These special offers nearly always consist of cheap off-peak daytickets, costing around 15/18 eur (valid mo-fr after 9.00-all dday sat/sun), BUT there is indeed a very big BUT:
they are NOT sold by NS or train-companies, but as customer-drawers by other shopchains, like supermarket AH, householdgoods Blokker, and today starting 27/9, a drugstore Kruidvat- 13,99, only valid sat/sun. So you need to scan folders and run if they go on sale.
Of course there is an easy way out: many are scalped and resold in the 2nd hand market for a few eur more- on an e-bay owned site named marktplaats.nl (tickets- NS or trein). Some are even arranged to be sold onward (this is illegal) after nr 1 has done his/her trip at a station, so nr 2 can travel later in the day.
That site treinreiziger lists them
Besides that NS itself has an e-shop spoordeelwinkel, where one can nearly always buy cheap-ish off-peak returns (mostly around 18/19 eur), plus some ''consumption'' in a national chain-cookies, sandwich etc. You do not need to use it. There is an even bigger BUT for you Brits: can only be paid using the Dutch banks direct online payment called I-deal.
Then there is that ultimate cheap: the GROUP ticket-which actually only needs at least 5-6 people to have the same Destination-not departure- for around 7-9 eur each. Facebook sites, mostly aiming temp. foreign students have been set up- they gather punters-mostly to populair towns like Ams/Rotterdam etc-you prove online youve paid (1 eur or so more for the organiser) and you get the code with which you can order the e-ticket and print it.
For anyone and aiming tourists-but not advertised at all-is the Holland travel Ticket- 59 eur flex or 39 eur off-peak: valid on ALL publ. transp. where chipcard is taken-incl bus/tram/metro and waterbus. Max return fare in 1 day is around 54/55 eur. Buy from any NS-machine selling tickets-cred cd taken, fee 50 cts more. This was introduced after pressure from parliament to help out the foreigners with this silly chipcard thing.
many Dutch relations can also be bought as e-ticket online by b-rail.be (Belgian rails=NMBS) as this takes cred crd without fee, thus circumventing the foreigner-fiendish attitude of NS.
Currently there is also a special offer for ANy BE station to ANY NL station for just 19 eur/single, 1 day, breaks allowed, not valid on Thalys, midweek: only mon-thur after 9.00. 33% further discount for junior<26. Untill around 5/10.