<p>The difficulty is calculated in multiples of difficulty 1, which is defined as a probability of a single hash to be valid of 1/(2^32), i.e., in expectation one PoW is found by iterating through all 2^32 possible nonce values.</p>

<p>So given a difficulty of 40640955016.576 we have a probability for a single hash to be a valid PoW of 1/(2^32*40640955016.576). This in turn results in the <a href="http://www.wolframalpha.com/input/?i=1%2F(2%5E32*40640955016.576)" rel="nofollow">~5.72e-21</a> given by blockexplorer.</p>

CC BY-SA 3.0
2015-01-01T04:01:57.640Z
Ah! So a difficulty of 1 has odds of basically 1 in 4.3 billion (2^32) for any given hash. And with the difficulty coincidentally at around 4 billion, the odds are 1 /(~4bn * ~4bn). That's mind boggling. Thanks!
Dan
CC BY-SA 3.0
2015-01-13T16:10:27.723Z
@fredsbend you're right - brain fart on my end.
Dan
CC BY-SA 3.0
2015-01-01T03:43:09.317Z
2015-01-01T03:43:09.317Z
cdecker
<p>Right now the network difficulty for mining is <code>40640955016.576</code>. And, according to blockexplorer.com, the current odds of finding a block for any given hash is <code>0.0000000000000000000057288784391318092718842084135055792</code>. </p>

<p>My question is, how is the "difficulty" and the odds of finding a block related? Obviously a difficulty of ~4 billion does not mean there's a 1 in 4 billion chance of finding a block (any modern ASIC miner could find a block in a heartbeat). So what does it mean exactly and how does difficulty and odds relate? And how can one calculate the odds based on the difficulty?</p>

<block><difficulty>
How Does Network Difficulty Relate to the Odds of Finding a Block?
Dan
# How Does Network Difficulty Relate to the Odds of Finding a Block?

(Asked by: username_0 on 2015-01-01)

Right now the network difficulty for mining is `40640955016.576`. And, according to blockexplorer.com, the current odds of finding a block for any given hash is `0.0000000000000000000057288784391318092718842084135055792`.

My question is, how is the "difficulty" and the odds of finding a block related? Obviously a difficulty of ~4 billion does not mean there's a 1 in 4 billion chance of finding a block (any modern ASIC miner could find a block in a heartbeat). So what does it mean exactly and how does difficulty and odds relate? And how can one calculate the odds based on the difficulty?

**Tags:** block, difficulty


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## 1 answers

### Answer by username_1 on 2015-01-01. Score: 4 | Accepted answer

The difficulty is calculated in multiples of difficulty 1, which is defined as a probability of a single hash to be valid of 1/(2^32), i.e., in expectation one PoW is found by iterating through all 2^32 possible nonce values.

So given a difficulty of 40640955016.576 we have a probability for a single hash to be a valid PoW of 1/(2^32\*40640955016.576). This in turn results in the [~5.72e-21](http://www.wolframalpha.com/input/?i=1%2F(2%5E32*40640955016.576)) given by blockexplorer.

> **Comments:**
> **username_0**: Ah! So a difficulty of 1 has odds of basically 1 in 4.3 billion (2^32) for any given hash. And with the difficulty coincidentally at around 4 billion, the odds are 1 /(~4bn * ~4bn). That's mind boggling. Thanks!  
> **username_0**: @fredsbend you're right - brain fart on my end.  

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