Topic: Distribution of bitcoin wealth by owner - page 33. (Read 153396 times)

Very interesting analyses rpietila, thanks for sharing.

Now FBI has climbed on the top of the list, they have a good reason to promote bitcoin now  

If your holding is...

BTC10,000 => TOP-125 (42)
BTC1,000 => TOP-1300 (760)
BTC100 => TOP-13800 (5700)
BTC10 => TOP-85000 (28000)

Safe figures (optimistic figures in parenthesis, reality likely in between)

I calculated 3 scenarios, which I deemed most important to find the upper and lower limits for number of holders in each holding bracket. I did only the extreme cases, and got results that in my estimation were each unrealistic in their own way, so they serve well as limits, within which the reality falls.


Case I. Very top-heavy distribution and 100,000 users.

#People	#Bitcoins	#TotalBitcoins
125	BTC10k+	7.5M
640	BTC1k-10k	1.8M
4900	BTC100-1k	1.4M
22k	BTC10-100	0.7M
36k	BTC1-10	0.1M
27k	BTC0.1-1	0.0M
10k	BTC0-0.1	0.0M

Case II. Very top-light distribution and 1.5 million users.

#People	#Bitcoins	#TotalBitcoins
42	BTC10k+	2.5M
875	BTC1k-10k	2.5M
8570	BTC100-1k	2.4M
75k	BTC10-100	2.3M
408k	BTC1-10	1.6M
778k	BTC0.1-1	0.4M
233k	BTC0-0.1	0.0M

Case III. Very top-light distribution and 100,000 users ("middle class model").

#People	#Bitcoins	#TotalBitcoins
50	BTC10k+	3.0M
1250	BTC1k-10k	3.5M
12500	BTC100-1k	3.5M
47k	BTC10-100	1.4M
28k	BTC1-10	0.1M
9000	BTC0.1-1	0.0M
2000	BTC0-0.1	0.0M

(I did not do the simulation of top-heavy and many small users, since it was the most unrealistic of all - and its datapoints would still have fallen inside the limits set by the other scenarios).


Therefore.... T h e   r e a l i t y

#People	#Bitcoins	#TotalBitcoins
42-125	BTC10k+	2.5M-7.5M
640-1250	BTC1k-10k	1.8M-3.5M
4900-12500	BTC100-1k	1.4M-3.5M
22k-75k	BTC10-100	0.7M-2.3M
27k-407k	BTC1-10	0.1M-1.5M
9k-778k	BTC0.1-1	0.0M-0.2M
2k-233k	BTC0-0.1	0.0M

With 80-90% confidence I think all the values fall within the limits above. The limits are extremely wide in smaller holdings, since I have less undisputable facts concerning them. But the nearer the top we go, the less variance there is.

It seems to be easiest to deduce the BTC1k-BTC10k bracket, for it is the narrowest. No matter what we assume concerning the other parameters, there is a sizable number of bitcoins owned by people in this bracket, and the number is bound by the distribution model so that no great variance exists.

It is possible to reconstruct the distribution in any past (or future, for that matter!) date with this model. After all the parameters are estimates anyway with wide tolerances. If somebody would take the time, we would have a nice series on how the coins are being distributed over time.

As for fairness, I assume you would like the coins to be distributed in a much more equal way than they are. That is completely unnatural and not observed in any economy. It is somewhat possible to equalize the income of people and the governments are doing it as much as they can (not that they cared about the poor but it is an end-all to be able to control as much economic activity as possible, which can nicely be achieved by excessive taxation and redistribution). But it is totally impossible to equalize people's wealth, since most people are unwilling/incapable of wealth accumulation and will therefore always own almost nothing, regardless of income. Even governments cannot do anything to the distribution of wealth, which is by nature a logarithmic phenomenon, obeying its own distribution. If governments aggressively go after private wealth, they aggravate the inequality, since the wealth is just collected in even larger stashes and middle class is destroyed.

Bitcoin distribution is the fairest when people have easy access to buy and sell them without hindrances. Then everybody can own as many as they deem fit. Satoshi will still own a million and most (currently: 99.99%) will own zero.

Minimum number of all users, or minimum number of users in the top brackets? Because we know we've had over 100,000 bitcoin users since Summer of 2011.

I am currently thinking to reduce the model to two parameters:
- number of users
- top-heaviness (number of bitcoins owned by people who own BTC10k or more)

Everything else would be according to the distribution model that I have derived and which corresponds to Silvervault behavior.

Then by allowing 3 values for each parameter, we would have 9 scenarios:

- Minimal top-heaviness would be that apart from Satoshi (BTC980k and possibly more with machines using another software) there would be only a few holders of BTC10k or more. Perhaps BTC2.5M (incl S) would be a realistic lower limit.

- Medium top-heaviness would be that 4 million coins are in this category.

