> Alternatively I think instead of displaying a meaningless number we ought
> to go by a percentage (the double spend improbability) and go by
> 'confidence'.


That is a great idea, and not too hard to implement.  A bit of code can
determine over the last N blocks, how many blocks that were at the current
depth of the present transaction were orphaned and divide that by the total
number of blocks solved (orphaned or not) while those N blocks were
solved.  That's the historical number (H), and then the "51% attack" number
(A) can make an explicit assumptions like "Assuming a bad actor has 51% of
the hashing power for 24 hours starting right now, the block holding this
transaction has an X% chance of being orphaned."  Report "# confirmations"
as "99.44% confidence" using [100% - max(H,A)].