The probability of mining a block is 1/(2

^{32}*D) for each hash. (D is Bitcoin difficulty) so the amount of time is dependent on the hash rate and luck. Difficulty is currently 336899932796. Let's invert the equation to see how many hashes are required (on average) to mine a block.

#hashes = 2

^{32}*336899932796

#hashes = 1,446,974,193,383,417,839,616

Let's use

Slush's pool. Their stated hash rate is 154.9 Ph/s so,

time to block = 1,446,974,193,383,417,839,616/154.9X10

^{15}Ph/s

time to block = 9341.3 seconds (or about 2 hours 35 minutes and 41.3 seconds)

Now look at a screen capture of Slush's public statistics:

Compare the actual time taken to find a block (under the reading glasses) with the calculated time of 2:35:41.3 and then check out the associated luck (under the sunglasses). As you can see, if blocks take longer than determined based on probability to find, the percentage luck is <100% and when the block is found sooner, luck is >100% in the long run though based on the

*Law of large numbers*, the average time to find a block should be very close to the calculated value.

If a pool is consistently below 100%, one would consider it unlucky and if it is consistently above 100%, one would consider it lucky. This can happen for periods of time when a pool has only a small percentage of the total network's hash rate but as I said, in the long run, it should even out.