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Title: math problem - probability of finding a block Post by: xorxor on March 24, 2013, 10:17:22 PM well, I would consider my self an advanced user and a maths geek but i failed to find an answer so I post in a newbie section, cause I feel like one now :(.
what is probability to find 60 blocks in a time that all calculators guess 183blocks should be found? in all time of the test there was no change in difficulty. I think it should be like 1/100.000 but these functions are very unintuitional so it could be 1/500 and 1/10000000000000000000. Title: Re: math problem - probability of finding a block Post by: hybrid on March 24, 2013, 10:28:51 PM well, I would consider my self an advanced user and a maths geek but i failed to find an answer so I post in a newbie section, cause I feel like one now :(. what is probability to find 60 blocks in a time that all calculators guess 183blocks should be found? in all time of the test there was no change in difficulty. I think it should be like 1/100.000 but these functions are very unintuitional so it could be 1/500 and 1/10000000000000000000. Try rephrasing your question. I'm not sure I understand. Title: Re: math problem - probability of finding a block Post by: DannyHamilton on March 24, 2013, 10:56:29 PM Am I understanding your question correctly?
Given 1830 minutes. With the assumption that the average time to find a block is expected to be 10 minutes, it would be expected that 183 blocks would be found in this time. You are asking what the chances are that exactly 60 blocks are found in that time, yielding an actual average of 30.5 minutes per block? Title: Re: math problem - probability of finding a block Post by: xorxor on March 24, 2013, 11:06:05 PM Am I understanding your question correctly? Given 1830 minutes. With the assumption that the average time to find a block is expected to be 10 minutes, it would be expected that 183 blocks would be found in this time. You are asking what the chances are that exactly 60 blocks are found in that time, yielding an actual average of 30.5 minutes per block? no. that would be impossible to calculate, cause you cant calculate who will buy how many new GPU's, who will deliver asic and when so no. lets say i have 8.7Thash pool. its a perfect 8.7Thash , all the time no new users , no downtime, no ddos, perfect 0% stale 8.7Thash - shoud be 4575btc -183blocks in a week in current diff. what is the chance to find 60 blocks in a week. what is a chance of being so ultra super unlucky - that is possible to calculate. the 8.7T number is imaginary, just to be compatibile with my 183 blocks question. Title: Re: math problem - probability of finding a block Post by: organofcorti on March 24, 2013, 11:13:22 PM If the expected rate of block arrivals in a given time interval is 183, then the chance of 60 blocks or fewer arriving in the same interval is 3.325578e-26.
http://en.wikipedia.org/wiki/Poisson_distribution Title: Re: math problem - probability of finding a block Post by: xorxor on March 24, 2013, 11:18:40 PM i understand a 3 times to long search for a block is nothing weird, should be 1 in 20 blocks on average.
but 60 times in a row? its like (1/20)^60 = 8,67e-79 but I'll take your 3.326e-26. stil impossible and not mine , so better in discussion I'm about to start. thank you! Title: Re: math problem - probability of finding a block Post by: organofcorti on March 24, 2013, 11:58:53 PM i understand a 3 times to long search for a block is nothing weird, should be 1 in 20 blocks on average. but 60 times in a row? its like (1/20)^60 = 8,67e-79 but I'll take your 3.326e-26. stil impossible and not mine , so better in discussion I'm about to start. thank you! This might be a bit more useful for planning - if 183 blocks are expected in a week, then for 99.9999% of weeks the range of blocks solved per week will be in the order of 126 to 246. If you're planning for a pool (and it wasn't just an example), remember difficulty. Title: Re: math problem - probability of finding a block Post by: xorxor on March 25, 2013, 12:07:53 AM no no, im not planning a pool. i just wanted to know is it possible to be that unlucky before i make claim that it's not. but i failed to be able to calculate it.
60 blocks in 183-blocks-time is like a: 1000 worlds, each has 1000 planets, every one has 1000 cryptocoins run on average by 1000 identical pools for one crypto. after a milion years of hashing, chance for one of this pools to be that unlucky for just a brief moment, is below 0.00000001 so i count that as - impossible! and that was what i wanted, possible or not. Title: Re: math problem - probability of finding a block Post by: organofcorti on March 25, 2013, 12:19:26 AM no no, im not planning a pool. i just wanted to know is it possible to be that unlucky before i make claim that it's not. but i failed to be able to calculate it. 60 blocks in 183-blocks-time is like a: 1000 worlds, each has 1000 planets, every one has 1000 cryptocoins run on average by 1000 identical pools for one crypto. after a milion years of hashing, chance for one of this pools to be that unlucky for just a brief moment, is below 0.00000001 so i count that as - impossible! and that was what i wanted, possible or not. Given your above assumptions, the chance would be one in 857, not one in one hundred million (as you've calculated). If you come across a crypto universe as you describe, and you manage to live there for a million years, it might actually happen. In a human lifetime on earth though, probably not. But not impossible - it could happen. |