning for human). PDP should be able to do the same.

I must add that even if we don't see how PDP does it, it doesn't mean it's not doable. And if engines do it with 6-man, PDP should be able to do it with 32-man tablebase.

Wouldn't a 32-piece tablebase make the chess engine redundant? The tablebase would contain all possible positions (no one knows exactly how many, but I read somewhere that it has been estimated at 10 to the power of 120), and for a won position it would give us the complete line leading to forced checkmate in a number of moves. Any deviations from this line by the winning side would prolong the game (or change the outcome), while deviations by the losing side would shorten the game.

Engine evaluations have no meaning for a tablebase. Any position is either a draw or forced checkmate in a number of moves. The only real mistakes are those that turn a win into a loss or draw, or a draw into a loss. However, the computer could, for example, be set up such that:

1) When losing, it delays checkmate as long as possible, 2) when winning, it minimises the number of remaining moves, and 3) in a drawn position, it minimises the number of replies that lead to draw.

As you explained, the problem the "perfect" computer faces, when defending a losing position such as the starting position with Knight odds to the opponent, would be that the moves that delay checkmate the longest may not be the ones that pose the greatest practical difficulties for a human player. However, there would simply be no way for the table base computer to calculate when to make a practical gamble and deviate from the theoretically optimal line.

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.

Yes, that was basically my idea as well (see the previous post).

<As you explained, the problem the "perfect" computer faces...> I have to emphasize that initially PDP was explicitly defined as NOT a computer. By definition, it is of divine origin, or an alien with knowledge of human nature, or even highly advanced humanoid with a 32 tablebase and the ability to make highly sophisticated decisions. That is, it can choose those lines which pose the greatest difficulties for humans, eg, if two lines have approximately the same value, it will choose the one keeping more pieces on the board or more complicated tactically or strategically. It will constantly try to take advantage of human weaknesses, whatever they may be.

<However, there would simply be no way for the table base computer to calculate when to make a practical gamble and deviate from the theoretically optimal line>

This is again about computers (which was not initially my idea), however, why not model the computer on PDP? That is, why can't a 32-tablebase computer be programmed to always choose those lines which keep more pieces on the board and create more complexity, thereby making it much more difficult for the human? The programming logistics of this are complicated (how to compare the value of "complexity" to the value of a given tablebase move, etc) but considering the immense complexity of chess, there is much room for programmers of such a machine to constantly improve it (afterall, chess programming has advanced amazingly from 19060's to the present day Houdini, and there is a lot more room left for improvement).

<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.

<There is very little the tablebase computer would be able to do about that, because it cannot force the human player to make mistakes>

A more sophisticated tablebase comp, which I described above, may very well be able to force the human into positions where it will be prone to make serious tactical/positional mistakes. Even-though the logistics of it are not clear but that doesn't mean programers from advanced civilizations wouldn't be able to do it. The main issue would be to compare complexity to the value of a given move. Eg, one move has value of +1.1 for human but the second more complex (keeping more pieces on board, tactically/strategically more complex) has value of +2 - should the comp chose the second one even if objectively (if two comps are playing) the first move is better for it?

I agree with your entire analysis and conclusions, however, as you said, delaying the mate as long as possible may not pose the greatest practical difficulties on the human player.

What does that actually mean? That along the games played, your machine <missed better chances> to beat its human opponent, and hence it missed chances to get better overall score vs its human opponent.

In other words, your machine did <not play perfect>, since it didn't get the maximum score vs that human. Hence it doesn't qualify as the "divine perfect player" that shach referred to.

Perfect play vs Carlsen with knight odds, has to be a collection of moves, that generates the max possible score that is <theoretically possible> vs Carlsen from that starting position.

So in each position, such machine must pick the move that results in Carlsen worst response. If we could have perfect evaluation, it means that it has to pick the move that minimizes the following difference: eval(position)-eval(position after machine move and Carlsen move).

Of course that can only be done if that machine can predict Carlsen's response to each move, and it also has to have perfect evaluation considering Carlsen's play (since there is no absolute perfect evaluation, it depends on the players as well).

Such machine cannot exist, but it should be the <theoretical "perfect play"> since it maximize the score vs Carlsen. Any other chess machine cannot be considered perfect.

