[ChrisV]

I don't really see what your point is?

So what if they're often betting opposite ways? If we combine their information, then on hands where they're betting opposite ways, they both have an exactly even money bet. On hands where they bet the same way, they each win slightly more than double what they won on their own (the "slightly more" part is counterbalanced by the fact that they are more likely to have seen opposite color cards).

There's nothing paradoxical about different pieces of incomplete information recommending different plays. That's why it's incomplete.

Of more interest to me (and I think more "paradoxical") is something I realised when typing the above. If the player who can see the bottom card started being able to see the two bottom cards instead, then even though his information is doubled, his earn per hand would only increase very slightly. This is because when he sees one red and one black, his information is useless and he has no edge at all. The other 50% his earn more than doubles, but he can only bet half his hands, so his earn per hand doesn't benefit much. Interesting that the value of the information decreases so drastically.