I checked the Silvervault numbers a bit more carefully and found out that the median holding is roughly $1000. Translated to Bitcoinworld, we would have equal number of people involved in Bitcoin, with a holding above BTC5 than we have below BTC5. If this is true, the whole bitcointhing would rest on very few shoulders.

What could cause it to be untrue?
- Faucets, donations, etc. combined with difficulty to sell (can these people be counted users? If you evangelized your friends by giving them a bitcoin in 2011, it is easily forgotten and lost) In Silvervault people can easily sell if they want out so this explains a small number of small holdings.
- ...

I also arranged the Silvervault data in log-scale brackets (I used 1-2, 2-4, 4-8, ... (AGD) for granularity) and found out that the greatest density of people is in the bracket with holding value of $3,000. If we apply this, the largest number of bitcoin holders would be in BTC10-BTC100 category, followed closely by BTC1-BTC10.

Silver is currently lagging behind. Bitcoin otoh is in its ATH. After a steep runup we do well to take into account that the bitcoin holders paid a lot less for their coins than what their price now is. It might lead to a top-heavy situation with inordinate number of excessive positions. Right now I see no special need for this, since most of the bitcoin holders by number have started in 2013, and the price has been roughly stable this year at $100 as well as 2012 investors can be approximated to have bought at $10.

Yes, I was joking. Believe me. Don't blame the hospital. I love big brother.

(Read my new thread, I am investigating the origins of the oligarchy )

I know exactly one person who believes in the accelerated crash and breach of 1 this year, and it is not even me. To add some credibility, he is the one who introduced bitcoin to me in 2010.

My take on the matter is that dollar reaches an interim bottom of 0.5 next april but I cannot make myself to believe in large action this year. Something between 3 and 2 would be a safe bet.

Here is a list of bitcoin-related activity. I would like to have better estimates available also, so please refer them here. Anyway, according to this one, bitcoin is overwhelmingly a first world thing (second world is now part of first FYI), and due to its highly technological nature, it is likely to appeal to the rich in medium and low-income countries.

A corollary would be that people who have bought bitcoins are wealthy, and therefore it is reasonable to conclude that they buy with rather large sums. My guesstimate of a typical first buy would be $100-$10000 with rather few buying either less or more. I run a precious metals shop, and also an automated silver depository. I have access to the statistical distribution of our customers' holdings, which has inspired this analysis.

Before this year, $100 would have fetched you an average of BTC10, and $10,000 would translate to BTC1,000. In 2013, $100 is about BTC1 and $10,000 would net you BTC100.

The important thing is that only a minority of people who have invested into bitcoins have less than BTC1. To fall into that category, one would have to be both poor and extremely conservative (yet willing to invest the time to learn..) and have bought in March or later, this year. All other scenarios lead to higher balance.

The history of mining can be divided into two periods: mining with existing equipment and mining with specialized equipment. When existing equipment was used, mining generated essentially free coins, and lots of them. Therefore all such miners have large balance (if any - we will later analyse the sold out phenomenon). After mining became an industry with investment calculations and GPU/FPGA/ASIC farms, the investments have generally been on par with the expected number of bitcoins generated. This kind of activity also produces rather large holders.

I have no knowledge if the bitcoin faucets and similar things have ever produced new bitcoin users/holders. I don't know what has generated the 1.5 million dust addresses (please help me!), but I doubt that it corresponds to many actual users.

On the other hand, services such as Easywallet or Instawallet (defunct) can host many users and mask their activity from the blockchain. Also exchanges can obscure the relationship between their cold wallets and the customers' balances that are stored there.

After delving into this matter in the last 1-2 days, I am tempted to drastically reduce the total number of bitcoin users, because I haven't found the mechanism that actually would have produced millions of sub-BTC1 holders so far. The number of investors will likely stay quite much the same after the update.

The same analysis applied to my original proposal yields the following results:

Bracket	#TotalBitcoins	log(total)	1 derivative	2 der.
10k+	BTC5.50M	6.74
1k-10k	BTC2.88M	6.46	0.28
100-1k	BTC1.60M	6.20	0.26	-0.03
10-100	BTC1.00M	6.00	0.20	-0.05
1-10	BTC0.50M	5.70	0.30	0.10
0.1-1	BTC0.30M	5.48	0.22	-0.08
-0.1	BTC0.03M	4.48	1.00	0.78

Now, this is my guess, and it is now verified to behave quite well (smooth 2nd derivative) according to what we would expect from a statistical distribution (I will iron out the kinks hopefully today to have a revised model, but that will not alter much - the parameters are more significant now and there is much to be done).