--

Specifically the strategy you suggested sounds very good: At each move maximize the min number of moves that Carlsen will need in order to force mate. It definitely generates the longest possible game, and hence leaves room for more errors on Carlsen's part.

However, not only that the above is not perfect play, it is very likely that a strong engine that poses <practical problems> would perform better than it. Because as we know, long slow but almost sure death, isn't expected to perform better than taking chances that can lead to faster death, but can also have better chances of the opponent making errors.

I think that you have some misconception of the way tablebase are used by engines: They are only used in case the engine recognizes a position as tablebase win or draw. When the engine recognizes such position, it <stops using> its engine evaluation part, and simply starts picking moves automatically from its tablebase. There is absolutely no need for evaluations from that point forward, since all the paths are solved to the end, and the machine just needs to pick the path that leads to its most favorable result.

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.

<shach: just let the PDP analyze arbitrarily deep, say 100, 150 or more ply [..]>

I don't see how that solves the problem of picking the optimal move for its specific human opponent at that specific point of time. Your PDP will get astronomic amount of variations, but in the end it will have to chose one single move out of them, and it has no way of picking the optimal one without predicting Carlsen's response.

<shach: That is, it can choose those lines which pose the greatest difficulties for humans>

But again: In each position there is no single move that will pose the greatest difficulties for <all> the humans, since different humans have different kind of difficulties (depending on their playing style for example). And even the same human can have more difficulties with one move on a given day, and on a different day he may find a different move (in the same position) to be more difficult to meet.

Hence the PDP you describe <cannot be optimal> by definition.

<shach: but why not do it in terms of the number of moves needed to the end of the game? >

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

Using tablebases, I assume an engine will strictly pick the fastest win or slowest loss as appropriate, but I believe several engines will continue to use their evaluation in a drawn tablebase position (restricting its candidates to moves that maintain the draw), especially if they have the advantage. For example, it may have practical chances in a rook+bishop vs rook endgame against a human, even if it is theoretically drawn.

<metatron: I think that you have some misconception of the way tablebase are used by engines>

Not at all! The point is that 32-man is a complete while 6-man is not; so 6-man requires a chess engine while 32 doesn't. The only need for an engine in case of 32 is for the evaluation of complexity of position vs tablebase move (as I describe below).

<I don't see how that solves the problem of picking the optimal move for its specific human opponent at that specific point of time>

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.

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. Even if preventing the exchange leads to the worse tablebase position for the PDP, it may still choose it in order to maintain the complexity of the game, thereby increasing the probability of the human making mistakes. The question the programers have to work out is how to value "complexity" vs best tablebase move; perhaps with the thousands of human games at their disposal, they can use statistical averages to assign values to various forms of complexity (perhaps even dividing it into various classes depending on number of pieces, combinations of pieces, etc, obviously this gets extremely complex; but if they are able to solve chess, perhaps they can do this too).

<Hence the PDP you describe <cannot be optimal> by definition>

If you mean because of the limited horizon (100 or so moves), than that is very clearly not a perfect (optimal) player. However, I think I did mention that limiting it would make it imperfect by definition. We need to make sure that we discussing the same thing: a true PDP vs a combo of computer and tabelbase, like in this present discussion.

<But again: In each position there is no single move that will pose the greatest difficulties for <all> the humans>

It doesn't have to be a single "perfect" move since we're not discussing a perfect player in the sense of the initially defined PDP. And, again, I think that relative to this discussion, difference of players plays almost no role at all. In principle, PDP is so much stronger than any human, that the difference of 100 or less points between the different players relative to the PDP is insignificant.

<<shach: but why not do it in terms of the number of moves needed to the end of the game?>

I already referred to this concept in my response to Bureaucrat..>

I didn't really find an answer. You just said that with this idea of evaluation of the move by it's deviation from tablebase, the PDP becomes imperfect, and I see your point there; however, in that discussion it was already given that it's not necessarily perfect since it's a combo of computer and tablebase and not a <divine> PDP.

Obviously I didn't mean that the machine will use (only) its tablebase in order to force a draw in case it has the advantage, and the machine is the one looking for a win in a theoretically drawn position..

