[peter-ebert]

Thanks I'll correct, I didn't know you could adjust the symbols as you go with arithmetic coding, got an example of that?

[foobarqux]

I think you could just have a different code for each given index and all the symbols seen until that point.

This seems to do something similar: https://en.wikipedia.org/wiki/Context-adaptive_binary_arithm...

[peter-ebert]

fwiw I was using the same math they did here to get 4.755 bits: https://en.wikipedia.org/wiki/Arithmetic_coding#Sources_of_i... [-(1/3)log2(1/3)-(1/3)log2(1/3)-(1/3)log2(1/3)]*3=4.7548

[foobarqux]

I think you are confused about probabilities and realized frequencies. A probability is a before-the-fact model. A realized frequency is an after the fact observation. If you flip a fair coin the probability of heads or tails is 50% but any given single flip will have a frequency of 1 for either heads or tails and 0 for the other. (What is true is that as you flip the coin a very large number of times the actual ratio you will see will approach 50/50 but that's definitely not true for say 8 tosses. This is called the asymptotic equipartition principle but it isn't really relevant here).