The family tree
Only two of the seven read a person at all. Filter by what each one is actually looking at.
How much each one is willing to say
The number of distinct readings a system is capable of producing — not what it claims, but what its own machinery can distinguish. Drawn on a log scale, because the range is three orders of magnitude wide.
What they are all made of
The same small kit of counting devices, most of it in place by the Han.
Then the tradition audited its own dice
Liu Yao is the only one of the seven in which anything happens at the moment of asking. There are two accepted ways to cast, and the claim in circulation is that coins make change more likely than yarrow stalks. Add the columns up.
Then we built all seven
A rule that survives implementation is a rule someone else can check. A rule that only survives prose is not. We wrote a working calculator for each of the seven and let the arithmetic argue back.