you could create a new variant, perhaps with a smaller range of cards, like maybe just the royals in all four suits, where everyone can see exactly how many of each card has been drawn. So you might hold the ace of spades, but you're aware that someone else holds it too. You'd have to take the burn pile in to account as well. Perhaps there would be some extra mechanic that burns more cards for every additional player in the game, so even if the ace is out, theres always a decent chance it might be in the burn pile