Aha, the topic is insects with many legs!  On topic! On topic! 

Er, was that question somehow embarassing, or too difficult to answer?

Shouldn't centipedes and millipedes be called hectopedes and kilopedes instead?

Clients are certainly entitled to full refunds, but whether they will get them depends on what BFL did.

Suppose that clients prepaid 40 M $,  then BFL spent 30 M $ running the company and building the hardware, and mined bitcoins worth 10 M $ with it.  That would mean 20 M $ net "profit" for them.  Some of that they might hide in the blockchain or other places, some they would spend on houses, cars, caviar, etc..  In that scenario, even if the FTC managed to locate and  auction all their possessions, it would recover 20 M $ at most, so they would be able to refund only 50 cents on each dollar.

That is how the compute the exchange rate to convert the price in dollars (from the merchant) to the price in bitcoin (that the client must pay).  It MAY be how they convert the bitcoins to dollars; but I suppose that the conversion is not immediate, and thus they may play the market a bit and/or sell off-exchange.

Arent't apologies fungible, I mean, couldn't he save them and give them to someone else?

Thanks for the link!

However, the 4-month gap in the OKCoin data (Feb to May)  is inexcusable, and invalidates some of their comments.  Bitcoinwisdom has got the OKCoin volume throughout that period, and it was in fact 15-25% higher than Huobi's.  Moreover, there are/were other exchanges in China besides those 3.  And MtGOX, not included in that aanalysis, had significant volume through the November rally. 

But even if a small subset were able to do this elementary arithmetic, and gave 35% chance to "2000$ in 5 years", they should be buying those coins for sale at 400$. 

As for waiting for cheaper coins: one must compare the plans (A) "buy 1.00 BTC with 400$ now, wait for price to reach 2000$, sell" with (B) "wait for price to drop to 350$, buy 1.14 BTC with 400$, wait for 2000$, sell". 

Assume that plan (A) has 35% chance of success within 5 years, that is, of price reaching 2000$ in 5 years.  To simplify the math, assume that the only alternative to success is total failure; that is, the price will suddenly crash to 0$ before the 5 years are over, without ever reaching 2000$.  Then the expected profit is 1.00*(0.35*2000 + 0.65*0) - 400 = 300$. 

Plan (B) will have smaller chance of success than plan (A).  Let's say that there is a 20% chance that the price will never get as low as 350$ in the next 5 years; in that case one will keep holding the 400$ in dollars to the end.  If the price does get down to 350$, the chance that it will recover and then rise to 2000$ must be less than 35%, because it has to climb 50$ more, in a shorter time.  Say that the chances are only 30%.  If again we assume, in the second case, that the only alternative to reaching 2000$ is sudden crash to 0$, then the expected profit will be  0.80*1.14*(0.30*2000 + 0.70*0) + 0.20*400 - 400 = 227$.

This math is oversimplified, of course.  For a proper analysis, one should consider more possible outocomes, besides success and sudden crash (which I don't think is likely), and other strategies besides (A) and (B).  The point is that the advantage of waiting for a lower price -- to have more coins to sell in the end -- may be negated by the risk of the price going up, and never reaching the expected low price; and by the smaller expected value, if the price does get that low.

Well, "the market's EV" is 400$.  Therefore, "the market" thinks, rightly or wrongly, that the chances of BTC being worth 2000 USD at any time in the next 5 years are somewhat less than 35%.  An investor who thinks that there is a 35% chance of selling for 2000$ within 5 years should be buying BTC for 400$, since  the expected profit would be at least 12% per year.  Since there are bitcoins for sale at 400$, and no one is buying them, the market's opinion is that the chances of "2000$ within 5 years" must be less than that.

To be sure, that must be the opinion only of all those who have looked at bitcoin and still have investment money on hand.  Those who have higher expectations for the price should have already all their money invested in BTC already.

Actually,  the 12%/year ROI above assumes that the only alternative to "2000$ within 5 years" is "price will immediatel crash to 0$".  But the market must not be that pessimistic about the alternatives: the price may do many other things, with significant probabilities, besides crashing to 0$.  So, the market's probability for "2000$ within 5 years" must be much less than 35%. 

There are several legal and practical reasons why they would probably have to (and want to) auction any BTC that they can recover from BFL, and refund clients in USD only.  For one thing, how many BTC should they return to someone who paid 10 BTC at some date in the past?  Namely what BTC prices should they use for that computation?

Would you accept my apologies for that typo?

As I have written many times before, I believe that the Nov/2013 bubble was caused by the opening of the "popular" Chinese market.  At least two articles in mainstream media claimed that in China there was a large population of amateur and semi-professional speculators, not particularly computer-savy, who used to trade all sort of commodities like fermented tea; and those people enthusiastically embraced bitcoin as a much better item of speculation.  The main Chinese exchanges Huobi and OKCoin opened in Beijing only a few months before the bubble, and grew enormously during it.

The Apr/2013 bubble, too, was probably driven by China, specifically by BTC-China in Shanghai.  Shanghai is a special economic zone, and BTC-China changed its management in early 2013 (and may have catered to computer types, rather than the amateur speculators above).

Almost all the large price changes since Nov/2013 can be traced to events that are relevant to Chinese traders, such as the Chinese government decrees that banned the use of bitcoin in commerce and finance, and various rumors and disclaimers about them.

