Bitcoin Forum

(Nothing in this post except ultra simple math - feel free to skip it if you already know how many blocks take more than 53 minutes to be mined)


I just happened to spot this block (http://blockchain.info/block-index/324520), 53 minutes after it was created. There was no other block in site ... 53 minutes without any blocked being mined.

Wondered a bit about what the odds for this event are. So here are my (very simple) calculations, in case you were curious.

1. I dug up this old question (http://bitcoin.stackexchange.com/questions/4690/what-is-the-standard-deviation-of-block-generation-times), which reminded me Bitcoin block times followed the exponential distribution (http://en.wikipedia.org/wiki/Exponential_distribution). It's basically like radioactive decay - each block has a "halflife time" of 10 minutes.
2. Realized that gamma = 10 minutes, and inputted 53 minutes into the cumulative distribution function.
3. Got 1-(e^-53/10) = 0.005

So, about 5 out of every 1,000 blocks take > 53 minutes to confirm. Nothing unusual about spotting a block like this every now and then.

A few interesting numbers:

1. The chance a block is not found within 10 minutes = 36.7%
2. Not found within 20 minutes = 13.5%
3. 30 minutes = 4.9%
4. 40 minutes = 1.8%
5. 50 minutes = 0.67%
6. An hour = 0.24%

(Divide by e = 2.718 to get the next number in line)

This part is factually incorrect. What half life means is that given a sample of radioactive material, half of it will have disintegrated in that time. This is not the case for BTC blocks at all, probably l'Hospital would be more adequate to calculate likeliness of blocks not being solved in 10 minutes (they have 1/diff chances to be solved each hash, so after diff hashes their chances to be solved are X).

Hence the double quotes.

I wrote half life in quotes. It is not exactly like half life, but it is analogous.

Imagine a million parallel universes all identical to ours (except for the seeds of random number generators in miners' computers).
After ten minutes from now, in exactly 1/e of these universes a block is not found, and in (1-1/e) of them, a block is found.

Technically 10 minutes isn't a half life, but rather

x = -ln(1/2) * 10 minutes =  6.931 minutes.

Each 6.931 minutes, in half of the universes (at least one) block is found, and in half of them no block is found.
(Thanks for pushing me to review this)

Not a math wiz...

shouldn't the network hashrate of something to do with the percentages?

So I should assume that network hashrate is a constant during these calculations?  perfect to keep a 10 minuter per block avg?


Cause my thoughts are, if half the miners dropout, a block will take longer to find with the same diff....yes?

sometimes i happened to make payment and exactly then such a block comes up :)

In one of those universes, a block will take 1 year to solve  :D

So it should happen roughly 10 times every difficulty period, not too unlikely.

I wonder how often this occurs though


EDIT: Fairly often I guess


Silly timestamps.