It was only as an adult that I realised nobody around me counted this way. You are the first person I have found who talked about this method, so I am glad to find this comment of yours.
255 if you use both hands!
More like 1023 if you also use thumbs but I prefer to use them as carry, overflow bits.
It's so natural, useful and lends well to certain numerical tricks. We should explicitly be teaching binary to children earlier.
When I was a kid I relized that I can count the fives on the right hand (1 finger for each 5 on the left), which brought me to 25.
It is only when I was traveling in Asia and watched people on markets that I realized that I can use my thumb to count my 12 other finger phalanges, which brought the total to 144. You just need to know your multiplication table of 12 :)
This gives you the range 0..99. Sweeet.