Chess will never be solved, here's why

Imperfect player guesses that game is perfect (and claims guess to be completely reliable).

Failing to follow the argument, I'm afraid.

My fault, not yours. I had misunderstood. See edited post.

A pawn as a higher ratio of total pieces more likely to produce a win?
That seems to be contradicted by a defending King getting in front of that pawn.
Or - getting the opposition.
...

My labels were perhaps misleading. I was speaking of a difference of  ≤1 in the sum of the values of the pieces for each side with the values Q→9, R→5, B→3, N→3, P→1 rather than, necessarily identical material or an extra pawn for one side.

I've changed the label and listed the endgames below:

USING UNCORRECTED SYZYGY POSITION COUNTS:

Game BR
Endgames with notional material difference at most 1 pawn(s)

# men additional to kings=0
KvK
total ESMs: 1
win % =0.00

# men additional to kings=1
KPvK
total ESMs: 1
667692 winning out of 994056
win % =67.17

# men additional to kings=2
KQvKQ, KRvKR, KBvKB, KBvKN, KNvKN, KPvKP
total ESMs: 6
20096412 winning out of 73668036
win % =27.28

# men additional to kings=3
KQPvKQ, KRRvKQ, KRBvKQ, KRNvKQ, KRPvKR, KBBvKR, KBNvKR, KBPvKR,
KNNvKR, KNPvKR, KBPvKB, KNPvKB, KPPvKB, KBPvKN, KNPvKN, KPPvKN,
KPPvKP, KQPvKQ, KRRvKQ, KRBvKQ, KRNvKQ, KRPvKR, KBBvKR, KBNvKR,
KBPvKR, KBPvKB, KBPvKN, KNNvKR, KNPvKR, KNPvKB, KNPvKN, KPPvKB,
KPPvKN, KPPvKP
total ESMs: 34
15031957290 winning out of 36932117436
win % =40.70

# men additional to kings=4
KRBPvKQ, KRNPvKQ, KBBBvKQ, KBBNvKQ, KBNNvKQ, KNNNvKQ, KBPPvKR,
KNPPvKR, KPPPvKB, KPPPvKN, KQQvKQQ, KQRvKQR, KQBvKQB, KQBvKQN,
KQNvKQN, KQPvKQP, KQPvKRR, KRRvKRR, KRBvKRB, KRBvKRN, KRNvKRN,
KRPvKRP, KRPvKBB, KRPvKBN, KRPvKNN, KRPvKBB, KBBvKBB, KBBvKBN,
KBBvKNN, KRPvKBN, KBBvKBN, KBNvKBN, KBNvKNN, KBPvKBP, KBPvKNP,
KRPvKNN, KBBvKNN, KBNvKNN, KNNvKNN, KBPvKNP, KNPvKNP, KPPvKPP,
KRBPvKQ, KRNPvKQ, KBBBvKQ, KBBNvKQ, KBNNvKQ, KBPPvKR, KNNNvKQ,
KNPPvKR, KPPPvKB, KPPPvKN
total ESMs: 52
1262729602320 winning out of 2598590952432
win % =48.59