In contrast, significant events that are relevant only to "the West" (the world outside China), such as Dell and other merchants "accepting bitcoins", have had practically no effect on the price.  To me it is pretty clear that the Western exchanges largely track the Chinese ones through arbitrage trading (which may be a significant fraction of their trading volume).

There are only a few large price swings that I cannot relate to any external event, in China or in the West.  In particular, I still have no explanation for the rally that lifted the price from ~450$ to ~650$ between May/20 and Jun/10.  But my guess is that it, too, was related to Chinese events and affected mostly the demand in China.

Anyway, I believe that the cause for the overall decline since Jan/2014 should be sought in China.  My guess is that, from February to May, those Chinese speculators grew increasingly disappointed with bitcoin -- not just because the stagnating price and the government's policies, but because they could not compete with the robots and other tricks used by the more sophisticated traders (which may have included insiders or special clients).  Since those amateur traders have no other use for bitcoin in China, they probably sold their BTC and withdrew the yuan.

The Chinese exchange owners admitted this problem in early May and promised to make the field more level by suspending leverage trading and curbing high-frequency trading (a promise that, according to Bobby Lee, they broke not long after that).

This hypothetical exodus of amateur traders could explain the general downward trend from February to May, superimposed on the sudden swings related to specific external events; and the remedial measures taken by the Chinese exchanges may explain why the price remained relatively stable during May. 

Thus, I see the drop of the last few weeks as being due to the Chinese traders returning to their state in early May.  The unknown news that caused the surge in demand after May 20 were apparently negated. 

In spite of all the losses so far, the price still seems to be quite a bit higher than what could be sustained by Western demand alone.  On Apr/11 we had a glimpse of what would happen if the Chinese were to pull out completely: in response to some bad news, that again was relevant only to the Chinese market, the price briefly dropped to ~340$. 


Yes, all these factors may be helping the decline.

Indeed, see my previous post.  The parameter T in those formulas is the actual mean time between blocks, defined by the current difficulty and current hashrate; not the ideal mean time.

I understand that block finding is a Poisson process where the probability of finding a block in any small interval of time dt seconds long is dt/T where T is the mean time between blocks.  Then, the probability of n blocks being found in an interval with length t is
exp(-t/T)*(t/T)^n/n!

In your example, t/T is 240 and we want the probability of n being 268 blocks or more.  The answer is
exp(-240)*sum(k=268..oo  240^k/k!
That is not easy to compute, but for those range of values the distribution should be close to a Gaussian distribution with mean 240 and standard deviation sqrt(240).  So we can instead compute the probability of a standard Gaussian variable (mean 0, variance 1) being greater than r = (268 - 240)/sqrt(240).  I can't compute that right now, will do that later...

The mean interval T between blocks depends on the current difficulty and the current hashrate.  Bitcoin's difficulty, IIUC, is adjusted at regular intervals to try to keep T at 10 minutes.  However, the adjustment is by large steps and is not instantaneous; so, if the hashrate drops for a while, or the difficulty has just been increased, T may be longer than 10 minutes for some time.  

In any case, even if the mean time T is exactly 10 minutes, the variance of the actual time between blocks is large, so the probability of having 6 or fewer blocks in an 80 minute interval is not that small.

I understand that Monero's difficulty is adjusted after every block instead of by steps, correct?  Even so, the algorithm would have to look at several past blocks in order to estimate the hashrate and compute the correct adjustment.  So, if there is an increase in the hashrate, it should take a while for the difficulty to be increased accordingly, and T would be less than a minute for a while.  And, in any case, the variance is substantial, for Monero too.

Why shouldn't everybody be curious about the stickiness of Phoradenron leucarpum's berries?

I don't know; does anyone care about mistletoe?

By my math, with 1 block per minute mean rate, one should see 4 blocks in the same minute about once every hour or so.  Is this correct?

Yeah, so what?

It is not an error of fact, but only the use of a theory that is not really relevant to the problem.

All you wrote is correct, but, as you note, NP and P (and the O() notation) are meaningful only if the number of bits n is considered variable, and they describe how the cost grows ultimately as n goes to infinity (informally, "just before n reaches infinity").  The theory has nothing to say if one considers a specific n (say, 256), or any n less than some fixed bound, (say, n up to 1 million bits).  In that case, the complexity classes cannot be distinguished: every function with a finite domain can be computed in polynomial time, indeed in O(1) operations.  This is a trivial observation that follows directly from the definitions.

So, even if inverting a generalized n-bit version of SHA were to be proved to be superpolynomial with respect to n, that would not say anything about the difficulty of inverting SHA256 for 128 or 256 bits -- which is what matters.   There may even be an algorithm, out there in the vast unexplored depths of the algorithm jungle, that can be implemented in practice and solves the Bitcoin Mining Puzzle -- for n = 256, specifically -- with less operations than it takes to compute the two rounds of SHA256.  (Needless to say, most cryptographers are betting their careers that there is no algorithm that is fast enough to be of practical use, much less one that fast.)

It is unfortunate that complexity theorists still teach computer science students that their theory has practical relevance, to the point of using the word "efficient" as synonym of "polynomial time".  In fact, that theory is as relevant to software development as the Banach-Tarsky paradox is to manufacturing.