For equal chance of all orderings, yes. "Equal chance of going first" is more flexible, though I expect at some point we hit a limit in expressiveness (at leas

For equal chance of all orderings, yes. "Equal chance of going first" is more flexible, though I expect at some point we hit a limit in expressiveness (at least) if we're still using 6 sided dice. I don't know whether any of those can be non-transitive, though. I'd guess that it's sometimes possible but it's only a guess.