Could go either way on this one

Pat Venditte, a junior at Creighton University, is the only ambidextrous pitcher in the NCAA. He uses a custom glove which works on either hand. A reliever, he pitches left-handed to left-handed batters and switches to right-handed for right-handed batters. He pitches more innings than the typical reliever since he has two arms to tire out.

According to the New York Times: "A switch-pitcher facing a switch-hitter could make a fine Abbott and Costello routine. Against Nebraska last year, a switch-hitter came to the plate right-handed, prompting Venditte to switch to his right arm, which caused the batter to move to the left-hand batter’s box, with Venditte switching his arm again. Umpires ultimately restored order, applying the rule (the same as that in the majors) that a pitcher must declare which arm he will use before throwing his first pitch and cannot change before the at-bat ends."

There has never been a switch-pitcher in the modern era of Major League Baseball, although in 1995, Greg Harris of the Montreal Expos did pitch one inning in this fashion, in what was considered a stunt. MLB scouts are reportedly looking at Venditte as a possible late round draft choice.