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

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As I understand your question it has two parts. One is how to calculate an approximation of someone's hash rate externally, like from a server or proxy that can see their mining results but not their actual hashing process or hash rate. The other part is how to calculate the probability that a block would be found after a given amount of work, or a given amount of time and hash rate.

I will write the formulas as javascript code, with X to the power of Y written as Math.pow(X, Y). You could run them in your browser by typing them into the address bar like for example javascript:alert((Math.pow(2, 32) * 27939) / 600).

Approximation of hash rate:

With an arbitrary target, count one share at difficulty X the same as X shares at difficulty 1. That's how pools deal with variable difficulty.

hashrate = (Math.pow(2, 32) * shares) / seconds-elapsed

An average of one share (at difficulty 1) is found for every Math.pow(2,32) hashes. This is only an average...

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Total noob here, I'm just guessing!

5 Ether per block during frontier apparantly. The calculation below is ignoring uncles, it's just for the static block reward.

The probability of mining a block should be uniformly
yourHashrate / totalHashrate.
Since a block apparantly is mined every minute (the difficulty is adjusted thereto)
etherPerDay = 24*60*5.
So after a day you can expect on average yourHashrate / totalHashrate * etherPerDay.

The stats currently state 3.1 GH/s as the total hashrate.
Assuming yourHashrate = 25 MH/s that yields
24*60*5*(25e6/3.1e9) = 58 Ether / day

Then again, I'd estimate the total hashrate to be maybe a hundred times higher when more miners run their rigs.
So a more careful estimate would be
24*60*5*(25e6/3.1e11) = 0.58 Ether / day.

Anything between (and outside of) these values is possible

Still open is the question of how likely it actually is to mine at...

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I don't know why you asked for questions if you...

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(If I may

repeat myself

a bit...) Mining is like having a lot of people throwing weighted coins (such that 1 millionth of the time it comes up heads) and telling you when they hit a heads. If one such "heads" is reported every 10 minutes (600 seconds), you can make a very accurate estimation of how many times per second the coins are being flipped. In this example:

(1,000,000 flips/heads) / (600 seconds/heads) ~= 1,667 flips/second

The network difficulty is how you adjust this 1,000,000 figure so that the 600 figure stays consistent as the network's total hash power (1,667) changes.

I don't know what a hash is either.

When

mining

, your computer creates a block of data, which has a list of all of the transactions it knows about, includes a transaction that pays you the mining bonus, and then hashes that. If the hash happens to be a small enough number (as defined by the difficulty), the block is valid. If it's not, you increment a random number...

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