Indeed. Shimazu have poor soil but after taking the three Imagawa provinces and building 100% farm improvements, can easily take on the Mori clan, even if they have already WM because he will overwhelm the Mori. But you must not wait too long, because otherwise the Imagawa will have already taken Shinano and have a lot o koku and you will not be able to take as easy as in the first rounds tyhe provinces. I usually make a fast 2YS and 2AS put my daymio in front, bring him in Bungo, because this way Imagawa has to split his forces to protect 2 proveinces that you can invade from Bungo, and for the first assault wich is in the province without the river (i always deal with that last) i bring also for a short time my forces from Nagato, they represent something for the numbers an help in the asault. After I take over his castled province, from where he has the port and can bring reinforcements. Don't forget to have a Mori alliance and resend you initial forces + 1 aditional back in Nagato, otherwise you will lose it to Mori. Last you take Imakava last province from you Iland and you prepare for the only way you can win with the Shiumazu, or the only way I have been able to, quickly make a geisha and start building your aliances with every daymio. After you have alliance wiyth everyone you can start to kill them. This way you will gain rich provinces without losing men. Have fun and welcome to Total War World.
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Believe and the wings of war shall be your guardian. God speed my sword, make my rage my power. Bless the land that has borned and raised me. Purify my soul God, allow me to be the one that rises in the blaze of glory, and let again victory be mine. In the name of Saint Andrew