Hi,
The great expert on this type of objects is Bill Neal:
He has also published several brochures about these mother-of-pearl gaming counters, which were especially appreciated in the 18th and 19th centuries in Britain. British families used to order sets (with initials or coats of arms incised) in China. Bill could even identify certain families. Usually you needed three types: jetons (usually round), fiches (elongated or in the shape of a fish) and contrats (rectangular), for playing at card games such as Whist, Boston, Pope Joan etc.
You find more info in: Vincent Lieber (ed.), Jetons de nacre et boîtes de laque, Château de Nyon 2017
as well as in
U. Schädler/Th. Thomsen (eds.), Crossing Games, Journeys between East and West, Museu Nacional de Arte Antiga, Lisbon 2022, the chapter by Vincent Lieber, "Mother of pearl gaming counters and games boxes: a precious trade", pp. 84sqq.
Cheers
Ulrich