Bitcoin mining is a Poisson process. See this previous post of mine:
Given that in two hours you would expect to find 12 blocks, then the chance of not finding any blocks in two hours is 0.000614%. This works out to a chance of 1 in ~162,755. Given that we get ~52,560 blocks per year, then we would expect a delay of at least 2 hours to happen roughly once every 3 years, on average.
In short, bitcoin is functioning as normal.
As I stated above, bitcoin mining is a Poisson process. You can read about this here: https://en.wikipedia.org/wiki/Poisson_point_process
You can model the distribution using the equation (as given on the linked page above):
P{N = n} = Λn * e-Λ / n!
If you take n to equal 0 (i.e. you won't find a block), and take lambda (Λ) to equal the number of blocks you would expect to find in a given time frame, then you can simplify that equation to
P = Λ0 * e-Λ / 0!
P = 1 * e-Λ / 1
P = e-Λ
Therefore, the probability of not finding a block when you would expect to find Λ blocks is equal to e-Λ. For example, the probability of not finding a block in 10 minutes, when you would ordinarily expect to find 1 block in 10 minutes, is e-1 = 36.8%
Given the equation P = e-Λ, then we can take the inverse to find the probability of finding a block: 1-P = 1-e-Λ. So the probability of finding a block in 10 minutes is 1-e-1 = 63.2%.
So, as I said above, the probability of finding a block in 2 minutes is therefore 1-e-0.2 = 18.1%.
You can model the distribution using the equation (as given on the linked page above):
P{N = n} = Λn * e-Λ / n!
If you take n to equal 0 (i.e. you won't find a block), and take lambda (Λ) to equal the number of blocks you would expect to find in a given time frame, then you can simplify that equation to
P = Λ0 * e-Λ / 0!
P = 1 * e-Λ / 1
P = e-Λ
Therefore, the probability of not finding a block when you would expect to find Λ blocks is equal to e-Λ. For example, the probability of not finding a block in 10 minutes, when you would ordinarily expect to find 1 block in 10 minutes, is e-1 = 36.8%
Given the equation P = e-Λ, then we can take the inverse to find the probability of finding a block: 1-P = 1-e-Λ. So the probability of finding a block in 10 minutes is 1-e-1 = 63.2%.
So, as I said above, the probability of finding a block in 2 minutes is therefore 1-e-0.2 = 18.1%.
Given that in two hours you would expect to find 12 blocks, then the chance of not finding any blocks in two hours is 0.000614%. This works out to a chance of 1 in ~162,755. Given that we get ~52,560 blocks per year, then we would expect a delay of at least 2 hours to happen roughly once every 3 years, on average.
In short, bitcoin is functioning as normal.
Im really numb about this post and I think it's a very nice comment, I'm not well feed in the area of mathematics but I'm wondering how did you come up with the original equation, from the whitepaper or was it self generated, just very curious and if possible I woudl have loved to know more about mining and how it works, maybe more technical stuff, I'm hungry to know deep things about it, maybe a link to older post about mining that woudl educate me about it
