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No, you can’t break through the Spartans with cavalry unless you use archer-cavalry. In general, you can use a combination of experienced catapults with regular stones and a massive charge of infantry, such as principes or legionary cohorts. The catapults disrupt the formation, the infantry fires, then the catapults stop firing, and the infantry engages in melee combat. If they don’t break through, cavalry can flank them.
