Quote from: deepceleron on January 12, 2013, 10:15:48 PM

Quote from: Meni Rosenfeld on January 12, 2013, 09:20:32 PM

Quote from: deepceleron on January 12, 2013, 09:12:35 PM

I misread the first post initially and did some incorrect math but still demonstrates this is a relatively likely event.

The probability of one block taking 127 minutes or more (simplified):
2^-12.7 = ~ 1/6654 = average one in 46 days worth of blocks

It's not 2^-12.7, it's e^-12.7 = 1 / 327748.

This is an example for an event that will probably not happen in 4 years, but still has a reasonable chance.

My result above is a binomial simplification of mining:

The probability of a block being solved after 10 minutes: 50%, or 1/2

The probability of a block not being solved after 10 minutes: 50%, (1/2), or 2 ^ -1
The probability of a block not being solved after 20 minutes: 25%, (1/2)*(1/2) = 1/4, or 2 ^ -2
The probability of a block not being solved after 30 minutes: 12.5%, or 1/8, or 2 ^ -3
....
The probability of a block not being solved after 127 minutes: 2 ^ -12.7, or ~0.015%

It's not a "simplification", it's just wrong. The probability of a block being solved within 10 minutes is not 50%, it's 63.21%. The probability that a block will take more than x*10 minutes to solve is exp(-x). 10 minutes is the mean, not the median.