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Neat. It actually seemed somewhat doable until I thought about it for a second. Assume that you can--by paying attention to pitching matchups--find players on any given day who have a .500 chance of getting a hit (seems about right since the best players average below .400 over the course of a season). To win this, you need to get it right 57 times in a row. So your odds of winning are 1 in 2^57 or 1 in 144,115,188,075,855,872. Even assuming that you can pick people with a .667 chance to hit the ball, your odds of winning are still only 1 in ~10,894,361,101.
Makes what DiMaggio did that much more impressive.
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