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Many pools offer a difficulty of 1 per share.

Since variable difficulty is a feature of a couple of pools, I'd like to understand how many shares would be created at varying levels of difficulty.

  • What is the formula to determine the average number of shares when the hashrate and difficulty are known?

This is a variation of the following question:

Given the probability of finding a block, and time taken, can I infer hashrate?

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One difficulty-1 share takes on average 2^32 = 4.3 billion hashes to find.

If your hashrate is X GH/s, then in one day the number of difficulty-d shares you'll find is

(X * 1000000000 * 86400) / (2^32 * d)

Or simply

20,000 * X / d

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