For betting on Major League Baseball, period. There's a sign in all MLB clubhouses, I understand, that spells this out. If you're managing a team, you can't even bet on a meaningless late season game between mathematically eliminated teams in the other league, the result of which would matter to no one else in that locker room but yourself and wouldn't have any effect on how your team played that day or how you managed the game,Pete Rose was banned for life for betting on his own team.
Rose loved playing the horses, and that was fine with MLB. As far as I know, he could have even bet on Japanese league baseball and not gotten into trouble. MLB is only concerned with the integrity of its own operatiion.