DeathAndTaxes
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Gerald Davis


August 30, 2013, 03:34:23 AM Last edit: August 30, 2013, 06:16:10 AM by DeathAndTaxes 

Calculations to support these probabilities? They do not seem accurate to me. That is the great thing about numbers, they don't need to "seem" to be accurate. They either are or they are not. You can compute them yourself and know definitively their accuracy. It's just that you write that as if you know what you talking about, but you clearly do not. So you already know how to calculate and validate or invalidate it.






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FloatesMcgoates


August 30, 2013, 03:49:44 AM 

Assuming you control 10% network hash
As per blockchain.info, there is an average of 7.58 minutes in between each block. Then in a period of 6 hours, 47 blocks would have been found. The possibility that AM found 0 blocks in those 47 is a simple calculation especially given how we are using 10%
(1.1)^47 = .007 , or 0.7%.
There are 120 chunks of 6 hours in a 30 day month. The possibility that at one point or another a 6 hour gap will open during a month is roughly (1.007)^120 ~ .43, or 43%
Not sure why people are arguing over statistics in here given how math is inarguable.




organofcorti
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August 30, 2013, 03:56:05 AM 

There is a ~3% chance of 0 blocks vs 3.6 blocks expected in 6 hours is due to luck. There is a ~1% chance of 0 blocks vs 4.8 blocks expected in 8 hours is due to luck. There is a ~0.2% chance of 0 blocks vs 6.0 blocks expected in 10 hours is due to luck. Assumes AM is operating at 10% of network hashrate (well technically 10% of the hashrate required to sustain the current difficulty), if AM is lower then the chances would be higher. Calculations to support these probabilities? They do not seem accurate to me. Also there are several errors in your post. All results are "due to luck" whether they are much lower than the expected value, exactly the expected value or much greater than the expected value. The word "chances" should be "probabilities." And it doesn't make any sense to say "~3% chance of 0 blocks vs 3.6 blocks." I think you mean to say "~3% chance of 0 blocks when the expected number of blocks is 3.6." Don't mean to be hard on you or anything. It's just that you write that as if you know what you talking about, but you clearly do not. So I don't want other readers to be misled by your post if it is completely inaccurate. Google "Poisson distribution" and then calculate for yourself. D&T is using the PMF here, so it's not hard to calculate for yourself. BTW, you quote "~3% chance of 0 blocks vs 3.6 blocks." D&T actually wrote: "There is a ~3% chance of 0 blocks vs 3.6 blocks expected in 6 hours is due to luck." (my bolding) What he wrote makes plain sense.




DeathAndTaxes
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Gerald Davis


August 30, 2013, 04:04:38 AM 

As per blockchain.info, there is an average of 7.58 minutes in between each block. Then in a period of 6 hours, 47 blocks would have been found.
Good point. I forgot the network is running faster than expected. I assumed 36 blocks in 6 hours.




FloatesMcgoates


August 30, 2013, 04:16:10 AM 

Hmm now that the other guy brought it up I have been thinking of whether bitcoin block mining probability should be calculated using Binomial distribution or Poisson distribution. I'm fairly sure that Binomial is the way to go if we make determinations based on having a fixed % of the network as in this case we have a specific number of trials n (47) and a constant probability p (.10).




Rebelution
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August 30, 2013, 04:23:24 AM 

Wow, 4 people that think they know statistics because they know what a distribution is and can google simple statistics concepts. But really you aren’t thinking critically enough. 1. Why do you guys think that AM’s rate of finding blocks is poission distributed? It is definitely not a poisson process, but I admit that that fact does not preclude its results from being poission distributed. That being said, due to the variance in AM's hash rate that friedcat has admitted, we know that it is not poisson distributed. 2. Many of you are missing a crucial point. The difference between the expected value for a GIVEN 6 hour period is a VERY DIFFERENT question from the probability that 0 blocks will be found in ANY ONE 6 hour period. Allow me to illustrate with an example, and I think even you condescending / smug posters will understand. The probability of flipping a coin 3 times and getting heads each time is VERY DIFFERENT from flipping a coin 50 times a getting a string of 3 heads in a row. I really hope you guys see why... Now, I know thinking is difficult but please try. Now think for an example how this concept applies to this situation. Do you see now? You guys are really my major problem with the bitcoin community in general. At first it seems like a community full of really intelligent people. But the more time you spend, you realize its actually full of condescending people that are pseudointellectuals. You guys think that because you have tons of posts that you are intelligent. But really that is not the case at all. Just because you took intro to stats you think that you know probabilities well, but you guys are misapplying the concepts. On top of that you act like egotistical dbags to people that are trying to help you see the error in your ways. Really concerns me about this community, and bitcoins' longevity... Especially you members with a ton of posts and activity. People assume that you guys are intelligent and know thingscouldn't you at least take a little bit of responsibility? Sorry for ranting, but it really is saddening




