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You can count past 1,000 on your fingers by using binary, instead of just 10
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Worst hypothesis, even if counting just to 8, you're still using a single hand, so it's an improvement over counting to 5 with fingers. Couple it with the other hand and you're counting up to 64.
There's also the Chisanbop method @hesh@quokk.au mentioned, for that your unbending joint shouldn't be an issue, and it allows you to count to 9 with a single hand (99 with both).