Only in case it is on the defensive side it will use its tablebase to force the draw of course.

<tbentley: Engines also use tablebases before reaching a 6-man (or whatever) position, if those positions are reached in their search, as they can be evaluated exactly as mate or a draw without having to search further>

shach, if we agree that the machine you describe is Not playing perfect, and it is a combination of highly powerful and sophisticated engine with a 32-man tablebases, then we have no disagreements.

I already mentioned in the beginning, that there is no definite answer as to whether such machine/entity would be favorable vs Carlsen with knight odds or not, we only have opinions and estimations about that.

I continued the discussion around the issue of defining a perfect playing machine from a position where perfect play leads to inevitable loss. But it seems like we have no disagreement here as well..

--

I'll just try to clarify some issues your raised:

<shach: your idea of the PDP having to choose an <optimal move for its specific human opponent> makes no sense to me at all [..] Chess is a purely mathematical game, [..] For example, what does it matter to a tablebase [..] >

The point is that chess can be considered "purely mathematical" when you remain in the domain of tablebases only, like the algorithm Bureaucrat suggested.

Once you try to find ways to "trick" humans into positions that should be complex for them etc. you <no longer> make cold "mathematical" decisions, but rather practical ones.

And since the goal is to pick moves that are most difficult for the human opponent, then isn't it obvious that the optimal pick would be the move that is most difficult for that specific opponent at that specific point of time? Such move has to maximize the chances of the machine, since it is the one that mostly improves (or least degrade) its position at that point of time.

Take for example Karmnik's famous blunder vs Fritz: A machine that looks for moves that are generally complex for humans to handle, might not come up with threatening mate on h7, because that wasn't really difficult for humans to see in general (I know I instantly saw that mate threat ..), but a machine that can predict Kramnik's oversight of that specific element at that specific point of time, would go for it and win immediately, while the general purpose machine might not win at all.

The knowledge of the kind of errors the human is going to make vs each move is what really makes such machine "divine" or "god", and it is the one that can set the optimal (theoretical) perfect play barrier (of course one can argue about improving it by predicting the human errors multiple moves ahead, and then we can get kind of "tablebases" per human at given point of time..).

<shach: <Hence the PDP you describe <cannot be optimal> by definition> If you mean because of the limited horizon (100 or so moves)>

I mean that it isn't optimal since it is expected to perform below the optimal (theoretical) machine that I presented..

<shach: I didn't see an answer to why this method would not be usable for 32-man if it's used for 6-man since the general idea is the same>

We're in agreement on that point. Perhaps to avoid the confusion I'll keep the PDP as defined previously, and call the sophisticated engine with a 32-man tablebases "TE" for tablebase engine (yea, I don't have much of an imagination).

I would emphasize, however, that we simply don't know how PDP operates since it is perfect by definition, and philosophically speaking, <divine> perfection is not something that we can completely understand. We as humans have only scratched the surface both in chess and programming, so much of what is possible is still simply unknown to us.

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. 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). If there is more than one line leading to the same basic result (say two lines with the same number of moves until the end of the game), it will choose the more complicated one. Perhaps this way we can keep it <perfect> without it being "merely" a tablebase since in terms of <perfection> the two or more different lines can be considered the same.

But I still think we're not advanced enough to know for sure how it operates; however, if you like, I am willing to discuss it further.

For us probably the more interesting question is not <perfection> but how a real highly advanced program will operate. I discussed previously the above idea for TE of a function which will be able to value <complexity> and compare it to a tablebase move, thereby able to prevent most exchanges and keep positions as complicated as possible. If this is doable (which I think it is), many human errors are unavoidable (we're helpless against mere 3300 engine precisely because we always make mistakes, surely we'll make much more mistakes against TE).

In regard to TE, the exact nature of it's opponent is inconsequential as it concerns itself only with the moves made by the human, mathematically scans the tabelbase and chooses the more complicated lines. But I guess your objection was in regard to the idea of perfection and PDP, but even then I don't think the exact nature of your opponent is of any relevance, exactly for the same reasons as for TE, with the only exception that PDP looks at equally <perfect> lines (say those leading to the end of the game with same number of moves) and chooses the more complicated one.