How does a difficulty increase affect a miner's income?

Question

At the time I write this, there are a lot of people getting into Bitcoin mining for the first time. Many buy ASIC hardware and are later surprised that their mining income suddenly drops due to a difficulty increase.

If I mine X bitcoins per day, then the difficulty goes up Y percent, how many coins do I get per day after this?

For instance, if my hashrate brings 1 BTC per day and the difficulty rises 30%, what is my average daily mining income with the same hashrate after this change in difficulty?

Answer 1

Your profit relates to the amount of hashing power you contribute to the network. Since your mining power is constant, your share of the total hashing power decreases relatively when the network's hashing power increases. I.e. we can deduce the following formula:

newProfit = currentProfit * currentDiff/newDiff.

At a currentProfit of 1BTC/d and a 30% increase in difficulty, you get:

(1BTC/d)*100/(100+30)= (1BTC/d)/1.3 = 0.76923077 BTC/d

i.e. your profit decreases by ~23%.

Answer 2

The target, which the difficulty is derived from, determines how hard hashing should be so that one block is found every 10 minutes, on average.

A 30% increase in difficulty means the network was finding blocks 30% too fast over the last 2015 blocks so as a result, your profits (assuming no other miners join or leave the network) will be about 23% (1 - 100/130) less. For example, 1 GH/s nets about 0.00098431 a day at the current difficulty. With an increase of 30%, this would mean about 0.00075716 per day, 0.00098431/0.00075716 is about 130%.

However, with all the mining equipment being added between blocks, it's likely you'll make a lot less.

Answer 3

With the increase in difficulty there is also a rise value of BTC that helps compensate for the decrease hash rate. Without miners Bitcoin would not see the completion of transactions therefore it seems unlikely for miners to go unpaid.