On paper at least, Yamato's deck armor is proof against 15 inch shells like Bismarck and Hood were armed with. There is no realistic way for either to properly defeat Yamato at longer rangers...while Yamato's guns can quite easily wreck Hood or Bismark at those ranges. Assuming she hits that is. Supposedly she can hit a battleship sized target at very long ranges. Even farther than Warspite and Scharnorst (which share the longest ranged hits at 24km.) Yamato opened fire at 37km at Samar. Yamato did argueably disabled an American escort carrier at 31km with a near-miss (shell exploded under the keel). Some count it as a hit and some don't. The shell reportedly hit the a crane or graised the side of the hull, and splashed into the water, then exploded under the hull, doing a lot of damage to the carrier. Enough to make her unusable as a carrier until they could get her home to be fixed. The evidance that it was Yamato comes from that there were only a few Japanese ships that could even shell at that range. And only one of them had six shells per salvo when steaming straight at the Americans. Kongo, Haruna, and Nagato all have four guns forward. Yamato has six. Also the Japanse used dyes in their shells. Kongo was yellow that day and was probably the most accurate of the Japanese ships at that fight. Yamato's were pink.
Are we assuming Yamato has her rudders jammed as badly as Bismarck, or is she just fine (but low on fuel so she can't just go out raiding, but must make for France)? Maybe engine trouble or economic steaming to keep her from outrunning the British?
Against KGV and Rodney? The 14" guns on KGV are not good at long range verses Yamato. Rodney's 16" guns have a chance. If the Royal Navy closes in like they did with BismarcK? That is asking for trouble. Yamato's armor isn't foolproof, but KGV, even as a new ship, is way outclassed. Rodney, being older and one of the Big Seven (with the Nagato and Colorado class ships armed with 16 inch guns in the 1920s) can cause damage and her armor is very good. But even British armor is not proof against 18.1 inch cannons at those ranges. If the British ship had trouble sinking Bismarck with shells and torpedoes, they are going to have even more issues sinking Yamato. It is not impossible, but you probably don't want to be in anything on the British side of things unless it is Rodney. If Yamato is practising fire to hit under the waterline? Yeah, that is probably not a good day to be British. They might still win due to numbers and deturmination. But Yamato in this case can only fight if it can't run. It isn't like Samar were it can turn around and go home. The Royal Navy is in the way.
Are we assuming Yamato has her rudders jammed as badly as Bismarck, or is she just fine (but low on fuel so she can't just go out raiding, but must make for France)? Maybe engine trouble or economic steaming to keep her from outrunning the British?
Against KGV and Rodney? The 14" guns on KGV are not good at long range verses Yamato. Rodney's 16" guns have a chance. If the Royal Navy closes in like they did with BismarcK? That is asking for trouble. Yamato's armor isn't foolproof, but KGV, even as a new ship, is way outclassed. Rodney, being older and one of the Big Seven (with the Nagato and Colorado class ships armed with 16 inch guns in the 1920s) can cause damage and her armor is very good. But even British armor is not proof against 18.1 inch cannons at those ranges. If the British ship had trouble sinking Bismarck with shells and torpedoes, they are going to have even more issues sinking Yamato. It is not impossible, but you probably don't want to be in anything on the British side of things unless it is Rodney. If Yamato is practising fire to hit under the waterline? Yeah, that is probably not a good day to be British. They might still win due to numbers and deturmination. But Yamato in this case can only fight if it can't run. It isn't like Samar were it can turn around and go home. The Royal Navy is in the way.