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Title: z Post by: znort987 on May 11, 2012, 11:02:10 AM z
Title: Re: Does variance stay constant as difficulty increases ? Post by: Pieter Wuille on May 11, 2012, 11:09:43 AM Assuming the actual hash speed of the network is constant for a longer period of time (which isn't true, but we can approximate), the time between blocks will always have the same distribution, regardless of the actual hash speed.
Title: Re: Does variance stay constant as difficulty increases ? Post by: kjlimo on May 11, 2012, 11:11:09 AM I'm shooting from the hip, but I'm leaning towards same.
I'm thinking about it from a bell shaped curve of time to solve next block. The shape of that curve (centered around 10 minutes) wouldn't change if there where 10,000 comps with a difficulty X or 1,000,000 comps with difficulty 100X. Title: Re: Does variance stay constant as difficulty increases ? Post by: Hawkix on May 11, 2012, 11:33:55 AM I have similar, slightly different, question:
Imagine you are very slow miner and at the start, the difficulty is so that you get 3 months estimated till you find a block. While you mine for the block, the difficulty keeps to increase each 2 weeks. Your chance to find block in next moment slowly rises due to distribution function, but also lowers as the difficulty goes up. I am not mathematician, but it looks like there may be situation when your chance to find a block actually lowers as the time progresses, so you have high probability (higher and higher) that you will end up with nothing. Am I right or do I miss something? Title: Re: Does variance stay constant as difficulty increases ? Post by: Pieter Wuille on May 11, 2012, 11:45:43 AM The actual distribution is an exponential distribution (http://en.wikipedia.org/wiki/Exponential_distribution), with lambda=1/600s (assuming difficulty is properly adjusted to the actual hashrate). This follows from the fact that block mining is a Poisson process (every fraction of time has the same, independent, chance for having an event).
Note that this is an idealized assumption: network delays cause the seconds immediately after a new block have a lower chance for producing a valid non-stale block. Also, I'm talking about actual block creation times, and not the times reported in their timestamps. Certain pools fiddle with these timestamps to increase the time work remain valid - they can, but that probably means the distribution is different when looking at timestamps (for example, it can be negative). In summary, under idealized assumptions, the shape stays identical. |