I play chess often, and I always noticed how pawn structures are very similar to the way that medieval battle formations worked, with pushing and flanking ect.
Was chess invented to help teach medieval, roman, or antiquity generals about battle formations, or was it used soley as a fun game that generals would sometimes play to pass the time.
Chess was likely invented in India in the 7th century CE. The name, chaturanga, translates to "four divisions of the military" (pawns were infantry, knights were cavalry, bishops were chariots, and elephants were rooks). After invention, chess was primarily played by members of the nobility, in India and later Persia. While you can certainly expect crossover between nobles and military commanders, our sources simply state that chess was played for leisure.
The best source on this remains the old, but good book by H. J. R. Murray entitled A History of Chess (1913).