Re: SoB, WW and AB
If you're holding a drawing hand, you'll hit it or you won't. If you do, you're likely to beat everyone, if not, you're likely to beat no one. In that case your probability of beating everyone is higher than you get by multiplication.
If you're playing against drawing hands, you could be in a situation where the cards that make one person's hands are different than the cards that make someone else's. In that case your chance of winning is less than you get by multiplication.
Suppose each of the four players has 9 outs on the river. Your chance of beating any one is 1 - 9/38 = 29/38 = 76%. If you raise that to the fourth power, you get 34%.
But if all their outs are different, there are only 2 cards that let you beat everyone, that's 2/38 = 5%. If they're all waiting for the same 9 cards, your chance of beating them all is your chance of beating any one of them, 76%.
The 34% would only be correct if there are 24 cards that beat you. That could be true if each player has five cards that help only him, plus four cards that help everyone. But there's no reason to assume this would be the case.
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