If I understand it correctly, this paper:
https://bitcoin.org/bitcoin.pdfon page 8 argues that the probability of an attacker generating an alternate chain depends on the number of confirmations (z), not on the time between confirmations. Is the analysis wrong?
I believe that paper is referring to the likelihood per attack. If the attacker has 10% hashrate and confirmation time is 4 blocks, they have a 1% chance of a successful brute force attack. If there are ~10,000 blocks per hour, they could have thousands of tries.
The first results at the top of page 8 would be the case of an attacker having 10% of the total hashrate. The calculated result is that if you have four confirmations (z=4) then P=0.0035, i.e., the probability of a successful attack is 0.35%. With six confirmations the probability of a successful attack drops to 0.02%. With ten confirmations the probability of a successful attack is 0.0000012 or about one in a million.
Note that this is independent of the confirmation rate. You can make the confirmation time as short as you want, and the analysis is the same.
You may be right banana, I had never really looked at that equation. If I was wrong, I can own that. Still, this idea that a confirmation of a minute vs 10 minutes. The block size is about to go to 20MB, can you imagine a 1 minute block time with 20MB block? It would cause so many forks.