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The Gini coefficient is a measure of the inequality of something's distribution, where a value of 0 represents total equality and a value of 1 maximal inequality.

Is it possible to perform this type of estimate on how bitcoins are distributed throughout the userbase? And/or is it possible to tell how this distribution is changing over time?

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The Gini Coefficient doesn't seem like it would be very useful for such a small economy. Ask again when bitcoin has a significantly larger network and you might get a useful answer. –  David Perry Aug 30 '11 at 22:35
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There is no real way to know. People might spread their holdings over several addresses, and one address can be a cold Mt. Gox store for a huge portion of the economy, and not owned by any single individual. –  ripper234 Aug 31 '11 at 0:58
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In its current form this question is not terribly constructive, since it is poorly phrased and has no real way of being answered. I would encourage a rephrasing such as "Is it possible to estimate the Gini coefficient for Bitcoins?" The answer to this would be no, but it would be constructive and helpful if answered well. –  eMansipater Aug 31 '11 at 1:00
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The fact that some folks don't see how to do it now is no reason to close the question. I suggest it be reopened. –  nealmcb Aug 31 '11 at 4:01
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I also think that the question is perfectly valid, and I would be very curious to read a good no answer, since I would naively expect it to be possible to at least approximate. –  Artem Kaznatcheev Sep 2 '11 at 0:54
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3 Answers

The owner of the Bitcoinica site has released some data from his site which may reflect the wider bitcoin economy. He gives a value for the Gini coefficient of:

Gini Coefficient = 0.87709

The Bitcoin Report site also releases a regular report on the number of bitcoins in the top 100 wallets. Although one person can own multiple wallets or a wallet of a exchange (e.g. MtGox) may contain coins with multiple owners so it is impossible to know for certain the real wealth distribution but it may have some correlation.

The Bitcoin Trader blog used the Bitcoin report data on the top 100 wallets and compared the data from May 1st and Oct. 29th 2011.

Top 100 wallets distribution.

From the Bitcoin Trader:

The distribution of coins among the top 100 has evened out, as can be seen in the chart.

Even though 1,310,000 Bitcoins have been mined since May 1st, the top 100 have still managed to increase their relative wealth, and now hold 29.8% of all the Bitcoins ever created!

While certainly not perfect these type of statistics may be give some indication of the trends in the wealth distribution in the bitcoin economy.

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The plateau at 50,000BTC looks suspicious - I wonder if a big holder has multiple addresses with 50,000BTC in each? –  Highly Irregular Jan 10 '12 at 0:32
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@HighlyIrregular a big holder had multiple addresses with 50,000 BTC in each. It was MtGox, and they combined 10 of them into a single 500,000 BTC address on 16th Nov 2011. See the transaction blockexplorer: blockexplorer.com/t/2aXLZLjoP6 –  Chris Moore Feb 8 '12 at 9:48
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Once you have the relevent statistics this is easy. Collecting those statistics is hard though, due to bitcoins level of anonymity. You would probably need to do a survey.

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I think this summarizes it entirely. There is no real way to track statistics of bitcoin users. –  Evil Spork Sep 3 '11 at 19:41
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you can look at the Gini coefficient between wallets; that should be relatively straightforward? Technically a single user can have many wallets, but I am sure this is atleast a good starting approximation, no? –  Artem Kaznatcheev Sep 5 '11 at 0:11
    
a question that peruses this approach is here: bitcoin.stackexchange.com/q/810/46 –  Artem Kaznatcheev Sep 11 '11 at 7:09
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@ArtemKaznatcheev there is no way to identify wallets from the blockchain, only addresses. A single wallet can handle anywhere from a few dozen to hundreds of active addresses and those addresses can't be linked together. –  DeathAndTaxes Nov 7 '11 at 5:33
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It is possible, you will first need to collect statistics on bitcoin usage.

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