Mining a block takes 10 minutes in average. But it may take 10 seconds or 10 weeks as well. Did anybody make a calculation, what's the probability that it will take a week to mine a single block under normal conditions (i. e. when difficulty is adequate to the total hashing power)?
I've seen many guesses and opinions about but a real calculation done by someone who understands the subject has not yet been done, or at least published.
It's a trivial calculation, and numbers have been published multiple times.
Mining a block takes 10 minutes in average. But it may take 10 seconds or 10 weeks as well. Did anybody make a calculation, what's the probability that it will take a week to mine a single block under normal conditions (i. e. when difficulty is adequate to the total hashing power)?
I've seen many guesses and opinions about but a real calculation done by someone who understands the subject has not yet been done, or at least published.
Bitcoin mining is a poisson distribution. It is far easier to just use a poisson distribution calculator (online, graphing calculator, mathematica).
In 1 hour the expected # of events (blocks) is 6. The probability that there will be 1 or less is ~1.7%
In 2 hours the expected # of events (blocks) is 12. The probability that there will be 1 or less is ~0.01%
In 24 hours the expected # of events (blocks) is 144. The probability that there will be 1 or less is essentially 0 (4.198 E-61)
Use the right terms, Bitcoin mining is a Poisson
process. The number of blocks in a period of time follows the Poisson distribution.
The numbers are good but I think it is more useful to think in terms of the time until the next block, which follows the exponential distribution. If the average is 10 minutes, the chance that the next block will be later than a day (1440 minutes) is exp (-1440/10) = 2.9 E-63.
As for the original question re a week, that's exp(-7*1440/10) = 1.7 E-438.