# men additional to kings=5
KRBPPvKQ, KRNPPvKQ, KRPPPvKQ, KBBBPvKQ, KBBNPvKQ, KBBPPvKQ, KBNNPvKQ,
KBNPPvKQ, KNNNPvKQ, KNNPPvKQ, KBPPPvKR, KNPPPvKR, KPPPPvKR, KPPPPvKB,
KPPPPvKN, KQQPvKQQ, KQRRvKQQ, KQRBvKQQ, KQRNvKQQ, KQRPvKQR, KQBBvKQR,
KQBNvKQR, KQBPvKQR, KQNNvKQR, KQNPvKQR, KRRRvKQR, KRRBvKQR, KRRNvKQR,
KQBPvKQB, KQNPvKQB, KQPPvKQB, KRRBvKQB, KRRNvKQB, KRRPvKQB, KRBBvKQB,
KRBNvKQB, KRNNvKQB, KQBPvKQN, KQNPvKQN, KQPPvKQN, KRRBvKQN, KRRNvKQN,
KRRPvKQN, KRBBvKQN, KRBNvKQN, KRNNvKQN, KQPPvKQP, KRRPvKQP, KRBBvKQP,
KRBNvKQP, KRBPvKQP, KRNNvKQP, KRNPvKQP, KBBBvKQP, KBBNvKQP, KBNNvKQP,
KNNNvKQP, KQPPvKRR, KRRPvKRR, KRBBvKRR, KRBNvKRR, KRBPvKRR, KRNNvKRR,
KRNPvKRR, KBBBvKRR, KBBNvKRR, KBNNvKRR, KNNNvKRR, KRBPvKRB, KRNPvKRB,
KRPPvKRB, KBBBvKRB, KBBNvKRB, KBBPvKRB, KBNNvKRB, KBNPvKRB, KNNNvKRB,
KNNPvKRB, KRBPvKRN, KRNPvKRN, KRPPvKRN, KBBBvKRN, KBBNvKRN, KBBPvKRN,
KBNNvKRN, KBNPvKRN, KNNNvKRN, KNNPvKRN, KRPPvKRP, KBBPvKRP, KBNPvKRP,
KBPPvKRP, KNNPvKRP, KNPPvKRP, KRPPvKBB, KBBPvKBB, KBNPvKBB, KBPPvKBB,
KNNPvKBB, KNPPvKBB, KRPPvKBN, KBBPvKBN, KBNPvKBN, KBPPvKBN, KNNPvKBN,
KNPPvKBN, KBPPvKBP, KNPPvKBP, KPPPvKBP, KRPPvKNN, KBBPvKNN, KBNPvKNN,
KBPPvKNN, KNNPvKNN, KNPPvKNN, KBPPvKNP, KNPPvKNP, KPPPvKNP, KPPPvKPP,
KQQPvKQQ, KQRRvKQQ, KQRBvKQQ, KQRNvKQQ, KQRPvKQR, KQBBvKQR, KQBNvKQR,
KQBPvKQR, KQBPvKQB, KQBPvKQN, KQNNvKQR, KQNPvKQR, KQNPvKQB, KQNPvKQN,
KQPPvKQB, KQPPvKQN, KQPPvKQP, KQPPvKRR, KRRRvKQR, KRRBvKQR, KRRBvKQB,
KRRBvKQN, KRRNvKQR, KRRNvKQB, KRRNvKQN, KRRPvKQB, KRRPvKQN, KRRPvKQP,
KRRPvKRR, KRBBvKQB, KRBBvKQN, KRBBvKQP, KRBBvKRR, KRBNvKQB, KRBNvKQN,
KRBNvKQP, KRBNvKRR, KRBPvKQP, KRBPvKRR, KRBPvKRB, KRBPvKRN, KRNNvKQB,
KRNNvKQN, KRNNvKQP, KRNNvKRR, KRNPvKQP, KRNPvKRR, KRNPvKRB, KRNPvKRN,
KRPPvKRB, KRPPvKRN, KRPPvKRP, KRPPvKBB, KRPPvKBN, KRPPvKNN, KBBBvKQP,
KBBBvKRR, KBBBvKRB, KBBBvKRN, KBBNvKQP, KBBNvKRR, KBBNvKRB, KBBNvKRN,
KBBPvKRB, KBBPvKRN, KBBPvKRP, KBBPvKBB, KBBPvKBN, KBBPvKNN, KBNNvKQP,
KBNNvKRR, KBNNvKRB, KBNNvKRN, KBNPvKRB, KBNPvKRN, KBNPvKRP, KBNPvKBB,
KBNPvKBN, KBNPvKNN, KBPPvKRP, KBPPvKBB, KBPPvKBN, KBPPvKBP, KBPPvKNN,
KBPPvKNP, KNNNvKQP, KNNNvKRR, KNNNvKRB, KNNNvKRN, KNNPvKRB, KNNPvKRN,
KNNPvKRP, KNNPvKBB, KNNPvKBN, KNNPvKNN, KNPPvKRP, KNPPvKBB, KNPPvKBN,
KNPPvKBP, KNPPvKNN, KNPPvKNP, KPPPvKBP, KPPPvKNP, KPPPvKPP, KRBPPvKQ,
KRNPPvKQ, KRPPPvKQ, KBBBPvKQ, KBBNPvKQ, KBBPPvKQ, KBNNPvKQ, KBNPPvKQ,
KBPPPvKR, KNNNPvKQ, KNNPPvKQ, KNPPPvKR, KPPPPvKR, KPPPPvKB, KPPPPvKN
total ESMs: 238
423497287507506 winning out of 730124977157238
win % =58.00