Now we are using this data.

I have converted your table to the "standard format" to put it in the same kind of "validity test" as Molecular's data:

Bracket	#TotalBitcoins	log(total)	1 derivative	2 der.
10k+	BTC2.35M	6.37
1k-10k	BTC3.15M	6.50	-0.13
100-1k	BTC2.49M	6.40	0.10	0.23
10-100	BTC1.20M	6.08	0.32	0.22
1-10	BTC0.35M	5.54	0.54	0.22
0.1-1	BTC0.05M	4.75	0.79	0.25
-0.1	BTC0.01M	3.90	0.85	0.07

Have a look at the 2nd derivative! This is the kind of behavior that is expected from a probabilistic process. I can conclude that Molecular's data is wrong, and your data is valid.

Now, the original question remains: how to parse a table of the bitcoin holdership, as opposed to address balance distribution.

In my opinion, this one gives us a great deal of hint of the parameters of the distribution though. Eg. the averages per bracket is good to know:

24k, 2.2k, 251, 29, 2.85, 0.38 - there is a certain logic in these also.

I have converted your table to the "standard format"

Bracket	#TotalBitcoins	log(total)	1 derivative	2 der.
10k+	BTC8.28M	6.92
1k-10k	BTC2.40M	6.38	0.54
100-1k	BTC0.55M	5.74	0.64	0.10
10-100	BTC0.28M	5.44	0.30	-0.34
1-10	BTC0.06M	4.74	0.70	0.40
0.1-1	BTC0.03M	4.44	0.30	-0.40
-0.1	BTC0.00M	3.88	0.56	0.26

My hypothesis is that a valid data should not have erratic behavior in second derivative. (This uncovers the place where you pulled the numbers from..) I will run the same check to the actual data regarding bitcoin address balances that dserrano5 just posted. That should behave nicely, since the data is generated by a statistical, probabilistic manner.

I understand the question, and it does not have an easy answer.

This thread is imho a quality read, concerning the distribution of bitcoins.

A large percent of the most active forum members have very high bitcoin balances and no intention to sell them. This must be taken into account when considering the situation that 20 million people want in. A really large slice of the cake is taken by the big holders.

It is mathematically improbable, not only to have more than 21 million holders of BTC1, but actually to have even 2 million such holders! To have more than 5 million is flat out impossible if free market remains and the large holders are not coerced out of their holdings.

Goat, I know the proof of my findings is not yet there in an unrefutable form, but the fact remains.

What comes to the topic, an easy estimate is ofter better than a difficult one (extrapolate):
year end - users - price
2009 - 20
2010 - 200 - 0.5
2011 - 2000
2012 - 20k
2013 - 200k - 500
2014 - 2M
2015 - 20M - 50k.

It is not inconceivable that when 22 million people have some bitcoins, one goes for $50k.

The logic is as follows:

Evidence

1. Your forum account is created in June-2011.

2. You have been forum active ever since and are Director in bitcoin-something.

3. You told you sold more than BTC1000 at $22 (Feb. 8, 2013)

Deduction


1. It is very rare to have a Jun-2011 account. This points to a person who has (with good probability) been able to mine/buy large amounts with
small cash outlay. (Hardly anyone creates an account without having the coins already.)

2. Being able to sell a significant amount at $22 points to me a long-term holding:

i) A believer who had bought recently would not have sold but bought more after being proven right. But you have been in all along.

ii) A newcomer who does not believe, would have likely sold more than a part after a quick double. Probably all of it. The newcomer would not be here today with thousands of messages though. And would probably not have had BTC1,000 in the first place.

iii) For a person with a good stash, who is in it for the long term, it makes perfect sense to sell a part after a quick double, after waiting for so long. Selling a part means selling at most half, which leaves at least half remaining. (The proceeds are enough to live from that day even until this day so no need to sell more.)

3. It is a lower bound that you would have BTC1,000 today. If you play wisely, you only sell a little at a time, and can earn BTC every year, so that your current holdings should be at least BTC3,000. The upper bound is that you resort to borderline lying, where you downplay the amount sold, and forget to tell that you bought back, and sold after very tight analysis only 10% of your holdings, then you might have BTC10,000 or more. I assume that anyone whose forum account is from 2011 or earlier, has BTC1,000-BTC10,000 unless proven otherwise.

