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Nominally it should take 14 days to find this many blocks, but how long does it really take? This time around the goal is to work out how long it takes to find blocks. To work out the behaviour I wrote a Monte-Carlo simulation that models the behaviour of mining during a block period.
The simulation was run 10 million times in each run shown here in order to get good smoothing of the data. As we'd expect, the average time to find blocks is indeed 14 days. Previously , I've talked about how Bitcoin hashing is a Poisson process. Towards the end of the difficulty change we're going to see blocks being found faster than at the start.
The observation is, of course, quite correct and the simulations here now account for that. The assumption is that hashing capacity comes online at a steady exponentially expanding rate, so, say, the hashing capacity assumed at 5 days is larger than that at 4.
Another complication is that the current difficulty level doesn't really indicate the the actual hashing rate of the network even on the day it's first set. In the article, " Lies, Damned Lies And Bitcoin Difficulties ", I showed that a more accurate starting measure was to multiple the new difficulty by the square root of the difficulty increase. The simulations account for this too. It also equates to a difficulty increase of This equates to a difficulty increase of It's interesting to note that doubling the hashing rate expansion per day doesn't correspond to doubling the next difficulty change because we get to the next change quicker and thus compensate faster too.
The numbers also have an interesting implication for the block reward halving dates though as the dates move closer all the time. It's worth noticing the effect of noise again. When we see a difficulty change at It could be even more divergent though! Over the last few days there has been much discussion about the GHash. IO mining pool's hashing rate. It clearly has a very substantial fraction but the error margins even across an entire block period are surprisingly large. As ever Bitcoin statistics often lead to more questions than answers!