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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?

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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 '15 at 4:01
  • @Dan 40 (forty) billion. That could be a costly mistake, thinking some hardware out there is a steal. – fredsbend Jan 13 '15 at 2:26
  • @fredsbend you're right - brain fart on my end. – Dan Jan 13 '15 at 16:10

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