[Animats]

Yes, as the number of wheels scales up, powered carry becomes necessary.

Another mechanism that's been used is sort of analog - differential gears, with two inputs and one output. Race track totalizators used that to add multiple unsynchronized inputs. Here's one from Adelade.[1] The machines were huge and heavy, but reliable.

(It is a tradition and a contract term in the gambling industry that gambling equipment companies are strictly liable for errors. As a result, that industry builds unusually reliable equipment. GTech once mentioned in an annual report that they paid out about 3% of revenue in error payments.)

[1] https://www.cs.auckland.ac.nz/historydisplays/SecondFloor/To...