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Mailing cash is scary and risky. Using Bitcoin doesn't remove the risk of fraud, but it removes the risk of your payment being lost/intercepted.

The winners are highly likely to evade taxes but have no need to launder. Money laundering is unnecessary because online gambling proceeds aren't illegal in most states, and even where they are the Silver Platter doctrine and the fact that AGs don't prosecute customers generally makes it not worth while. I played poker for a living in a state where it is illegal to do so and still just claimed taxes legally (which is unusual for a poker player).

any different in terms of anonymity

The idea, in theory, is that the use of BitCoins cannot be tracked by a third party. That is to say, Silk Road, you and your dealer are the only ones who know about the purchase. In theory all three of you do not keep records of the sale, unlike credit card companies, which keep records of EVERYTHING.