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

4

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?

Dan

Posted 2015-01-01T03:04:53.147

Reputation: 155

Answers

4

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.

cdecker

Posted 2015-01-01T03:04:53.147

Reputation: 7 878

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 – 2015-01-01T04:01:57.640

@Dan 40 (forty) billion. That could be a costly mistake, thinking some hardware out there is a steal. – 4276 – 2015-01-13T02:26:49.283

@fredsbend you're right - brain fart on my end. – Dan – 2015-01-13T16:10:27.723

Asked: 2015-01-01T03:04:53.147

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Active: 2016-03-16T10:22:39.110