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August 30, 2013, 04:24:36 AM 

There is a ~3% chance of 0 blocks vs 3.6 blocks expected in 6 hours is due to luck. There is a ~1% chance of 0 blocks vs 4.8 blocks expected in 8 hours is due to luck. There is a ~0.2% chance of 0 blocks vs 6.0 blocks expected in 10 hours is due to luck. Assumes AM is operating at 10% of network hashrate (well technically 10% of the hashrate required to sustain the current difficulty), if AM is lower then the chances would be higher. Calculations to support these probabilities? They do not seem accurate to me. Also there are several errors in your post. All results are "due to luck" whether they are much lower than the expected value, exactly the expected value or much greater than the expected value. The word "chances" should be "probabilities." And it doesn't make any sense to say "~3% chance of 0 blocks vs 3.6 blocks." I think you mean to say "~3% chance of 0 blocks when the expected number of blocks is 3.6." Don't mean to be hard on you or anything. It's just that you write that as if you know what you talking about, but you clearly do not. So I don't want other readers to be misled by your post if it is completely inaccurate. Do you understand what a distribution is? Yes, do you know how to apply distributions to answer probability questions?




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August 30, 2013, 04:27:26 AM 

Calculations to support these probabilities? They do not seem accurate to me. That is the great thing about numbers, they don't need to "seem" to be accurate. They either are or they are not. You can compute them yourself and know definitively if they are or are not. It's just that you write that as if you know what you talking about, but you clearly do not. So you already know how to calculate and validate or invalidate it. Fair, next time I will avoid being polite and state it more frankly. You do not know what you are posting about, your numbers are wrong, and you are misleading posters that don't know probability and statistics well. The calculations depend greatly on assumptoins, parameters, length of time to view, etc. That is why I wanted you to post your calculations, so as a community we could work through them and arrive at a reasonable result.




FloatesMcgoates


August 30, 2013, 04:28:04 AM 

There is a ~3% chance of 0 blocks vs 3.6 blocks expected in 6 hours is due to luck. There is a ~1% chance of 0 blocks vs 4.8 blocks expected in 8 hours is due to luck. There is a ~0.2% chance of 0 blocks vs 6.0 blocks expected in 10 hours is due to luck. Assumes AM is operating at 10% of network hashrate (well technically 10% of the hashrate required to sustain the current difficulty), if AM is lower then the chances would be higher. Calculations to support these probabilities? They do not seem accurate to me. Also there are several errors in your post. All results are "due to luck" whether they are much lower than the expected value, exactly the expected value or much greater than the expected value. The word "chances" should be "probabilities." And it doesn't make any sense to say "~3% chance of 0 blocks vs 3.6 blocks." I think you mean to say "~3% chance of 0 blocks when the expected number of blocks is 3.6." Don't mean to be hard on you or anything. It's just that you write that as if you know what you talking about, but you clearly do not. So I don't want other readers to be misled by your post if it is completely inaccurate. Do you understand what a distribution is? Yes, do you know how to apply distributions to answer probability questions? Okay genius, if they do not seem accurate why dont you give an "accurate" figure. I am sure you will be able to do so given how you are a self proclaimed expert in such matters.




