1. Why other people pool hopping is a problem for you (a 24/7 single pool miner).

2. Why proportional pools, not pool hoppers, are the fundamental issue.

First of all, we're going to assume that there is a proportional pool called Pool A, which mines at 90GH/sec without our miner.

Now, we have a miner, let's call him Bob, he runs a 10GH mining operation and he's trying to work out why hopping is an issue. To do this, we're going to make the numbers easy to work with. One block's regular length will be defined as 10 difficulty, which under normal circumstances (zero hopping) will equate to 10 units of time.

So, if Bob statically mines on Pool A, and nobody else is hopping, he should make approximately 5BTC (10% of 50BTC, as he's 10% of the hash rate) every 10 units of time.

**0.5 BTC per time unit**is Bob's expected yield.

Now let's see what happens to Bob if 50% of the pool hops after 5 time units (this is circa optimal). This means the pool will do the first half of the block at 100GH/sec, and the second half at 50GH/sec. In this scenario, Bob will be 10% of the pool for half of an average block, and 20% of it for the other half.

This means that in the first half he will earn 2.5 BTC, and in the second half, he will earn 5 BTC (20% of 25 BTC). On an average-length block, we can see that Bob is not negatively affected by hopping as the block will take 15 units of time, but he will get 7.5 BTC, still

**5 BTC every 10 units**.

From here, it's hard to see where the issue with hopping is, but we have to explore different length blocks to better understand the issue. Let's say, as happens in real mining, that instead of all 10 difficulty-unit blocks, we have a 5 unit block, and then a 15 unit block.

Without hopping, Bob will be 10% of the pool for 20 time units, and will make 10 BTC, or 0.5 BTC per time unit.

With hopping, Bob will earn 5 BTC from the 5 difficulty block, as the hoppers won't hop and he'll keep being 10% of the pool for the whole thing, this will be 1 BTC per time unit.

From the second block, he will earn 1.66 BTC from the first third of the block (1/3 of his 5 BTC for the block), and then 3.33 BTC for each of the second difficulty-thirds of the block. This totals out at 8.33 BTC, but this block will have taken 25 units of time to complete.

In case you didn't follow the maths.

First third - 5 difficulty - 100 GH - 1 diff:1 unit time - 5 units time

Second third (after 5 time units) - 5 difficulty - 50 GH - 1 diff:2 unit time - 10 units time

Third third - 5 difficulty - 50GH - 1 diff:2 unit time - 10 units time

This means that he's made

**13.33 BTC in a total of 30 units of time**for the short block and the long block, which is significantly lower than his expected BTC/time unit yield.

This return is only

**0.44 BTC per time unit**. This is

**12% lower**than he'd normally get!

On a longer block, it's even worse returns than this, and deviates even further from his expected yield, but a shorter block doesn't make up for it as the hoppers won't hop on those. Doing the maths for a 25 difficulty block, a 2 difficulty block and a 3 difficulty block, Bob would make 19 BTC in a staggering 50 units of time, which would be more than 20% below his expected 25 BTC.

If there was no hopping, these 3 blocks would have earned him 15 BTC in 30 units of time.

*Obviously this is based on a huge proportion (50% of the MH/sec) jumping, which isn't likely right now, but the number of people using hopping techniques is only going to rise, and any loss due to this should be unacceptable to a miner.*

But don't complain at other people for screwing you because they're pool hopping. You facilitate them doing it, it's their right to do it, you're screwing yourself. If you offered someone $10 an hour for a 5 hour shift or $7 an hour for a 10 hour shift, they'd take the 5 hour shift. This is what the hoppers are doing by maximising their own returns.

The answer is better pools, not calling people out for doing something they have a right to do.

**tl;dr: By using a proportional pool 24/7, you may as well be paying a significant (up to 12%) fee.**