yes thats correct now i understand.
but for exemple, ian coleman says thats 1.67 bit per event meanwhile the other site says its 2.58. so can i assume its an error?
Yes, the average entropy is 1.67 and that's because you have:
1 bit x 2 outcomes + 2 bits x 4 outcomes = 10 bits / 6 outcomes = 1.67 bits on average.
The 2.58 is curious.
The only thing I can think of is that log2(6) = 2.58.
When thinking in bits, the maximum entropy you can get is log2(n) where n is the number of possible outcomes.
Log2 (base 2) is because you basically transform the inputs into 2 outputs (0 or 1).
But, 2.58 can't happen because actually the maximum entropy you get by the dice rolls is 2 (for 4 out of the 6 outcomes).
Sorry but I am not strong in math, but I think we 've covered your questions.