Partly one reads of the catastrophic effects of sinking the hash rate. From extremely slow transactions to the freezing of the blockchain is the speech. But how is the block time related to the hash rate?
Just a few years ago, there was a dreaded apocalyptic scenario: what happens if Bitcoin loses a significant amount of the hash rate? Pessimists saw this as a devastating chain reaction that could freeze bitcoin. In times after a Bitcoin-Halving or a Hard Fork such doomsday concepts are pushed into the background a little bit, but they are not gone.
How likely is such a scenario? To clarify that, here are two estimates made. The first thing to discuss is the problem of classical probability theory. It will then be seen that a look at Bitcoin’s performance data confirms this estimate.
To take all readers, let’s briefly repeat what block time, difficulty and hash rate are. For a more detailed introduction to mining, please refer to the corresponding tutorial. As is known, miners play a key role in the Bitcoin ecosystem: their calculations ensure that the blockchain is built in a decentralized consensus by creating new blocks for the blockchain.
The miners summarize transactions. From these transactions, the hash (the checksum) of the previous block, the timestamp, and a count variable (the nonce), a new hash is generated. The Bitcoin protocol requires a specific form of this hash: it must start with a defined number of zeroes. One measure of the probability of reaching this target is the difficulty. The miner who first finds a hash that meets these criteria will receive newly generated Bitcoin and transaction fees as a reward for his efforts – and the block thus generated will be accepted as a new block of the Bitcoin blockchain.
The Bitcoin protocol optimizes this process with the goal of finding a new block approximately every ten minutes. If this happens faster, the requirements for new blocks to be generated are increased. If this happens slower, these requirements, and thus the Difficulty are adjusted as well.
Unlike other cryptocurrencies such as Monero, the Bitcoin protocol adjusts the difficulty only every 2,016 blocks. With a target average block time of ten minutes, that’s two weeks.
Finally, the hash rate is a measure of the computing power of the network. So should the hash rate break dramatically, this would mean finding blocks too slow for about two weeks. This could, according to the doomsday scenario, lead to the fact that more and more miners jump off – after all, mining would not be worthwhile without the further development of the blockchain. In the end, a frozen Blockchain would stand.
The search for a block matching the target is a random iterative process. As a model system, the system can be freely illustrated by the motto “Let’s imagine jans stupid” as a dice game. Let’s say the goal is to roll a six. With a cube in hand, the probability is 1/6, with two dice at just 31 percent. Three dice lead to a probability of 42 percent. With even more dice, the probability is approaching more and more the 100 percent:
This relationship could also be reversed. The average duration for “throwing” a six behaves antiproportional to the dice. The number of throws to be made up to a six will decrease with the number of dice. This number of throws, in turn, is a measure of the time it takes to find a six:
In the model system considered, the number of throws would only be doubled if the number of dice drops by more than 75 percent. The thought experiment can be transferred to the mining process of Bitcoin. Each cube would stand for a miner in this consideration, the six would be the target and the average number of throws would correspond to the block time that would be with a given amount of dice (ie a high hash rate) on a roll. The result of this model consideration would be that only with a removal of a large part of the dice, the duration increases until the throwing of a six strong.
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