Rebelution
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August 30, 2013, 04:50:06 AM 

Simple answer: we don't know because AM's hash rate does not conform to any common distributions. Also I am quite comfortable admitting that it is a difficult problem, and other posters on this board could probably make better calculations than me. IMHO Admitting your own limitations is perfectly OK...
But I said 4 posters weren't thinking critically enough, but I was not counting you because I believe your calculation is reasonable. You were the only one to recognize the concept that a GIVEN 6 hour period is different than ANY one 6 hour period.
You assume a distribution function that is not accurate, but it is reasonable. Realistically, given that we know that AM's hash rate is varying (sometimes it is higher and sometimes lower as friedcat as mentioned several times that blades occasionally go down), your percentage is probably too low. But really from any given hash rate estimation (ie 10 blocks found in 6 hours), all you can do is construct confidence intervals about the hash rate. For example, we can say things like, AM's hash rate is likely between 30 and 60 THash/s for a X time period. As you get more data you can improve the accuracy of the hash rate, but the problem with collecting more data is that you now you have an issue with nonstationary data.
We will never know what AM's hash rate was exactly over a given time period, but we can construct reasonable ranges. Just all the pseudointellectualism and misleading of other posters kind of infuriates me, so I apologize if I come off too strong. Its just that the smugness / condescending posts bother me.




DeathAndTaxes
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Gerald Davis


August 30, 2013, 05:05:42 AM Last edit: August 30, 2013, 06:09:09 AM by DeathAndTaxes 

1) Hey Rebelution anyone ever tell you that you are an ass? The only one being smug or condescending is YOU. Try rereading the thread. I don't mind being wrong, I have been wrong a lot in my life. If you're never wrong you aren't learning. At one time I didn't believe pool jumping could affect rewards of static miners in proportional pools. Lots of passionate debates back and forth. Meni had to utterly school me seriously, before I realized I was wrong. It was a great learning experience and better helped me understand block solutions. The point is he provided numbers, scenarios, and counter arguments. You came in and said (paraphrased) "You're wrong the numbers don't seem right to me". Really? That is your way of opening up a intellectual discussion in an nonsmug, noncondescending manner? I would hate to see it when you are trying to be insulting.
2) Bitcoin mining IS a poisson distribution. The fact that you don't believe it doesn't change the fact that it is.
3) You are right we DON'T know the hashrate but we don't need to. If Friedcat supplied more data (like # of hashes for each block and since the last block) we could do a more accurate assessment. Still you may not have noticed I said "for 10% of the network". We can calculate the probability that a theoretical entity with 10% of the network would only find 0 blocks when the expected value is 3.6 in a poisson distribution. That happens to be 2.7% which is why I said ~3%. Similar calculations have been used to ensure a pool isn't cheating its miners.
3a) I did fail to consider the network is operating faster than the target of 10 minutes per block, so it should be an expected 4.7 blocks not 3.6 blocks in 6 hours for an entity with 10% of the network hashrate. I gave credit to that correction.
4) If the probability that an entity would only find 0 blocks in this six hour window is 3%, then there is a 97% probability that the event is because the actual farm deviates from the hypothetical one due to one or more reasons which may be of interest to a miner.
Reasons such as: * the farm has now power or connectivity. * the farm has been forked off the main chain due to a bug and the farm is finding >0 blocks they are just not seen by the rest of the network. * the farm is no longer 10% of the network. * the farm is duplicating work due to a bug (more than one rig looking for the same solution).
Modeling the probability of a hypothetical farm is useful to see just how unusual an event. Miners shouldn't be concerned about variance ("bad luck", "good luck") but not all deviations from the expected are variance. It may be the expected is no longer what is assumed. For example a farm which is offline has an expected outcome of 0 but not knowing that we assume the farm has an expected 3.6 because it is online and has 10% of the network. The lower the probability that the event would occur, the greater the possibility that there is a reason other than variance for the deviation The probability an entity with 10% of the network would find 0 blocks in 6 hours is 3%, however the probability that it would find 0 blcks in 24 hours is 5.5*10^7th. Either one could be due to "bad luck" but I would be more concerned the latter is due to the farm being offline or some other difference which makes the actual farm different than the hypothetical one.




organofcorti
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August 30, 2013, 05:38:58 AM 

