As far as I am concerned, Bismarck hasn't got a hope of defeating Yamato, only of escaping and living to fight another day.

No way could Bismarck's horizontal armour withstand an 18.1" shell, and even the vertical armour would likely be penetrated.

Yamato, on the other hand, is designed to withstand 16" shells, so Bismarck's 15" would have a real job to effect a critical hit.

The German gunfire would be more accurate, but the effect of the Japanese shells would be far greater once they did hit.

My parallel with this hypothetical battle would be the opening stages of the Battle of the River Plate, between Graf Spee and the British heavy cruiser Exeter.

The difference between gun calibre is the same, three inches, and the difference in displacement is roughly similar (as a ratio).

Exeter: 6x8" guns. Graf Spee: 6x11" guns.
Bismarck : 8x15" guns. Yamato: 9x18" guns.
Exeter: 9000 tons? Graf Spee: 12000 tons?
Bismarck: 42000 tons Yamato: 64000 tons.

Graf Spee, despite some inefficient splitting of her main battery between Exeter and the two light cruisers, still managed to devastate the Exeter - although the British ship remained afloat and made it back to harbour.

I suggest that the result between Bismarck and Yamato would be similar to this. Bismarck would score several hits on Yamato but probably fail to knock out any of her main turrets, and Yamato would knock out most of Bismarck's turrets but probably not sink her with a single critical hit.

Yamato's turret faceplaces (front plating) were completely impenetrable, even by her own guns.