Poisson Process

A Poisson process is a statistical model where events happen independently at a constant average rate but with random timing. Bitcoin block discovery is a near-perfect Poisson process - each hash attempt is independent, the probability of finding a valid block is constant given the current difficulty, and the resulting block arrivals follow an exponential distribution.

What this means in practice:

• The expected time between blocks is 10 minutes, set by difficulty retargeting.
• The actual time between any given pair of blocks is random. Half the time it's under 7 minutes; about a third of the time it's over 12 minutes; a few times a year a block takes over an hour.
• There's no "due" block. A 30-minute gap doesn't make the next block "more likely soon." Each second of hashing is independent of every prior second.

Why this matters for users:

• Block time variance is normal. People who see a 50-minute gap and worry the network is broken are misreading the statistics. The network is fine; the variance is built in.
• Confirmation count matters more than wall-clock time. For settlement security, the question is "how many blocks have been mined on top of my transaction," not "how many minutes have passed."
• You can compute probabilities. Given the network's current hash rate, you can calculate the probability of a block appearing in the next N minutes, of N blocks in 1 hour, of zero blocks in 1 hour, etc. All standard exponential-distribution math.

For miners, the Poisson nature of block discovery is the source of revenue variance - and the reason pooled mining is so popular. Solo mining means your revenue is one big lump every N months with a giant variance window. Pooled mining smooths the Poisson distribution into a steadier income stream.

A "Poisson process" is the technical name for "random independent events at a constant rate." Bitcoin is the most famous real-world example of one.