Will computers ever solve chess?

There's no "sensibility" determination involved in solving chess.  But even if there were, and even if your million factor were to be true, 10^38.7 is still unreachable by any reasonably foreseeable technology.  You posited that chess could be solved by burning the candle at both ends because we could drop the number of positions to 10^20, which is why you'll take anything you can grasp...but even allowing for 10^38.7, you've got 1,000,000,000,000,000,000 times more positions to go.

#6901
Take a look at the sample positions from John Tromp: at first glance it is clear that none of these results from a real game, i.e. none has any relevance. In a real game underpromotions to knight, rook, or even bishop do happen occasionally, but are very rare. In no real game anybody will underpromote to a 3rd rook or a 3rd bishop or a 3rd knight. Promotion to a second queen does happen rarely, but 3 or more queens per side are fantasy.
Hence to solve chess only sensible and legal positions need consideration.
Legal means: possible to reach from the initial position.
As sensible I propose: possible with one chess set of 32 pieces and an additional spare queen of each color.

Now not all possible, sensible, legal positions need to be visited to solve chess.
Of the 5 x 10^20 possible positions, Schaeffer needed to evaluate only 10^14 to prove that checkers, played perfectly, results in a draw.

You can contort all you want to, but you will never get 10^40+ down to 10^20.  Ain't gonna happen.  Chess is not checkers.

One thing that has to happen is that each side has to make a move that is the best move to be played, otherwise he loses. There might be a couple of sensible moves at the beginning, usually one best move toward the end, so I don't see a lot of possibilities.  

Nope. 

Said it before. Sometime the simple and correct answer to the OP’s question is worth restating.

no

Yes, before the end of this century.

Not in our lifetimes.

#6916
That depends on your age.
In 1970 it was unthinkable that a chess engine would ever beat a human grandmaster, or that we would know exactly how to play 7 men endgames.
Maybe IBM will do it like they made Deep Blue.
Maybe Google will do it like they made AlphaZero.
Maybe the Lomonosov University will do it like they made 7 men table bases.
Maybe a loner like Ken Thomson will do it like he made 5 men table bases.
Maybe a loner like Schaeffer will do it like he solved checkers.

None of those are going to happen.  Also, it was not remotely unthinkable that a chess computer would eventually outplay humans...it's almost an inevitability, in fact.

Beating a human GM is like a grain of sand compared to the beach of solving chess.  

You can say nay all day, but whether you like it or not, sooner or later chess will be solved.

Not.  In.  Our.  Lifetimes.

Reality is on my side, so, get ready to apologize 25-75 years from now.

"The one thing I’ve learned in all of this is to never underestimate the advances in technology" - Jonathan Schaeffer

You're still 20-25 orders of magnitude off your ideal scenario.  That's a little more than "an advance".  That's a little more than a revolution, frankly ...

You might as well just call for a magic spell, or God to give you the answer.  Just as likely as things sit.

I hope you live long enough to see it happen.

My name isn't Methuselah...

It's an interesting question how often we are really surprised by a change in knowledge or technology. I mean to the extent of being pretty sure about something or a possibility and this being proven false. It is more common either for us to start uncertain or for the difference to be less blatant.

Any advance that could solve chess will be hugely more significant for other reasons.

As an analogy, DeepMind achieved a huge leap in the performance of computers at difficult finite combinatorial games of perfect information (most notably go, but also chess), but far more significant is their applications of the same base technology (advanced deep learning) to the protein folding problem.  The human race is little affected by the best go player being a computer, but there is huge potential in the new capability to analyse the behaviour of any protein (a sequence of amino acids) without spending a year or two in the laboratory.

https://youtu.be/XcpsZUyvn2Q

#6926
Chess was called the drosophila of artificial intelligence.

#6926
Chess was called the drosophila of artificial intelligence.

Why was it called the drosophilia of AI, isn't drosphilia a fruit fly or something?