Wow, 4 people that think they know statistics because they know what a distribution is and can google simple statistics concepts. But really you aren’t thinking critically enough.
1. Why do you guys think that AM’s rate of finding blocks is poission distributed? It is definitely not a poisson process, but I admit that that fact does not preclude its results from being poission distributed. That being said, due to the variance in AM's hash rate that friedcat has admitted, we know that it is not poisson distributed.
It's a nonhomogenous poisson process wrt time. If the hashrate is kept stable, then it's a homogeneous poisson process with respect to time. 2. Many of you are missing a crucial point. The difference between the expected value for a GIVEN 6 hour period is a VERY DIFFERENT question from the probability that 0 blocks will be found in ANY ONE 6 hour period. Allow me to illustrate with an example, and I think even you condescending / smug posters will understand. The probability of flipping a coin 3 times and getting heads each time is VERY DIFFERENT from flipping a coin 50 times a getting a string of 3 heads in a row. I really hope you guys see why... Now, I know thinking is difficult but please try. Now think for an example how this concept applies to this situation. Do you see now?
Yes, the distribution's CDF is different to the expected value. So? Simple answer: we don't know because AM's hash rate does not conform to any common distributions.
Yes it does. I can prove it with 95% confidence. Would you care to make a bet? I'll place 100 btc of mine against 10 btc of yours that I'm correct, and that: 1. When ASICMiner's hashrate is stable, the number of blocks per time period is a homogenous Poisson process. Blocks per unit time will be poisson distributed and time between blocks exponentially distributed. 2. When ASICMiner's hashrate is not stable, the number of blocks per time period is a nonhomogenous Poisson process. Time between blocks will be only exponentially distributed if the cumulative intensity function is used to estimate a "time stretch", which is then applied to the actual block solve times. So, want to take me up on my bet? You guys are really my major problem with the bitcoin community in general. At first it seems like a community full of really intelligent people. But the more time you spend, you realize its actually full of condescending people that are pseudointellectuals.
On behalf of all pseudointellectual condescenders, I apologise.




Rebelution
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August 30, 2013, 05:45:30 AM 

Response to DnT:
My apologies if I came off condescending. My entire career I have worked with numbers and have a “feel” for probabilities, but I was not totally sure that you were incorrect. I was just hoping you would post your calculations so I could identify the issues. It is definitely a tough problem, so figured would be best to work together.
Normally I would just ignore this error, but please look up the difference between “your” and “you’re.” I mean this sincerely because such blatant errors are red flags for sloppy thinking in the professional world. You state that you are a CEO in your signature, so I am hoping you will take some pride in what you post. Also your sentences are so poorly constructed that it is sometimes difficult to understand your meaning. It is a forum, so minor errors and fragments are expected. But your terrible writing really does make it difficult to understand your meaning sometimes. For example, your “sentence” under 4. It is difficult to interpet, but I will do my best. You should really try using periods and constructing proper sentences. Sentences are truly easier to understand than rambling fragments. With respect to your points:
1. I wrote in my initial post, “Don't mean to be hard on you or anything,” because I did not want you to take it personally. Being wrong really isn’t a big deal. People make mistakes all the time. We are human, and it is a part of the human condition. As I stated initially, I just don’t want your misguided analysis to mislead others.
2. ASICMiner’s rate of discovering blocks is certainly NOT a poission process. As I wrote earlier, this does not mean that the results are not poisson DISTRIBUTED. But again, I can state with great certainty that the distribution of AM’s mined blocks is NOT poission distributed. It is likely a reasonable approximation for large periods of time assuming NONSTATIONARY DATA, but it is certainly not reasonable for a 6 hour period. It is also not reasonable assumption for an individual miner’s results. For the entire network, a poission distribution seems appropriate.
3. You failed to consider much more than that.
4. This point is the fundamental error in your analysis. Again, please try to think about this for a second before responding. Yes, your calculations are reasonable for a GIVEN 6 hour period. But you are trying to apply these questions to answer the question, “What is the probability that a 6 hour period will occur with 0 blocks?” I admit that I am assuming a bit, but it seems to be the intent of your calculations. The probability that 0 blocks will be found in a GIVEN 6 hour period IS MUCH DIFFERENT than the probability that a 6 hour period will occur in which no blocks are found. Please think about this for a second…It’s really not that difficult.
“there is a 97% probability that the zero blocks founds is NOT due to bad luck and instead due to some non luck reason.” These are exactly the type of statements that reveal your ignorance of probability and statistics. All events are the result of luck and “nonluck” to use your term, regardless of the resulting value. You can say things like, “wow, that is lucky.” Meaning a low probability event occurred. Yet all outcomes are equally a product of luck and other “nonluck” factors…
I apologize if I came off as a bit of an ass, but I think you are just overreacting to me pointing out the errors in your calculations / logic.
EDIT: I believe you edited in that part to add the part about being wrong? Glad you edited that part, and I totally agree. You should definitely become accustomed to being incorrect.




