E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Fulhams, or Fullams.
Loaded dice; so called from the suburb where the Bishop of London resides, which, in the reign of Queen Elizabeth, was the most notorious place for blacklegs in all England. Dice made with a cavity were called gourds. Those made to throw the high numbers (from five to twelve) were called high fullams or gourds, and those made to throw the low numbers (from ace to four) were termed low fullams or gourds.
For gourd and fullam holds
And high and low beguile the rich and poor.
Shakespeare: Merry Wives of Windsor, i. 3.
Fulhams. Make-believes; so called from false or loaded dice. (See above.)