An NZ Lotto Standard entry is four lines for NZ$8 (NZ$2 per line) twice a week. Each line picks 6 from 1–40 plus a Bonus Ball drawn afterwards. Division 1 (all 6 mains) is around 1 in 3.84 million per line. The First Division prize is fixed at NZ$1 million and Must-Be-Won — when nobody wins for four straight weeks, the prize pool is forced down through the divisions until somebody walks home with the lot.
Adding Powerball is NZ$1 per line. You don't pick the Powerball number — it's drawn from 1–10 alongside the Lotto draw, and your line just rides on whatever number you were assigned. Your chance of matching all 6 mains plus the Powerball lands at roughly 1 in 38.4 million.
Pure expected-value math says the Powerball booster is mathematically rational only when the jackpot crosses a certain threshold (and assuming a single winner takes the lot). At NZ$50M that threshold is comfortably crossed — but on a fresh NZ$10M opening week the odds of a multi-way split mean the actual EV is tighter than the headline jackpot suggests.
Practical advice: if you'd play NZ Lotto either way, the +NZ$1 Powerball is a low-friction lottery-on-top-of-lottery. If you wouldn't play NZ Lotto without Powerball, you're really buying Powerball — and at that point the larger Australian Powerball jackpots (when they're rolling) are sometimes the better dollar-for-dollar bet, even with the steeper odds.
Whichever way you go: stick to entry sizes you'd be okay setting on fire. NZ Lotto + Powerball is a recreation, not an investment.