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You won't be able to search specific users or cards for trading
You'll get a randomized list like Wonder Pick and if you see a card you like, you can make an offer with any card you own.
If the offer is rejected, the trade listing is removed from your randomized list
In the backend, the trade list isn't even real players but a randomly generated list that heavily favors generating low value cards. Whether the trade offer is accepted is RNG as well