So how could you possibly coordinate on a tie-breaking strategy?

I'd use alphabetical ordering, and assume my opposite would too. So clubs would come before spades, black before white, etc.

Now, if your opponent doesn't use the same language (or doesn't use a language, only unicode symbols), it almost becomes a game of chance, like "here's an aarvark and a wapiti, the same animals have been shown to some (non-english speaking) Chinese guy, you each get to choose one, if the two of you choose different ones you get a hundred bucks".