User blog comment:Deedlit11/Googology in Magic: the Gathering/@comment-5150073-20130412144609/@comment-1605058-20130413122051

I don't really understand your argument, but n-state machine doesn't have to be bounded by recursive ordinal. There exist universal Turing machines able to simulate (indirectly, of course) machines with more states. So ordinal corresponding to them can be no smaller than w_1^CK.