- In steep top-heaviness, there would be many large holders who have all along wanted to own the largest number of coins possible, individually or in concert. The number would be BTC7.5M (leaving only BTC4M to everyone else, since we assume that 0.4M is lost).

- Minimal number of users I could say is 100,000

- Base case is the 350,000 that I derived in my last post.

- Upper limit would be maybe 1.5 million. This would require figures from webwallets and exchanges to verify.

When 400 people are just one :
https://blockchain.info/address/1FfmbHfnpaZjKFvyi1okTjJJusN455paPH

That makes me feel warm and fuzzy.

Let's see it from the other side. Could the distribution become fair?

Can you compare it with 2009 / 2010 / 2011 / 2012 Rptiela?

And: did you think of entities instead of persons? Gox, ex-SR, Miner-Guildes, Satoshi Dice, Just Dice, blockchain.info (and so on) - all entities with large volume.

Seconded. When we do financial projections, we typically include best-guess scenario, and also include best-case and worst-case. Can you provide something like this with a list of parameters that would change? Also, did my explanation of my own situation help with the BTC1,000+ calculations any?

Well, the nice thing is, all those top holders have an extreme interest in making sure bitcoin succeeds, and are pumping that money into bitcoin businesses and projects, AND they want someplace to actually spend those coins. And at the same time, all us poor plebes want to be able to get our hands on those coins, and have quite a few wealthy bitcoiners willing to give up their coins for our jobs and products, even if they are of questionable quality  

I want to learn more how the equation came up?

That $400 withdrawal model breaks down for Cyprus lol

The average investment is no longer assumed to be $1000. I believe it's now $3000 based on rpietila's silver purchase model (seems this comparison has a few faults but better than just guessing).

No argument from me. I agree with you. I think that looking Ponzi-like is A barrier, not THE barrier. I still feel that until my 8000 year old aunt can use and keep safe Bitcoin while using Windows at the library, it will remain marginal.


Does this remind anyone of the Drake equation? LOL.

Rpietila, this is the most fascinating thread in a LONG while. Thanks. What happens if you change some of your assumption parameters?

“- average investment in bitcoin is $1000 (buy outright, or mining equipment)” I wonder about this assumption. Why that particular number? What if you change this to the maximum amount one can withdraw from an ATM in one day? Say, $400 - a guess(!). I know...

I would disagree that Bitcoin looking like a ponzi will be the cause of low uptake.

I suspect it's too sophisticated for most people and will just need adoption to come via recommendation. At some point it'll reach critical mass and be accepted just like Paypal.

I still remember the time when if you mentioned Paypal, people would look at you like some sort of computer nerd. These days it's commonplace to find it at any online store.

No-one cares that I've used PayPal to pay, just that I did. That's where I see Bitcoin when it's finally adopted by the masses.

Yes. Thanks rpietila, for starting this thread. It's quite the eye opener. It is making me rethink whether I want to hold a currency with such a top heavy distribution. Disturbing to have your beliefs challenged, but useful.

I KNOW it's not a Ponzi pyramid scheme, but the shape of the adoption curve, and the growth pattern is similar enough that potential adopters might be thinking that, if it looks like a duck, and quacks like one too, then maybe...

That has to be a long term problem for mainstream take-up.

Here, the important parameters I used were:

- average investment in bitcoin is $1000 (buy outright, or mining equipment)

- estimated the percentage of holders whether they had invested at $100, $10, $1, $0.1 or $0.01

- Ones invested at $100/BTC still have their whole investment, others have sold 20%, 40%, 60% or 80%, respectively.

- Calculate weighted average, how much is the present value of an average remaining bitcoin investment (=$3,400, which is quite small for the reason that 80% were estimated to have bought in at about $100)

- Divide bitcoin market cap by the previous figure, obtaining number of holders (700,000).

- arrange the number of people in a certain log-bracket so that they approximately conform to bell curve (found out in other similar data that thy do) and satisfy the constraints of total bitcoins and the known stash of Satoshi and some idea of the top-heaviness of the distribution. <= it is essentially a parameter, how many coins to allocate to BTC10,000+ bracket. I think the realistic range is BTC3M to BTC7M, including Satoshi's 1M.

- almost nothing in the distribution changes if the number of holders is 200k instead of 600-700k. The bulk of the bitcoins is held by the top, and their number is inversely correlated to their average holding. The average holding must follow certain rules so there are not many parameters.

edit: Ah, as I was writing, I remembered that average remaining investment was calculated with bitcoin price of $100 instead of the current $200. This makes the total number of bitcoin users 350,000, which I think is very realistic considering other metrics.

This is a really interesting thread with great detective work.

Hopefully Bitcoin doesn't end up with a 1%er problem but at the rate we're going at - I'm not sure how that would be avoided.