What did a medieval royal laundress earn?
5 pounds a year.
About $1,100 a month in today's gold.
A month of that pay weighs about as much as 2 dice in gold.
Five pounds a year to wash the royal nursery's linen.

Where the money came from
In 1424 the king, Henry VI, was a child of two. Born at Windsor, he had become king before his first birthday. That year the council gave his household a budget of 10,000 marks, half of it from the taxes on wool. The women servants of his chamber are named in the royal records: Margaret Brotherman, Agnes Jakeman and Matilda Fosbroke, his daily nurse. A laundress served beside them, but no one wrote down her name. Each received £5 a year, the same as each of the minstrels the boy king kept on from his father's household. Joan Astley, probably his nurse since birth, had just won a rise from £20 to £40, eight times the laundress's pay. The household book of a later king, Edward IV, shows how a royal laundry worked. Two men ran it. They fetched the king's linen, washed it tenderly and handed every piece back, or paid for any that was lost. They drew white, grey and black soap from the household's spice store and gathered ashes from every chamber and kitchen of the court. In their busiest times the laundry's staff shared six loaves, four dishes from the kitchen and three gallons of ale a day. If there was a queen in the household, women laundresses served her chamber.
Sources: kinghenryvi.com · kinghenryvi.com 2 · kinghenryvi.com 3 · archive.org
What a royal laundress's pay bought in 1350
a gallon of ale: less than a day's pay
a plough: 6 days' pay
a fur-lined garment: 4 weeks' pay
a year at Oxford: 23 months' pay, more than a whole year of it
a craftsman's townhouse: 3 years' pay, more than a whole year of it
Every price of 1350, with its source, is on the prices page.