BTW, yet another way to do it (more compact than the bitwise and prime options) is the Cantor pairing function https://en.wikipedia.org/wiki/Pairing_function
... z = (x+y+1)(x+y)/2 + y - but you have to sort x,y first to get the order independence you wanted. This function is famously used in the argument that the set of integers and the set of rationals have the same cardinality.
mm. I did see this when I was figuring it out. The sorting first was the specific thing I wanted to avoid, because it would've been by far the most expensive part of the operation when looking at a million poker hands and trying to target several players for potential collusion.