You are right -- there are no Self laundries on the Nieuw Amsterdam.
You have a choice of sending out laundry and paying piece by piece -- very expensive, or laundry by the bag -- $20 for as much as you can stuff into a bag, or unlimited laundry -- usually about $7 per day.
Thanks Krazy Kruizers for the info. I'll be doing a 2 night Pre Stay in Vancouver before the cruise. Looks like I'll have to send out some laundry. At least Princess had Self laundries on the ships that I have sailed on.