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My response to the 10 fingers thing is that it's easier to do certain calculations in your head. A lot of those calculations are larger than 10, anyway, so your fingers don't help.
A third of 24 is 8. A third of 60 is 20. It becomes second nature after a while.
One place I used this a lot was 40k. In between rolls, I grouped my dice into sets of 4. When the next roll called for 12 dice, I quickly pick up 3 sets. If it's 10, pick up two sets plus two dice from a third set. Made it really quick to count. At least for the base rolls, a lot of the stats in 40k tend to work in multiples of 4, so this worked out.