Indeed. See the "bitcoin snack machine" for some hard numbers: https://bitcointalk.org/index.php?topic=423.0

> The network nodes only accept the first version of a transaction they receive to incorporate into the block they're trying to generate. When you broadcast a transaction, if someone else broadcasts a double-spend at the same time, it's a race to propagate to the most nodes first. If one has a slight head start, it'll geometrically spread through the network faster and get most of the nodes.

> A rough back-of-the-envelope example:

  1         0
  4         1
  16        4
  64        16
  80%      20%

> So if a double-spend has to wait even a second, it has a huge disadvantage.

I'm not sure anyone has put the infrastructure into place, though.

That has nothing to do with rolling back or 51% attacks. A racing attack and a 51% attack are different things.

Oh, you're probably right. It seemed related because the further back an adversary wanted to roll back to, the more hash power they'd need to get ahead. But it's a different category.

I wonder if there has been an analysis of how much hash power you'd need relative to how many blocks in the past you'd want to roll back.

That analysis is actually in the original 2008 bitcoin whitepaper:

https://bitcoin.org/bitcoin.pdf

If you have 51% of the power, you can roll back everything if you spend enough time on it. If you have 30%, you have a 4% chance of being able to catch up from 10 blocks behind, even if you spend infinite time on that specific fork.