Satoshi's target recalculation off-by-one bug?

[nullama]

I was reading Karpathy's implementation of Bitcoin from scratch in Python, and he commented:

            # recalculate the target at every epoch (2016 blocks), approx 2 week period
            # note that Satoshi had an off-by-one bug in this calculation because we are
            # looking at timestamp difference between first and last block in an epoch,
            # so these are only 2015 blocks apart instead of 2016 blocks apart ¯\_(ツ)_/¯

I think he is actually correct. That number should be 2015, and not 2016, right?

Or is there something I'm not considering?

[gmaxwell]

It was probably actually an off by one bug, OTOH, dividing by one off there is the minimum variance unbiased estimator for that process (it's scaled by (n-1)/n), so in that sense it's the correct measure (perhaps accidentally).

[j2002ba2]

I think it's not off by one bug. It seems, that the genesis block took several days to mine - mined with much higher difficulty - so it was omitted from the difficulty calculation.

[BattleDog]

Gotta love that we're still reverse-engineering decade-old code trying to figure out if the creator was playing 4D chess or just shipping fast and breaking things before that was a Silicon Valley mantra.

Karpathy's Python implementation is solid homework if anyone wants to actually trace through this themselves instead of armchair theorizing.