Spoiler for Simple 62.5%I'm not done thinking about this (nor have I really tested the ideas I posted previously), but this came to me in the shower (I'm convinced a large portion of the world's great epiphanies happen there).
The first two cards are throwaways, and the orientation tells what suit the other person will guess for cards 3-26. The suit will be the one that shows up most often (worst case, they all happen 6 times).
For the orientations of 3-26, they give an extra bit to the information for 27-50. So you can get all of those.
Lastly, the final two cards are simple to get as plasmid pointed out earlier.
In the case of a very large, but finite, deck, this would give at least a quarter of the first half, and all of the second half. So worst case is 50%/4 + 50% = 62.5%.
In the case of a regular deck the total is 0*2 + 24/4 + 24 + 2 = 32 cards guaranteed correct = 61.54%
Spoiler for What if
the two throwaways told you what to guess for up and down 3-26? Wouldn't that guarantee at the least half of those cards? Making 0*2+24/2+24+2=38 guaranteed correct or 73.07%?