Mmmh... The evaluation may be less biased than Q-learning, but if the evaluation is less biased, you need more training and/or more search after the training, so it's always a trade-off. Idk wether it would be more effective to solve chess. It's always the bias-variance dilemma, NFL... you know .

The paper you reference is about MuZero,

Ah! I missed the fact that it was a separate development to AlphaZero.

which is based on A0 (but it does not outperform the latter). For A0, It seems that Q-learning is not suited for NN, right?

Not sure what you mean, but deep Q-learning is a powerful general reinforcement learning paradigm which might be reasonably hypothesised to be near optimal. (The discrete version can be proven to be optimal in one sense).

So they replaced the discount factor γ and a temporal-difference learning, with a learning based on a modified MCTS search. The Lc0 team calls this search PUCT (Predictor + Upper Confidence bound Tree search), rather than MCTS. Basically, "each search consists of a series of simulated games of self-play that traverse a tree from root state sᵣₒₒₜ until a leaf state is reached"¹ (italic mine). Moves for each simulation are selected according to the current NN, which uses two parameters: a probability vector for the moves to be played (the policy) and the predicted value for the node. The search returns another vector of probabilities for the moves to be played. During learning, these games are played until a terminal node (the end of the game) is reached, where a definitive score is assigned to the root node. At this point the parameters used by the NN (the policy vector p and the predicted outcome v) are updated to minimize respectively the difference with the probability vector resulting by the search and the outcome of the terminal node. So at the beginning the search is random, but every time a terminal node is reached, the parameters are refined. During the search, moves with a combination of high probability, high value and low visit count are selected more.

So it does resemble very much an Actor-Critic learning.

You have explained it well and clarified a couple of key points. The complete idea is very neat.

But choosing a move because it has a higher probability to be played, or an average better score, is nevertheless an heuristic.

It sure is! Neural networks learning from batches of empirical data are 100% heuristics.

¹ https://arxiv.org/pdf/1712.01815.pdf

Please see my note in Red near the top of the quote of your post.

...

@playerafar

The number of KPK positions according to Wilhelm/Nalimov is also 331352.

Very roughly rounding off ...
for odd numbers of men to go with the Kings ...
then percentages of wins went 70 then 40 then 60.

Irksome that.   There's no apparent trend.
Shucks !   Hopes are Dashed.  

I don't think its hard to calculate by hand. 
Although I won't guarantee it would match that number.
It Probably Would !!  
A sum of three terms for a King in corner/edge/interior multiplied by 2 and then 48 ?
Unfortunately not quite that simple - as one or both Kings might take one or two of the pawn's 48 possible squares

You wouldn't match it exactly if you ruled out all illegal positions. Both Nalimov and Syzygy allow positions like this https://syzygy-tables.info/?fen=8/8/8/8/8/5k2/4P3/4K3_b_-_-_0_1 (but not with White to move).

You wouldn't match it exactly if you ruled out all illegal positions. Both Nalimov and Syzygy allow positions like this https://syzygy-tables.info/?fen=8/8/8/8/8/5k2/4P3/4K3_b_-_-_0_1 (but not with White to move).