Almost none.
She had a grossly inadequate screen (1 CL, 8 DD), very poor gunnery control and a even worse record in combat (an Iowa would have sunk every ship in Taffy three in about two hours), seriously deficient and variable quality armor (the turret face armor for her main battery was the heaviest armor ever put to sea, while most of her armor, while heavier than U.S. ships in thickness was of poorer quality, similar to the immediate post WW-I RN plate), and even her AP 18.1" shells would have had great difficulty with the American STS plate and its decapping design. Worst of all she would be faced with more enemies than she had main turrets.
The U.S. ships, both the Iowas & South Dakotas, had exceptionally good gun laying and aiming radars, with the Iowa's 16"/50 direction being the best ever attached to a heavy gun. American armor was superior to the IJN, had the ability decap AP shells, and U.S. ships were the only ones ever made with an INTERNAL STS vertical armor plating box protecting the magazines from splinter damage, American armor scheme made U.S. ships much more "survivable" than Yamato. Both American classes had exceptional armor and in virtually the same thickness and effectiveness, with the BB-61 weight difference being due to the larger 16"/50 gun (just the barrels themselves, not including the larger breeches and much larger turrets, added close to 200 tons to the design), greater overall length (+200'), additional secondary armaments, and larger power plants.
Lastly, and perhaps most critically, the U.S. escort would have been far larger, more than capable of holding the small IJN screen at bay and allowing the heavies to deal with Yamato (this specific engagement is just about the only one that would actually justify the money wasted on the CB design since it would be useful for demolishing the enemy light unit at long range). The American ships would also, thanks to both their radar aiming and escorts, be able to fight at close to max range and, if necessary or desired, from behind heavy smoke screening from their escorts.. American AAA and available fighter cover would also mean the Japanese would be denied use of airborne spotting to track fall of shot.
As an aside: The Americans didn't require a back-up plan. Mitscher had ELEVEN carriers (7 CV & 4 CVL) carrying right around 1,000 aircraft, the U.S. send the equivalent of four deck-loads after the Yamato, leaving the remaining aircraft to continue to conduct regular operations in support of the Okinawa invasion. Four hours after the first aircraft took off (and the flight time to the Yamato from the carriers was just about two hours) Yamato went dead in the water; 23 minutes later she capsized and exploded. In other words, it took the aircraft about two hours to send her to the bottom. She sank at 14:23, meaning the Americans could have done it all over again with four fresh deck-loads before the day watch changed.
Mitscher actually asked his screen commander, Willis Lee, if he wanted to take his heavies and deal with her and her escort. Lee declined, more or less telling Mitscher he didn't want to waste the time and effort on Yamato.
