ZZXZMSN

The constructor comment about “double down” as an early theme says this differently, but I noticed that the Roman numerals were the first four powers of 2: 1, 2, 4, 8. Once I had grokked the theme, I think I was expecting 1, 2, 3, 4 (or I, II, III, IV). It feels like THREE as a letter sequence would be hard to find - but I bet one of you will come up with an answer and clue for it.