I think it isn’t impossible to imagine a theoretical system that maps neatly onto their cards, without falling afoul of the interconnected types of IP law in question. I think it would be impossible to achieve in a real world application, because of the comprehensibility issue. Imagine a spectrum. At one end is a perfect 1:1 card copy. This is perfectly easy to understand, up to being able to play the game. It also stomps all over both copyright and trademark law. At the far end is a free floating pseudorandom reference number. This is probably perfectly fine from an IP law perspective, but absolutely impossible to understand. As you move to make it comprehensible, you move closer to infringement. With something like a game based on an auto parts company they might be able to do it, but for a litigous company whose entire existence is grounded in IP, you couldn’t get close enough to comprehensible before they would have sufficient ammo for a lawsuit.
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