<p>In hopes of making this a useful answer in the long run, I will show how one can answer this question in general, then give an example using today's values.</p>

<p>Let <em>d</em> be the current Bitcoin difficulty, which can be found, for example, with the <code>getdifficulty</code> command in Bitcoin Core, or from any of a number of sites by searching Google for "bitcoin difficulty".  The average number of hashes needed to mine one block is then <em>h</em> = 2<sup>32</sup><em>d</em>.</p>

<p>Suppose you have mining equipment with a total hash rate of <em>r</em> hashes per second.  The time <em>M</em> needed to mine one block is of course random.  Since each hash is effectively an independent trial of mining a block, all of which have the same very small probability of success, and those trials are executed very rapidly, the distribution of <em>M</em> is well approximated by an <a href="http://en.wikipedia.org/wiki/Exponential_distribution" rel="nofollow">exponential distribution</a> with rate <em>r</em>/<em>h</em> Hz.  As such, the probability <em>p</em> of mining at least one block within some fixed time <em>t</em> seconds is <em>p</em> = <strong>P</strong>(<em>M</em> &lt; <em>t</em>) = 1 − <em>e</em><sup>−<em>tr</em>/<em>h</em></sup>.  If you choose values for <em>t</em> and <em>p</em>, you can solve for <em>r</em> to determine what hash rate you would need to have probability <em>p</em> of mining a block within <em>t</em> seconds.</p>

<p>You can then look at a page such as <a href="https://en.bitcoin.it/wiki/Mining_hardware_comparison" rel="nofollow">https://en.bitcoin.it/wiki/Mining_hardware_comparison</a> which lists the hash rate of various mining hardware, and decide how many units of your favorite miner you would need to achieve that hash rate.</p>

<p>As an example, suppose you want a 50% chance of mining a block within 30 days. As of right now the difficulty level is <em>d</em> =  39 603 666 252. Taking <em>p</em> = 1/2 and <em>t</em> = 60*60*24*30 = 2 592 000, you find </p>

<blockquote>
  <p><em>r</em> = 45 486 834 753 298</p>
</blockquote>

<p>or about 45 Thash/sec.  Let us suppose you wanted to standardize on the ASICMiner BE Prisma, which, according to the page linked above, generates 1.4 THash/sec, draws 1.1 kW of electrical power, and costs US $600.  You would need roughly 32 such devices, at a total cost of US $19 200.  You would use 35.2 kW of electricity.  (By contrast, electricity service to single family homes in the US is often a maximum of 24 kW (100 A at 240 V).)  At a typical electricity cost of US $0.10 per kWh, that would cost you US $3.50 per hour, or US $2 520 per month.</p>

<p>This assumes that the mining difficulty does not increase significantly over the course of the month, which is not a good assumption (it typically increases every 14 days or so).  The expected mining rewards from this setup would continue to decrease as the difficulty increases over time.</p>

CC BY-SA 3.0
2014-11-12T03:50:24.533Z
2014-11-12T03:50:24.533Z
Nate Eldredge
<p>What's the minimum setup that you guys know, that can, today, mine at least 1 block alone, without the use of mining pools?
<p>I know I wouldn't be able to afford it, but just by curiosity...</p>

CC BY-SA 3.0
2014-11-12T02:43:51.900Z
It really depends on how long you're willing to wait.
Nick ODell
CC BY-SA 3.0
2014-11-12T03:06:16.053Z
@NickODell: Indeed.  [Paper and pencils suffice](http://bitcoin.stackexchange.com/questions/21030/what-is-the-approximate-hashrate-of-a-human), if you're willing to wait about 695 quadrillion years.
Nate Eldredge
<mining-profitability><difficulty><hashpower>
What's the minimum setup to mine a block alone?
Guelando 3
# What's the minimum setup to mine a block alone?

(Asked by: username_0 on 2014-11-11)

What's the minimum setup that you guys know, that can, today, mine at least 1 block alone, without the use of mining pools?

I know I wouldn't be able to afford it, but just by curiosity...

**Tags:** mining-profitability, difficulty, hashpower

> **Comments:**
> **username_1**: It really depends on how long you're willing to wait.  
> **username_2**: @username_1: Indeed.  [Paper and pencils suffice](http://bitcoin.stackexchange.com/questions/21030/what-is-the-approximate-hashrate-of-a-human), if you're willing to wait about 695 quadrillion years.  

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## 1 answers

### Answer by username_2 on 2014-11-12. Score: 4

In hopes of making this a useful answer in the long run, I will show how one can answer this question in general, then give an example using today's values.

Let *d* be the current Bitcoin difficulty, which can be found, for example, with the `getdifficulty` command in Bitcoin Core, or from any of a number of sites by searching Google for "bitcoin difficulty". The average number of hashes needed to mine one block is then *h* = 232*d*.

Suppose you have mining equipment with a total hash rate of *r* hashes per second. The time *M* needed to mine one block is of course random. Since each hash is effectively an independent trial of mining a block, all of which have the same very small probability of success, and those trials are executed very rapidly, the distribution of *M* is well approximated by an [exponential distribution](http://en.wikipedia.org/wiki/Exponential_distribution) with rate *r*/*h* Hz. As such, the probability *p* of mining at least one block within some fixed time *t* seconds is *p* = **P**(*M* < *t*) = 1 − *e*−*tr*/*h*. If you choose values for *t* and *p*, you can solve for *r* to determine what hash rate you would need to have probability *p* of mining a block within *t* seconds.

You can then look at a page such as <https://en.bitcoin.it/wiki/Mining_hardware_comparison> which lists the hash rate of various mining hardware, and decide how many units of your favorite miner you would need to achieve that hash rate.

As an example, suppose you want a 50% chance of mining a block within 30 days. As of right now the difficulty level is *d* = 39 603 666 252. Taking *p* = 1/2 and *t* = 60\*60\*24\*30 = 2 592 000, you find

> *r* = 45 486 834 753 298

or about 45 Thash/sec. Let us suppose you wanted to standardize on the ASICMiner BE Prisma, which, according to the page linked above, generates 1.4 THash/sec, draws 1.1 kW of electrical power, and costs US $600. You would need roughly 32 such devices, at a total cost of US $19 200. You would use 35.2 kW of electricity. (By contrast, electricity service to single family homes in the US is often a maximum of 24 kW (100 A at 240 V).) At a typical electricity cost of US $0.10 per kWh, that would cost you US $3.50 per hour, or US $2 520 per month.

This assumes that the mining difficulty does not increase significantly over the course of the month, which is not a good assumption (it typically increases every 14 days or so). The expected mining rewards from this setup would continue to decrease as the difficulty increases over time.


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