Everyone knows about the "Attack 51%"" on Proof-of-Work blockchains. However, not everyone knows about the rules of regular adaptation of mining difficulty in the Bitcoin network. Based on these rules, we will consider the strategy of miners, which allows to increase profits, but at the same time reduces the overall network hashrate and resistance to "Attack 51%". We will show that the use of this strategy is beneficial to each miner individually, but it is disadvantageous to all as a whole. This is a classic "Tragedy of the commons" situation. We will consider the reasons why miners still do not apply the described strategy, and when they will start to do it.

2. It is more profitable to turn off your
mining rig for some time
Let’s calculate parameters

3. Big miner is able to:
• Deposit the amount to the
cryptoexchange
• Start generating blocks without this
transaction
• Wait for the exchange balance to update
• Publish a generated chain of blocks
• It will be longer than public one
• Withdraw the amount from the
cryptoexhange

4. Who has already suffered attacks?
• Monacoin
• Bitcoin Gold
• ZenCash
• Ethereum Classic
Screenshot taken 05.2019

5. • After every 2,016 blocks, the Bitcoin mining difficulty is adapted
• Target: 1 block every 10 minutues
• 2,016 blocks take two weeks
• If a hashrate is added or removed during this period:
• It does not affect the reward for other miners
• It affects the speed of block production
• If 99% of miners stop mining:
• The next block takes 16 hours
• The next adaptation takes four years

6. • Rig owners can switch pools (usually due to economic reasons)
• But pool owners usually decide what to mine (ex. BTC/BCH,
ETH/ETC)
• Imagine that the total hashrate will be stable over time

7. For simplicity, assume you control one half of a Bitcoin hashrate
• Keep the rig on – get the reward for 1,008 blocks (50%)
• Or
• Wait for the designated period to finish
• Turn off your rig
• Wait four weeks while other miners create 2,016 blocks
• Bitcoin will halve the difficulty for the next period
• Turn on your rig
• You will get the reward for 1,008 blocks within just a week

9. • Income for regular mining for five weeks is 5/2*1008 = 2,520 blocks
• Income for smart mining is 1,008 blocks but you pay for one week
• Suppose electricity costs 90% of the reward
• In regular mining profit will be 2,520 * 10% = 252 blocks
• In smart mining:
• profit = income – costs = 1,008 – 0.9*1,008/2 = 554.4 blocks
• Smart strategy will be more than twice as lucrative

11. • Let’s assume
• You control portion x of the total hashrate
• The total reward for all 2,016 blocks is A
• The total electricity cost for two weeks is C
• We deliberately disregard the depreciation of the rig
• Then in regular mode, profit is Ax-Cx

12. • If a smart miner turns off his rig
• Others mine 2,016 blocks times longer
• For example with x = 1/3, it will take one and a half times longer to
finish the task
• After adaptation and turning on
• The task is completed (1 − x) times faster than the planned two weeks
• For example with x = 1/3 it will take 2/3rd of the regular time (app. 10
days)
• The total duration of the two periods will be * 2 weeks

13. • If A = C (zero margin) smart strategy allows to get profit Ax2
• If C = 0 (free electricity) smart strategy gives profit Ax, regular strategy
gives >2Ax

14. • With margin M = (A − C)/A what is the optimal x?
• This equation reaches its maximum at x = 1 - √M
• For example with M = 4%, miners should disable 80% of hashrate

16. • Hashrate grows over time
• If BTC price grows (more income - can afford bigger costs)
• Due to technology (new equipment is more effective – 16nm vs 25nm)
• Using smart strategy is useless
• Network will not drop difficulty anyway
• One day hashrate will stabilize
• Income will be close to costs
• With a margin of 6.25%, it is profitable to turn off 75% of rigs (but no
more than that)

18. • Yes, it is
• In case of low marginality, the price of the existing mining rig is low
• No revenue – playing honestly is not viable
• This is a common concern
• In cases where all miners could cooperate, it would be better to:
• Turn off all the equipment except one device and share all the revenue
without costs
• Like nuclear disarmament: proportional reduction of nuclear weapon
arsenals

19. • There is no risk while the hashrate rises
• The hashrate can't rise forever
• For stable hashrate and mining marginality (6.25%), it is better to turn off
75% of rigs to drop the difficulty and save electricity
• It is viable to implement a 51% attack if your rigs don’t bring in enough
money