I'm trying to understand the formulas for successfully mining a block (without a pool) based on hashrate over time (i.e. to chart the probability of finding a block at various historical points compared to network hashrate at the time).
It seems like this post is exactly the formula I'm looking for, but it doesn't actually add up. I'm awful at math so I can't tell if I'm missing a step or if the post is wrong. If there's a better/more accurate way of figuring this out, please share, but I'm specifically interested in learning if this is wrong or not and why.
It says the probability of being the one to successfully mine a block with 13.5 TH/s and a network hashrate of 11,000,000 TH/s = 0.00000122
Then it says:
Now, in a month, there are N=6*24*30 mined blocks. To find the probability of winning one award in a month, we use the Bernoulli trial formula
N*p1*(1-p1)^(N-1) = 0.0026
Now when I put that in Excel with N=4320, I get .005243, I only come up with the same answer when I divide N by two for N=2160, but I can't figure out any reason for that to be the case. Am I missing something or is this just a typo? Is this formula even a good way of approximating this?