A little intuition on how ridiculous positions may not be so ridiculous. Throw some reachable set of material on the board (<=32 pieces, with enough pieces and pawns missing to make the number of excess pieces possible by promotion) on the board until you get a position that is legal (a large proportion) and you will get a position where Stockfish will provide some material balance between say -200 and 200.
It is to be expected that the distribution of the evaluation is not thinner than average near the middle, so at least 0.5% of these positions will be in the range -1 to 1 evaluation and for it to be entirely plausible the positions are a draw to an oracle (some won't but these will be made up for by others that appear to have larger evaluations that are in truth more difficult draws).
That means a quite large fraction of random positions are perfectly reasonable ones for optimal play to go to (if chess is a draw), and this is true for all chains through such positions, which can certainly start from a normal position such as the initial position.
Taking one such random position with an unusually large number of knights for example, you can work backwards from that position to reach an exponentially growing number of other positions by optimal play. It may be only when you reach say 10^9 such positions that one of them involves the possibility of an underpromotion to a knight (this is excessively pessimistic - underpromotions comprise at least 1 in a 100,000 perceived best moves in high level chess games).
You can repeat this process for multiple promotions to find that it is indeed perfectly reasonable for optimal play to reach positions with large numbers of underpromotions.
Note that each step of this process - working back from a position with odd material balance to an underpromotion - traverses a tiny fraction of the set of legal positions, say N positions (I generously allocated N=10^9 but was well aware a lot fewer would probably be needed on average), so a position with M underpromotions can reasonably find a path back to a position with no underpromotions by retrogade analysis looking at N * M positions, a very tiny fraction of the whole.
An intuitive error would be to think this number would be N^M, which would become very large for large M.
. They would make a fool of themselves if they were demanded to provide the optimal strategy in reasonable time and the game didn't end in a draw.
@Marattigan
To weakly solve a game it is enough to provide an optimal strategy in a reasonable time, so to save storage space, you can leave out some lines and provide them on demand, but you have to know, after tests, that they can be provided on demand.
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
For chess, If one sits at the board against SF and has weakly solved the game, s/he will make some moves using the proof tree, some others can be calculated by an engine, but it must hit an endgame tablebase or an already solved position in reasonable time. Instead, if s/he uses an engine just to evaluate the position as usual, they will likely draw against an equally strong silicon opponent, but the moves would be just the result of evaluations/guesses: if they use the same engine 10 years later against a much stronger opponent, they would lose most of the games. If chess was indeed weakly solved, on the other hand, they would replicate the same outcome with the very same silicon ally even 1000 years later.
You need only provide one opening line (half tree) if you weakly solve a game as a win. You have to provide a full half tree for each side if you weakly solve it as a draw.
That was apparently not done.
Of 300 openings only 19 were shown to draw. A further 100 validly excluded as transposition of moves, but the remaining 181 dismissed by the assertion that it would be possible to prove them drawn by alpha-beta pruning (without details of how that could lead to a proof) but without actually performing the computations.
I may be reading it wrong, but it is at least difficult to find either further details or an available database of the results computed. No database - no weak solution. Most of the lines still to be computed - no ultra weak solution either.
Btw. you have a touching faith in the reliability of computer results obtained over decades on different machines involving large amounts of data.