What partial orders on suits are used in games?

Total orderings are common, though there are a lot of disagreements. In poker (when it's needed) and bridge (when bidding) the ranking is clubs < diamonds < hearts < spades. In 500 bidding it's usually spades < clubs < diamonds < hearts.

Trick-taking games switch to a partial order in each trick, where the lead suit ranks above two suits, but below a trump suit.

Are there any games that exhibit the diamond partial order? Or other idiosyncratic orders?

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taken from the birdsite:
J D Hamkins today points to an imop philosophically interesting discussion about the role of Zorn's lemma at

https://mathoverflow.net/questions/436346/zorns-lemma-old-friend-or-historical-relic/