will chess ever die out once its fully solved?

Do you recall the moves of games?  Famous games?  Games you've played?

I recall plenty of games, but not the details of move order.  I can intentionally recall games, but if I don't play over them daily the details begin to fade.

I also think the strength of memory is linked to visualization ability (blind chess), giving us something like what our friend here mentioned; a talent of visual memory and visualization abilities.  I'd like to test and quantify that, too, if I ever get the chance.  I also have similar ideas regarding the development of skill in mathematics, based on quality and quantity of information and memory. . . and I truly think it's possible to develop software and procedures that truly facilitate expert skill and memory in things like chess and mathematics, given a persons capacity and interest level.  It may be that things are also genetically determined; that some people will just find it more difficult to improve than others simply because of they way they're wired up.  But then the whole idea is to change the "wiring" - neuroplasticity.  For the most part I think establishment science and education professionals aren't very interested in so-called "human optimization" research, and so I think we need the proverbial paradigm shift before such research becomes the rule rather than the exception.

Interesting topic anyways!   

Euclid 5050:

     There were studies done by French cognitive scientists on the French national team (circa 1930) that found that the only areas in which all of them were in the top fraction of 1% of the population were visualization and visual memory. Duchamp's friend Man Ray was also on the team (he didn't get to play often due to an occasional attempt to try to arrange the pieces in a visually-pleasing pattern rather than considering chess necessities) and had a history similar to Marcel's.

     Sorry I can't cite the source. My wife (then a psychology student at UC Berkeley) unearthed them in the university library when I became interested in chess. That was 50 years ago and we split some time back, but you seem to be well-informed on the subject so perhaps you may be able to find them should you wish to.

No, it is still definitely countable.

For example, 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 

Since there are no captures, 

(i) White has 4 different moves, thus 4! ways of "rearranging" the moves, i.e. 

A = {e4Nf3Bc4Ng5, e4Nf3Ng5Bc4, e4Bc4Nf3Ng5, e4Bc4Ng5Nf3, Nf3e4Bc4Ng5, etc.}

(ii) Black has 4 different moves, thus 4! ways of rearranging the moves.

Thus there a total of 4! * 4! = 576 ways of reaching the said position.

Now, for captures:

1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Nxd5

Note that exd5 must occur after d5 and Nxd5 must occur after exd5.

For d5, it can occur 3! times on move 1, 3! times on move 2, 3! times on move 3, and 3! times on move 4, since m(d5) < m(exd5) < m(Nxd5) -> m(d5) < 5.

Thus, exd5 can occur 3! times on move 2, 3! + 3! times on move 3, 3! * 3 times on move 4, and 3! * 4 times on move 5. Said logic can be applied to Nxd5: 3! times on move 2, 3! * 3 times on move 3, 3! * 6 times on move 4, and 3! * 10 times on move 5.

Thus, there are a total of 4! * 4! * (3! * 10) * (3! * 20) = 4147200 ways of reaching said position.

The same logic can be applied for checks, castle, etc.

Speaking of chess being solved, whatever happened to Ponz and that dumpster fire thread of his with almost 10,000 posts? Usually he resuscitates it every few weeks but I haven't seen it in months. Hope he's ok.

He's following Giri's footsteps: not touching any social media-stuff for a while now.

#957
"there are a total of 4! * 4! * (3! * 10) * (3! * 20) = 4147200 ways of reaching said position."
No there are many many more ways to reach the same position.
White can start with Nc3 and black Nc6. Then the knights can jump all over the board and return to their berth. Then a pawn can move 1 square. Then the knights and a bishop can jump and return. Then the pawn can move another square. Then the knights and the bishop can jump. Then another pawn can move 1 square. Then the knights and bishops can jump all over the board. Then the pawn moves another square.
The number of games is much much larger than the number of positions.

#933
"The game has, by a much newer and better estimate, 10^44 total legal positions."
No, that is obsolete too: the newer and better estimate is now 3.8521*10^37.
https://arxiv.org/pdf/2112.09386.pdf 
It is even lower when starting from 26-men positions i.e. start analysis after 3 trades.
See table 3 of the reference.

You are misrepresenting the study (shocker).  10^37 is for positions without promotions.  The 10^44 estimate is still correct.

#962
Without excess promotions. There can be promotions, but not to more pieces than in 1 box of chess men and not to 2 same color bishops. That makes sense. The vast majority of the previous number 10^44 are with multiple queens, rooks, knights, and same color bishops. Look at the sample of the 10^44.
The new number 4*10^37 is not even an estimate: it is an upper bound.

Again, you are incorrect. Do you not see that every move that I wrote is intentionally written to not be accomplished by other moves than said moves?

Anyway, why are you both talking about this irrelevant rubbish, which is as bad as Coolout's? It's all about semantics in a way. In calculating the number of relevant lines you use the most efficient way of reaching a position and all the rest is redundant.

If it's irrelevant rubbish, then don't even bother to mention about it. Also, "the rest" is not redundant at all. It's actually necessary to calculate.

It's only relevant if it alters the colour that has the move in a given position. People have been complaining about the irrelevancies continually repeated by another member and this nonsense is no better.

It's funny how CooloutAC thumbs ups your numbers as if he knew any better one way or the other .

Your premise is incorrect, as it has always been in every thread you have tried to insert it into.  You cannot solve chess with these shortcuts.  At best, you could claim that chess is most likely a draw...which is where we are already.

#964
You wrote ways of reaching said position, not ways of reaching said position in the shortest way.

#965
The number of games is irrelevant: there are many, many games that lead to the same position.

Transpositions are relevant.
1 e4 c5 2 Nf3 Nc6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 e5 6 Nbd5 d6 7 Bg5
is the same as 1 e4 c5 2 Nf3 e6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 Nc6 6 Ndb5 d6 7 Bf4 e5 8 Bg5
1 e4 e6 2 d4 d5 3 exd5 exd5 4 Nf3 Nf6
is the same as 1 e4 e5 2 Nf3 Nf6 3 Nxe5 d6 4 Nf3 Nxe4 5 d3 Nf6 6 d4 d5.
There even are transpositions between seemingly unrelated openings like the Petrov and the Queen's Gambit Accepted, between the Sicilian and the Scotch.

The number of games is irrelevant and only the number of positions matters.

Hmm, you're right. Then I'll add that. My bad.

Coolout seems pretty bright to me. I think he struggles to keep himself looking like he's dumb and he's pretty much given up on it. If you look at some of what he writes, when he maybe forgets himself, it's just like a normal-to-bright person.