4. Yes I know that bitcoin is not life and life can go wrong and you lose most of your bitcoins to bad bets as you don't realize how precious they are. But even in this case, considering your position, I think here we have a 4-figure Countess.

Thanks, very good! Might it be possible to have the sums also, so that:
#bracket, #totalBtcInBracket

This would verify my above thesis about the "well-behavior" constraint for the distribution, and also be useful for calculating the average holding inside a given bracket. These all matters are interrelated.

Unless it is difficult, you could leave out unspent 50 BTC:s from this one.

I will soon update, this is just the theory part to my reply

Your guesswork does not obey the mathematical distribution models that I firmly believe it should obey. This flaw is apparently because you did not use equilength (in log scale) brackets.

The distribution of bitcoins should, in my understanding, conform to one of these distributions, where X=log(number of bitcoins) and Y=(number of owners of the given number of bitcoins).

Now, if we calculate the integral over a bracket (which is one unit-length of the X-axis), we find the total number of bitcoins held by people in that bracket.

From the mathematical, probabilistic nature of the distributions, follows that the total bitcoins owned by people in different brackets cannot behave arbitrarily. Ie. the parameters are:
-how many bitcoins do the top owner(s) have
-how many owners are there in total
-one or two parameters to define the shape of the curve.

This can easily be checked by arranging the data to log-equilength brackets and demanding that the number of bitcoins owned by people in the bracket is either continuously higher than in previous bracket, or lower. At most the 1st derivative should have 1 root and behave nicely.

I would use the following:

<20% daily fluctuation
20-35% flashcrash
35-65% middle-of-the-move correction
65%-90% once-per-year event
>90% epic crash

Thanks. The initial crash dipped straight to the 1st Fibonacci level, and the second selloff is almost there in the 2nd level. If it had gone a few bucks lower, I would think that's it. Now I hope that we revisit the lows. No money at stake because I did not sell (it was a troll).

Perhaps I'll just have to send some to Bitstamp to be able to play..

Chart showing that in one day bitcoin can crash 50%, rise 100%, crash 50% and again raise 100%, with high volume, in the biggest and best exchnge MtGox.

(Bitstamp figures used) If we set the beginning of the current upmove to $122, which was the base in early October, and the high point to $205.4, we have the following Fibonacci levels:

1st: $173.5
2nd: $153.9
3rd: $141.7

I have been successfully trading but watching the 2nd level almost always. If we are talking about a daily move, the base is the plateau in the last 12-24 hours, if medium-term move, the base is the last consensus when price was flat for several days or weeks.

We already touched $157 and now the price is going up with a vengeance. There are several scenarios:

- Price will continue to go up, and surpass the intermediate high of $205 in a few days, so that this will be remembered as a flashcrash. In February-March we had several of them, shaving off 20-30% of the price but leaving no mark except on those who sold out and did not manage to buy back in.

- Price will fall back to where we started ($120s), which questions the viability of the whole supposed uptrend or this October, turning it to a bull trap. meh87 is advocating this.

- We are currently experiencing a Fibonacci retracement on our way to higher highs. This would point to a reasonable probability of revisiting $150s, and underline the support found there. If I had money in the exchange, I would try to fish from there, and not hope for going any lower. If several days pass and the uptrend is resumed, the scenario still holds but the opportunity to buy has already passed.

Actually I was wondering why I had put you on ignore, since your posts were sensible and nice to read (as I checked today). But it was this obsession on me that was becoming tiresome and derailing the thread.

I am just probing the sentiment. It seems that you have good memory, but the sense of humor is not any better than in last spring.

(I got frightened contact to my mobile, perhaps it is in order to cancel and nullify the previous post.)

No I did not sell anything. Yes, I believe $300k is a realistic long term scenario. Yes, I was wrong whether it would happen this year. No, I don't care as much as you think I should.

That's it folks. I sold all Failure to overcome previous ATH creates a massive double top, it is hard to say where the price will go, but in 6 months my guess would be in the $13-$50 range. Thank you

I think it works just fine. Thanks a lot!

If we have a reasonable estimate of the largest holders, number of holders, and shape of the curve, the blanks can be filled with mathematics. The accuracy of the estimates determines how good the result is, but it cannot be arbitrarily bad since we know certain things such as the total number of bitcoins. Anyway, the thread is there as a rally point for a community effort to research on the topic and arrive at better understanding.