"chess has a branching factor from 31" ++ Some positions can have 31 legal choices, but average only 3 that do not transpose: 3^80 = 10^38
Not "some", the average middlegame position. Some have as high as 40. Your 3 number is one I have seen from only one source, you...and you are distinctly unreliable for numbers.
"until you can perfectly evaluate a single position" ++ 1 e4 e5 2 Ba6? loses for white, without needing any game tree. The perfect evaluation of 1 a4 cannot be better than that of 1 e4, without needing any game tree.
This logic has never worked, sorry. You might as well extend your mistaken premise and say that 1 e3 is not winning because 1 e4 is superior, or 2 Be2 is not winning because 2 Bc4 and Bb5 are better.
"Whether AB or BA are actually identical in result is not something you can determine"
++ Of course move order matters, but when the same position results, it is the same and needs only consideration once.
Chess is full of transpositions: the branches come back together in the same node.
"you are not actually working with 10^44" ++ I work with 10^38: nobody promotes to a 3rd rook, bishop, or knight in a real game, let alone in an optimal game.
"you double, triple, and possibly quadruple count the elimination of positions"
++ No. The reduction from 10^44 to 10^38 is by eliminating underpromotions to pieces not previously captured, i.e. to a 3rd rook, bishop, or knight. The reduction from 10^38 to 10^34 (or 10^32 per Tromp) is to eliminate positions that make no sense, i.e. cannot result from optimal play by both sides. The reduction from 10^34 (or 10^32) to 10^17 is by assuming perfect Alpha-Beta search for the weak solution.
Once again...you cannot achieve perfect Alpha Beta search. Your Tromp number I will not believe coming from you, you have misrepresented him before.
"Your argument tries to apply it's largest reduction twice" ++ No.
@12172
"how long can a chess game go until someone gets an advantage and how long can the opponent prolong not getting checkmated?"
++ The ongoing ICCF World Championship Finals now has 109 draws out of 109 games and they end in draws in average 39 moves. https://www.iccf.com/event?id=100104
"How many calculations would it need for that to be "solved"?"
++ Weakly solving chess needs to consider 10^17 positions = Sqrt (10^37*10 / 10,000).
The 17 ICCF World Championship finalists looked at 1.9*10^17 positions = 90*10^6 positions/s/server * 2 servers/finalist * 17 finalists * 3600 s/h * 24 h/d * 365.25 d/a * 2 a
"chess games do have a max possible move count with the 50 move rule"
++ The 50-moves rule plays no role at all.
Games end in draws in average 39 moves, long before the 50-moves rule can trigger.