This game is different from the card game Fan Tan.
For the Piecepack Games version, see Piecepack Fan Tan.

Stewart Culin describes it in his book "The Gambling Games of the Chinese in America" as:

"a game usually played upon a mat-covered table, with a quantity of Chinese coins or other small objects which are covered with a cup. The players guess what remainder will be left when the pile is divided by four, and bet upon the result. The name means "repeatedly spreading out," and refers to the manner in which the coins or other objects are spread out upon the table."

The equipment needed to play include:

The playing mat (called the t'an ching)
Coins, buttons, or something that is numerous and can be spread out
A cup or cover for the coins (called a t'an kun)
A rod used to separate the coins (called a t'an pong)

It takes two people to run the game, One is called the "t'an kun" (ruler of the spreading out) and the other one is called the "ho kun" who acts as a cashier.

Culin writes that the game is believed to have been invented by Kwan Chung, a renowned statesmen of antiquity who died in 645BC. Culin also mentions the likelihood that the game was invented for soldiers as a way for them to pass the time in camp.

This game is identical to the Phillipine game Capona.

This Japanese website has some great pictures of Fan Tan and its parts.