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Why is luck a major part of Bitcoin mining?

As mentioned on the Help->Mining page, Bitcoin mining is like rolling a dice.
Finding a block wont happen just after every 100% Difficulty of hashes everyone on the pool does, it will happen randomly, but on average, after thousands of blocks, about once every 100% Difficulty of hashes.
So this means that sometimes it will not take very long to find a block, but sometimes it will take a long time to find a block.
It's random.

Do we know what to 'expect'?

Yes indeed, we do know what to 'expect' when mining for Bitcoin blocks!
The random properties of Bitcoin mining follow what is called a Poisson Distribution (link: here)
After many results, it will look like a bell shaped curve, where in the middle it will be highest around the 100% Difficulty mark, and on the edges it will be lowest approaching the 0% Difficulty and 1400% and beyond Difficulty points on each side.

So what does this mean?

It means that we can say how often to 'expect' to find different Difficulty blocks as long as we have found a large number of blocks.
So here's a table of Bitcoin block finding probabilites:

DifficultyCDFProbability Above
50%0.39346934031 in 1.6
100%0.63212055881 in 2.7
200%0.86466471681 in 7.4
300%0.95021293161 in 20.1
400%0.98168436111 in 54.6
500%0.99326205301 in 148.4
600%0.99752124781 in 403.4
666%0.99871885361 in 780.6
700%0.99908811801 in 1096.6
800%0.99966453741 in 2981.0
900%0.99987659021 in 8103.1
1000%0.99995460011 in 22026.5
1400%0.99999916851 in 1202604.3

What this table means, using the 200% example, is that on average, over a large number of blocks, 1 in 7.4 blocks will be over 200%
Yes that means that blocks over 200% Difficulty are actually expected to be quite common!

In the long run it all balances out since you also expected to get enough short blocks to make up for the less regular long blocks.
However, since the process is pseudo-random, you cannot expect luck to change each time we get a long, or short block.
Every block found is independent of every other block found, so it will of course be random when luck will change from good to bad or bad to good.
We may get a number of high Difficulty blocks in a row, or may get a number of low Difficulty blocks in a row, but we do not ever know in advance what the next block will be, and it doesn't matter what Difficulty the previous found block was.

20th Aug 06:25:20 UTC sync: 2 Copyright © Kano 2014-2018 0.0452s