On behalf of a colleague doing Chinese studies I would like to ask if anyone happens to know Indian dice of a shape similar to the Chinese ones in the attachment. They have been used for divinatory purposes by Buddhists since the 6th c. CE, so Indian influence seems at least possible. Here is a description of how to produce them (Zhancha shan'e yebao jing 占察善惡業報經, T. 839, 902b23 ff.):

善男子！欲學木輪相者，先當刻木如小指許，使長短減於一寸，正中令其四面方平，自餘向兩頭斜漸去之。仰手傍擲，令使易轉，因是義故，說名為輪。又依此相，能破壞眾生邪見疑網，轉向正道，到安隱處，是故名輪。Good man! The ones who wish to learn the divinatory method of the wooden tops (lit. "wheels"), they should first carve a branch about as big around as a little finger, making it less than one cun [10 cun = 1 chi 尺; 1 m about (3-)4 chi, so less than 3 cm] long. Right from its middle they should let its four sides each be even [i.e. In the center, carve it into a square shape] with the slides sloping inward toward the two ends. They should raise them in the hand and throw them so that they revolve easily. This reason explains why they are called "top/wheel". Moreover, relying upon this divination one can destroy the heretical views and net of doubts of sentient beings, [causing the person] to turn toward the Right Way [so that] they arrive at a place of safety and security. For this reason it is called a "top/wheel".