I believe it was first proposed on the the basis of the 3-4-5 man Nalimov tables and the values for 6 and 7 man tables have morphed from predictions into verified measurements. Also the conjecture has so far proved itself as a predictive method. I should note that the points shown on the graph for 3 to 7 men (8 to 10 are only predictions) form a better straight line than I ever managed in my physics pracs at school. (Guy Haworth sadly died very recently.) This is available via the following link: The most convincing pointer I have come across so far is "Haworth's Law". Records in chess problems have already been far exceeded in tablebases so far generated, so I think these can be discounted as a pointer to the answer. OP asks for the longest win under basic rules, so Snag 1 in answer wouldn't apply. An email with preliminary results by Marc Bourzutschky argues possible exchanges lower the record lengths, and for this reason the author expected we already are close to the natural maximum. If you now expect any additional piece will break the record exponentially: Nope. Snag 2: The 8-piece table base are fervently in the works, don't hold your breath.We have a contender, though: see here on CSE, found accidentally. This would be best asked in a chess programmers community. To my best knowledge, the record holder for this variant is unknown, and it would be quite a feature to repeat all the calculations. Snag 1: If we now play by the 50 move rule, that game would have been drawn long ago.EDIT: Newsflash! Make that 584 (contains a promoted B). I give another with some additional info: see here. The current record holder for the longest mate with ignoring the 50 move rule was implicitely given by Allure in his link: 549 moves.For time and space reasons, though, the table bases are currently known only for 7 pieces at most. For example KQ/K is at most #10 for any position. By listing all mate positions, then working backwards (finding all mate in 1, then mate in 2 etc.), a computer can in principle know the value of any position without a doubt. This is also probably the maximum - there are only so many Black pawn tempo moves and long zugzwang triangulations to give the move to Black, so you won't get much more than 300 moves that way (this even holds with positions which are illegal due to impossible chains of pawn captures). The longest "mate in n" which is also testedly correct (in the pre-computer age there were even longer attempts) is around 300 moves. The answer is "yet unknown, but we have a known current record holder".
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