Section 11 of the whitepaper answers a precise question: if an attacker controls a share of the hashing power and secretly mines a rival chain, how likely is it to catch up with the honest chain once your payment is z blocks deep?
The odds fall fast
The answer drops exponentially with each block. With 10 percent of the hashrate, the attacker's chance of catching up from 6 blocks behind is about 0.02 percent. With 30 percent, it takes 24 blocks to bring the chance under 0.1 percent.
- Attacker with 10% of hashrate, 6 blocks deep: about 1 chance in 4,000.
- Attacker with 30%: 6 blocks is not enough for that level, about 24 are needed.
- Attacker with more than 50%: no number of blocks is enough.
Six blocks, about an hour, became the convention for large payments: a cautious margin against any realistic attacker. Exchanges often ask for fewer on small deposits and more on very large ones.
▶ SEE IT IN THE MACHINEThe calculation is in the paper standing at the back of the hall, section 11, Calculations.