The author is also wrong when he states, "We used the entire sequence, not just the number of heads", but the the calculation only uses the number of heads and

The author is also wrong when he states, "We used the entire sequence, not just the number of heads", but the the calculation only uses the number of heads and tails, and not the sequence. The calcuation used: > sum[p^12*(1 - p)^8 | p <- [0,0.1..1]] / 11 Does not have anything marking position. You would get the same results with the sequence HHHHHHHHTTTTTTTTTTTT as TTHHTHTTHHTHTTTTHTTH To say "In other words, we’ve shown it’s fine to forget the particular sequence and only count the number of heads after all. What is not fine is doing so without justification." is a confused conclusion from his statements, he hasn't actually justified it, he's just used a calculation that doesn't use position (but he claimed it did) then when it got to the same answer ignoring position then said "so position doesn't matter!". But you would have a hard time believing sequence 1 above was random.