I've searched around the internet and most just say that it reduces the chances but the exact numbers haven't been declared. For someone who might be developing a Bitcoin payment system or accepting Bitcoin on their website or for a service this should probably be more clear than it is. We should not blindly trust because it is the standard. I do not doubt that the standard has solid reasons I am more intrigued on why we have come up with that magic number. Does 6 confirmations reduce an attack by >99%?
I ask because the wiki is no longer up to date but this information was answered before on there. Take this quote as an example:
Transactions with 0/unconfirmed can be reversed with not too much cost via Finney attack and race attack, but in some cases may still be acceptable especially for low-value goods and services, or ones which can be clawed back.
For transactions with confirmations, the website (https://people.xiph.org/~greg/attack_success.html) can be used to calculate the probability of a successful doublespend given a hashrate proportion and number of confirmations. Note that in the reality of bitcoin mining today, more than 6 confirmations are required. (60 confirmations to have <1% odds of succeeding against an entity with 40% hash power). See Section 11 of the (https://bitcoin.org/bitcoin.pdf bitcoin whitepaper) for the AttackerSuccessProbability formula.
The only problem with this quote is that it talks about more confirmations preventing an attack which I understand but it talks about up to 60 confirmations to fully mitigate the attack so why are we using a 6 confirmation standard when there is still a chance of an attack succeeding is it because it is so low chance that it realistically will never happen? For transactions with confirmations, the website (https://people.xiph.org/~greg/attack_success.html) can be used to calculate the probability of a successful doublespend given a hashrate proportion and number of confirmations. Note that in the reality of bitcoin mining today, more than 6 confirmations are required. (60 confirmations to have <1% odds of succeeding against an entity with 40% hash power). See Section 11 of the (https://bitcoin.org/bitcoin.pdf bitcoin whitepaper) for the AttackerSuccessProbability formula.
The reference https://people.xiph.org/~greg/attack_success.html returns a error and does not have the information any more.
Quote from: https://bitcoin.org/bitcoin.pdf
Running some results, we can see the probability drop off exponentially with z.
q=0.1
z=0 P=1.0000000
z=1 P=0.2045873
z=2 P=0.0509779
z=3 P=0.0131722
z=4 P=0.0034552
z=5 P=0.0009137
z=6 P=0.0002428
z=7 P=0.0000647
z=8 P=0.0000173
z=9 P=0.0000046
z=10 P=0.0000012
q=0.3
z=0 P=1.0000000
z=5 P=0.1773523
z=10 P=0.0416605
z=15 P=0.0101008
z=20 P=0.0024804
z=25 P=0.0006132
z=30 P=0.0001522
z=35 P=0.0000379
z=40 P=0.0000095
z=45 P=0.0000024
z=50 P=0.0000006
Solving for P less than 0.1%...
P < 0.001
q=0.10 z=5
q=0.15 z=8
q=0.20 z=11
q=0.25 z=15
q=0.30 z=24
q=0.35 z=41
q=0.40 z=89
q=0.45 z=340
q=0.1
z=0 P=1.0000000
z=1 P=0.2045873
z=2 P=0.0509779
z=3 P=0.0131722
z=4 P=0.0034552
z=5 P=0.0009137
z=6 P=0.0002428
z=7 P=0.0000647
z=8 P=0.0000173
z=9 P=0.0000046
z=10 P=0.0000012
q=0.3
z=0 P=1.0000000
z=5 P=0.1773523
z=10 P=0.0416605
z=15 P=0.0101008
z=20 P=0.0024804
z=25 P=0.0006132
z=30 P=0.0001522
z=35 P=0.0000379
z=40 P=0.0000095
z=45 P=0.0000024
z=50 P=0.0000006
Solving for P less than 0.1%...
P < 0.001
q=0.10 z=5
q=0.15 z=8
q=0.20 z=11
q=0.25 z=15
q=0.30 z=24
q=0.35 z=41
q=0.40 z=89
q=0.45 z=340
The Bitcoin whitepaper has this information which I assume is related to confirmations but this does not make any sense to me. What is Satoshi trying to say here?