Well, you're correct about the formula not being accurate because I ignored chains longer than 9. However, the amount of 10-chains is pretty small compared to 9-chains. I did some testing which showed that the amount of 10-chains is only about 2% of the amount of 9-chains.

Wow I didn't know 10-chains are that rare. Thanks for pointing it out. My own mining gets at least 5% because I happened to spot a few blocks were 10's.

I wonder what the distribution of number of blocks so far found from length 7 to length 13 is, and how it is related to the intrinsic Cunningham chain length distribution (of number of chains vs length), which is constant and has scientific value. At any difficulty the instantaneous distribution of found number vs. chain length is the intrinsic distribution multiplied by a miner length preferrence profile averaged across the whole network (at that moment). To get the average miner response profile, we have to know which miner are producing how many chains, which is not eazy to measure.