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Imagine you're playing some casual tennis with a friend ... and all of a sudden SERENA WILLIAMS shows up and asks if she can join in??

That's exactly what happened in San Francisco Sunday night ... when two guys lost their minds when the GOAT walked up to their court.

Williams was taking an evening stroll at Mission Dolores Park with her fiance, Alexis Ohanian, when she decided to make the pit stop ... just to see how the guys would react.

It was cool -- Serena came onto the court and posed for pics -- but she didn't play a full set with the guys because she didn't have the proper footwear.