user14721: What is the probability distribution of solving a block, given the same difficulty. 
So if I try to mine multiple times using the same difficulty, is it normal distribution with mean of 10 minutes? What is the variance? Or is it some other distribution? Or maybe even deterministic chaos? 

user32356: The expected time (mean) for a new block is of course 10 minutes, assuming constant hashrate, and no block propagation time.
The tricky part is that there is no such thing as a point in time. You can only ask only for an interval. 
Let's illustrate this. First it is important to not fall for the Gambler's fallacy. Luck has no "memory". Thus if no block has been found (or if a block has just been found), what is the chance of a block being found in the next minute? The easy answer would be 1/10 = 10%. Or in the next second? 1/600 = 0.16667%. But this is not quite true.
If you ask how often a block is found before or after 10 minutes, you are asking for the cumulative distribution function (CDF) of the exponential distribution.
We can use Wolfram Alpha to plot this:
cdf exponential distribution λ=1/600
How many blocks are found after the mean (600 seconds)?
exp(-600/600) = exp(-1) ~= 36.788%

How many blocks are found before the mean?
1-exp(-1) ~= 63.212%

How many blocks are separated by more than 1, 2, 5, 10, 20, 30, 60 minutes?
exp( -1/10) ~= 90.484%
exp( -2/10) ~= 81.873%
exp( -5/10) ~= 60.653%
exp(-10/10) ~= 36.788%
exp(-20/10) ~= 13.534%
exp(-30/10) ~=  4.979%
exp(-60/10) ~=  0.248%

So what is the chance of finding a block in the next second/minute?
1-exp(-1/600)  ~= 0.16653%
1−exp(−60/600) ~= 9.516%

Bonus: How many blocks are found between 5 minutes an 20 minutes?
exp(−5/10)−exp(−20/10) ~= 47.120%


user575: The time between consecutive blocks follows the exponential distribution, with mean (roughly) 10 minutes. This means that the variance is 100 minutes^2.

14721: <p>What is the probability distribution of solving a block, given the same difficulty. </p>

<p>So if I try to mine multiple times using the same difficulty, is it normal distribution with mean of 10 minutes? What is the variance? Or is it some other distribution? Or maybe even deterministic chaos? </p>
 32356: <p>The expected time (mean) for a new block is of course <strong>10 minutes</strong>, assuming constant hashrate, and no block propagation time.</p>

<p>The tricky part is that there is no such thing as <em>a point in time</em>. You can only ask only for an <strong>interval</strong>. </p>

<p>Let's illustrate this. First it is important to not fall for the <a href="https://en.wikipedia.org/wiki/Gambler%27s_fallacy" rel="noreferrer">Gambler's fallacy</a>. Luck has no "memory". Thus if no block has been found (or if a block has just been found), what is the chance of a block being found in the next minute? The easy answer would be <code>1/10 = 10%</code>. Or in the next second? <code>1/600 = 0.16667%</code>. But this is not quite true.</p>

<p>If you ask how often a block is found <em>before</em> or <em>after</em> 10 minutes, you are asking for the <a href="https://en.wikipedia.org/wiki/Cumulative_distribution_function" rel="noreferrer">cumulative distribution function</a> (CDF) of the <a href="https://en.wikipedia.org/wiki/Exponential_distribution" rel="noreferrer">exponential distribution</a>.</p>

<p>We can use Wolfram Alpha to plot this:</p>

<p><a href="http://www.wolframalpha.com/input/?i=cdf%20exponential%20distribution%20%CE%BB%3D1%2F600" rel="noreferrer">cdf exponential distribution λ=1/600</a></p>

<p>How many blocks are found <strong>after</strong> the mean (600 seconds)?</p>

<pre><code>exp(-600/600) = exp(-1) ~= 36.788%
</code></pre>

<p>How many blocks are found <strong>before</strong> the mean?</p>

<pre><code>1-exp(-1) ~= 63.212%
</code></pre>

<p>How many blocks are separated by more than 1, 2, 5, 10, 20, 30, 60 minutes?</p>

<pre><code>exp( -1/10) ~= 90.484%
exp( -2/10) ~= 81.873%
exp( -5/10) ~= 60.653%
exp(-10/10) ~= 36.788%
exp(-20/10) ~= 13.534%
exp(-30/10) ~=  4.979%
exp(-60/10) ~=  0.248%
</code></pre>

<p>So what is the chance of finding a block in the next second/minute?</p>

<pre><code>1-exp(-1/600)  ~= 0.16653%
1−exp(−60/600) ~= 9.516%
</code></pre>

<p>Bonus: How many blocks are found between 5 minutes an 20 minutes?</p>

<pre><code>exp(−5/10)−exp(−20/10) ~= 47.120%
</code></pre>
 575: <p>The time between consecutive blocks follows the <a href="http://en.wikipedia.org/wiki/Exponential_distribution" rel="noreferrer">exponential distribution</a>, with mean (roughly) 10 minutes. This means that the variance is 100 minutes^2.</p>
