The Battle of Plataea was the decisive ground battle during the second Persian invasion of Greece. It took place in 479 BC near the town of Plataea in Boeotia, between an alliance of Greek city states, including Sparta, Athens, Corinth and Megarida, and the Persian Empire of Xerxes I. For lack of a clearer picture of the situation Mardonius was led to a strategic operational error, but we believe he could still have tactically won if he had better employed his main forces, that is, his cavalry (not dispersing it). and the historically cited elite infantry, which we will consider to be one of the Immortals divisions, probably ceded by their king and father-in-law for the continuation of the ground campaign. In the simulation it will be considered that the Greek device was unbalanced by the confusing nocturnal withdrawal, relying on the shocking action of the hoplite masses, particularly from the Spartan East Wing, to balance and / or reverse the situation the following day. The equilibrium of the Persian device will be based above all on the hold of the opposing wings by the infantry, allowing penetration through the center and subsequent overflowing of the flanks, by the cavalry and the heavy infantry (the “Immortals”).