<p>Try using the an open source program called <strong><a href="http://www.fourmilab.ch/random/" rel="nofollow noreferrer">ent</a></strong>. Here are the results for rolling a die six times with the result vector of &lt;666666>.</p>

<p><strong>% echo -n "666666" | ./ent</strong></p>

<p>Entropy = 0.000000 bits per byte.</p>

<p>Optimum compression would reduce the size
of this 6 byte file by 100 percent.</p>

<p>Chi square distribution for 6 samples is 1530.00, and randomly
would exceed this value less than 0.01 percent of the times.</p>

<p>Arithmetic mean value of data bytes is 54.0000 (127.5 = random).
Monte Carlo value for Pi is 4.000000000 (error 27.32 percent).
Serial correlation coefficient is undefined (all values equal!).</p>

CC BY-SA 4.0
2018-10-22T11:03:17.177Z
2018-10-22T11:03:17.177Z
skaht
<p>You may find this old thread on bitcointalk helpful -> <a href="https://bitcointalk.org/index.php?topic=24268.0" rel="nofollow noreferrer">https://bitcointalk.org/index.php?topic=24268.0</a></p>

<p>There are 2^160 possible addresses in Bitcoin. To put that in perspective there's an estimated 2^63 grains of sand on all of Earth's beaches, <a href="https://web.archive.org/web/20150213194957/http://www.hawaii.edu/suremath/jsand.html" rel="nofollow noreferrer">citation</a>. </p>

<p>If you have a die and roll it 99 times, you have 6^99 different possible combinations. The number of different possible outcomes is <a href="https://www.wolframalpha.com/input/?i=6%5E99" rel="nofollow noreferrer">so large</a> that even with a dice that has imperfections causing less entropy the likelyhood of someone else rolling the same 99 numbers is astronomically unfeasible. </p>

CC BY-SA 4.0
2018-10-24T04:25:27.310Z
2018-10-24T04:25:27.310Z
m1xolyd1an
<p>I want to generate my own private key with dice and/or other very entropic phenomenon. But how can I calculate if my data have a good entropy ? I mean if I throw dice in a certain way too much time maybe my outcome will not be trully random, maybe my dice is not a very good dice and have imperfection etc.</p>

<p>So can I just throw it 300+ and if I don't have 0.166666% each result (1,2,3,4,5,6) it's not good ?</p>

<p>Also I want to write my own series of dice result just to compare how deficient is my brain when I try to generate true randomness.</p>

<p>Thanks</p>

CC BY-SA 4.0
2018-10-22T07:05:48.373Z
This seems more a questions for statistics SE or mathemticals SE site.
Pieter Wuille
CC BY-SA 4.0
2019-01-07T18:00:45.897Z
I'm voting to close this question as off-topic because it's a statistics question unrelated to Bitcoin
G. Maxwell
<math><statistics>
how to calculate Entropy from series of outcome?
Shazzad Kabir
# how to calculate Entropy from series of outcome?

(Asked by: username_0 on 2018-10-22)

I want to generate my own private key with dice and/or other very entropic phenomenon. But how can I calculate if my data have a good entropy ? I mean if I throw dice in a certain way too much time maybe my outcome will not be trully random, maybe my dice is not a very good dice and have imperfection etc.

So can I just throw it 300+ and if I don't have 0.166666% each result (1,2,3,4,5,6) it's not good ?

Also I want to write my own series of dice result just to compare how deficient is my brain when I try to generate true randomness.

Thanks

**Tags:** math, statistics

> **Comments:**
> **username_1**: This seems more a questions for statistics SE or mathemticals SE site.  
> **username_2**: I'm voting to close this question as off-topic because it's a statistics question unrelated to Bitcoin  

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## 2 answers

### Answer by username_3 on 2018-10-22. Score: 1 | Accepted answer

Try using the an open source program called **[ent](http://www.fourmilab.ch/random/)**. Here are the results for rolling a die six times with the result vector of <666666>.

**% echo -n "666666" | ./ent**

Entropy = 0.000000 bits per byte.

Optimum compression would reduce the size
of this 6 byte file by 100 percent.

Chi square distribution for 6 samples is 1530.00, and randomly
would exceed this value less than 0.01 percent of the times.

Arithmetic mean value of data bytes is 54.0000 (127.5 = random).
Monte Carlo value for Pi is 4.000000000 (error 27.32 percent).
Serial correlation coefficient is undefined (all values equal!).


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### Answer by username_4 on 2018-10-24. Score: 0

You may find this old thread on bitcointalk helpful -> <https://bitcointalk.org/index.php?topic=24268.0>

There are 2^160 possible addresses in Bitcoin. To put that in perspective there's an estimated 2^63 grains of sand on all of Earth's beaches, [citation](https://web.archive.org/web/20150213194957/http://www.hawaii.edu/suremath/jsand.html).

If you have a die and roll it 99 times, you have 6^99 different possible combinations. The number of different possible outcomes is [so large](https://www.wolframalpha.com/input/?i=6%5E99) that even with a dice that has imperfections causing less entropy the likelyhood of someone else rolling the same 99 numbers is astronomically unfeasible.


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