# How Does Network Difficulty Relate to the Odds of Finding a Block?

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?

## 1 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 given by blockexplorer.

• 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
Jan 1, 2015 at 4:01
• @Dan 40 (forty) billion. That could be a costly mistake, thinking some hardware out there is a steal.
– user4276
Jan 13, 2015 at 2:26
• @fredsbend you're right - brain fart on my end.
– Dan
Jan 13, 2015 at 16:10