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davidcyclebackJeff is correct. Hal's bad charecter will keep him out. If he had super numbers he'd have a chance, but he doesn't. Yes, Ty Cobb had bad charecter but he had super numbers.
Whether or not he was caught, I'm sure a lot of people assume Chase bet on baseball or did similar things. They likely figure, Joe Jackson is banned and Chase probably did much worse than Jackson. While Bill James readily admits Chase's great talent at the then essential position first base, the way James describes him in a book Chase might have well been Nosferatu risen from the grave. Duly note, I'm sure the eerie description had as much to due with Jame's bias and artistic flourish as with Chases himself.