Rebelution
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August 30, 2013, 06:08:40 AM 

It's a nonhomogenous poisson process wrt time. If the hashrate is kept stable, then it's a homogeneous poisson process with respect to time.
LOL no shit you idiot. If it we knew that the hash rate was constant, this entire discussion would be irrelevant. We would just be able to more accurately predict the hash rate as we collected more data. Nonstationary data would not be an issue. Yes, the distribution's CDF is different to the expected value. So? Its a bigger issue than that. The whole point is that calculating the probabilities of mining 0 blocks for a GIVEN PERIOD is different than calculating the probability that a 6 hour period will occur with 0 blocks mined. Please see coin flipping analogy... This is not hard. I do admit that I am assuming that DnT is making the calculations so that he can predict the probability that a given 6 hour period will occur with 0 blocks. I agree that his calculations are reasonable for expected value calculations for a specific 6 hour period. They are not reasonable for the conclusions he is trying to make. Yes it does. I can prove it with 95% confidence. Would you care to make a bet? I'll place 100 btc of mine against 10 btc of yours that I'm correct, and that: This statement does not make much sense. Either you can "prove" it to be true or you cannot. It is binary. 1. When ASICMiner's hashrate is stable, the number of blocks per time period is a homogenous Poisson process. Again, no shit. The entire point of calculating the probabilities is that we know that the hash rate is NOT stable. So, want to take me up on my bet? Your illogical assumptions that contradict the entire point of performing the calculations make it a fairly nonsensical bet. I agree, if you assume a constant hash rate, then yes, the results are poission distributed. You guys are really my major problem with the bitcoin community in general. At first it seems like a community full of really intelligent people. But the more time you spend, you realize its actually full of condescending people that are pseudointellectuals.
On behalf of all pseudointellectual condescenders, I apologise.
Not sure if sincere, but OK. I would have preferred a community full of intelligent people and stimulating discussion, but I am OK with these dynamics as well. It just does not bode well for mainstream acceptance... Hopefully another cyprtocurrency with better PR and community won't capture bitcoin's position as market leader. But unfortunately with a community of condescending idiots like you, I fear that may not be the case. I hope I am wrong, and I hope the cryptocurrency that finally wins will not be invented by a bank or huge corporation. Regardless you clearly already took the gloves off with your first post which is fine with me. Heated debate with personal attacks is also fine with me. "Come at me bro."




hammurabi


August 30, 2013, 06:14:32 AM 

This is going to be good... And the winner is... the guy who made most accurate prediction : )

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TsuyokuNaritai


August 30, 2013, 06:21:42 AM 

I apologize for starting WWIII. Who knew? And the winner is...
The only winning move is not to play. How about a nice game of chess?




stripykitteh
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August 30, 2013, 06:23:19 AM 

I'll just leave this here...




Franktank


August 30, 2013, 06:27:02 AM 

I apologize for starting WWIII. Who knew? And the winner is...
The only winning move is not to play. How about a nice game of chess? WWIII is Word War III, right? With all these grammatical corrections, someone may have forgotten the letter "L" somewhere...




organofcorti
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August 30, 2013, 06:27:39 AM 

It's a nonhomogenous poisson process wrt time. If the hashrate is kept stable, then it's a homogeneous poisson process with respect to time.
LOL no shit you idiot. If it we knew that the hash rate was constant, this entire discussion would be irrelevant. We would just be able to more accurately predict the hash rate as we collected more data. Nonstationary data would not be an issue. I didn't realise you understood that  since if you did you could have just posted that you understood the difference (which you didn't, not by name anyhow) and also calculated probabilities for blocks solves in n minutes for a given day and time yourself. Since you didn't I thought perhaps you didn't know about or understand the difference. I was not trying to imply I was an idiot. So if you understand nonhomogenous Poisson processes, then you understand it's possible to estimate the intensity function and cumulative intensity function yourself  then you can easily calculate the probability of n blocks in a given time period and set this discussion to bed. When you post the results I'll be quite interested to see how different the probabilities actually are.




Rebelution
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August 30, 2013, 06:28:40 AM 

Haha yea, I admit I got a little overly heated... Sorry for the derail all... Except the people who accused me of being of course You guys are idiots EDIT: Never said I knew how to calculate, just that DnT's calcs were clearly wrong.




