Mining pools are an indispensable part of digital currency mining. They provide a platform for miners to work together, effectively reducing the risks and uncertainties of mining. So, why do mining pools exist? Why is variance so important in this process? Let’s dive into these questions together.

The existence of mining pools is not accidental, but is to solve the mining problems faced by individual miners. In the mining process of cryptocurrencies such as Bitcoin, you can imagine how difficult it is for a single miner to complete a block mining alone. This has led to miners joining mining pools one after another to increase the chance of successful mining by working together, sharing computing power and rewards.

The existence of mining pools allows miners to share the risks and costs of the mining process. In a mining pool, miners cooperate in mining and add their own computing power to increase the overall mining efficiency. Even if a miner has less computing power, in a mining pool, there is still a chance to obtain stable mining rewards through cooperation. Compared with independent mining, the chance of success is greater.

In addition, mining pools can help miners avoid uncertainty in mining. During the mining process of a single miner, due to the influence of luck, multiple consecutive blocks may not be successfully mined, which will lead to significant fluctuations in the miner's income. In a mining pool, miners share rewards. By sharing the uncertainty equally, each miner can obtain mining rewards more stably, reducing the volatility of earnings.

In addition to the importance of mining pools, variance also plays a crucial role in the mining world. Variance is an indicator used in statistics to measure the degree of data dispersion, and in mining pools, variance reflects the uncertainty of miners’ mining rewards. A higher variance means that the miner's mining rewards fluctuate more and the income is unstable; while a lower variance means that the mining rewards are less volatile and the income is more stable.

Mining pool managers usually set reasonable reward mechanisms to minimize the variance of miners' mining profits. Through a carefully designed reward distribution plan, mining pools can balance the income gap between miners, reduce the variance of overall mining rewards, and improve the stability of miners' income. This stability is crucial for miners and can help them better plan their mining profits and reduce the risks caused by uncertainty.

In mining pools, the importance of variance is self-evident. By reducing the variance of mining rewards, miners can obtain more stable income, which improves the motivation and sustainability of participating in mining. At the same time, the existence of mining pools also provides a platform for miners to work together to jointly deal with risks and challenges in the mining process.

To sum up, the existence of mining pools is not a simple collective behavior, but to better deal with the uncertainty and risks in the mining process. As an important indicator to measure the volatility of mining rewards, variance plays a vital role in mining pools. Through the cooperation mechanism of the mining pool and reasonable reward design, miners can obtain mining rewards more stably, improving the overall mining efficiency and income stability. Therefore, the importance of mining pools and variance cannot be ignored. Together they form an indispensable part of the digital currency mining ecosystem.

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Why do mining pools exist? In Bitcoin, miners join mining pools for two reasons. One is to avoid the hassle of running a full node - this can be mitigated by requiring miners to include proof of blockchain recoverability. The second is to reduce the variance of their mining returns (
Variance: used to measure the deviation between a random variable and its mathematical expectation).

But why does variance matter? After all, statistically speaking, it all boils down to the same expectations. Are people really so risk averse?

A miner controls a portion p of the mining power, thereby obtaining the corresponding probability p of mining each block. This obeys the Bernoulli distribution (Translator's Note: Bernoulli distribution, Bernoulli
distribution is a discrete probability distribution, also known as two-point distribution or 0-1 distribution. If the Bernoulli test succeeds, the Bernoulli random variable takes the value 1. If the Bernoulli test fails, the Bernoulli random variable The value of the variable is 0. Note its success probability as p, failure probability as (1-p)), and variance = p(1-p). Since all blocks are independent, there are 365 days24 hours6 blocks in a year, and the annual variance is 65246p(1-p). At the same time, the expected return is 65246p.

The relative standard deviation is the square root of the variance divided by the expected return, that is: sqrt[365246p(1-p)] / (65246p) or sqrt[1/p-1] /
sqrt[65246] ~ sqrt[1/p-1] / 229.26

If you control 10% of the hash power in the network, then your annual relative standard deviation is 1.3%; if you control only 1% of the hash power, the relative standard deviation is 4.3%; if you control only 0.1%, then the relative standard deviation is 13.8 %; For a weak miner with only 0.01% of the computing power (remind you, this miner still returns 11 Bitcoins every month), the annual relative standard deviation will increase to 43.6%.

But so what? Why not take the risk?

The reason is of course because mining costs are fixed (mining costs are
fixed). A miner must therefore compare this return to the relative standard deviation of his expected return. A miner who wants to earn an expected return on investment of 10% and controls 0.19% of the hash power will give him a 16% chance of losing his money at the end of the year.

One can calculate the ratio of these two numbers, which is called the Sharpe index (a measure of the average return per unit of risk). The profit margin should be calculated and listed there, but it tends to be close to 0 anyway.

If the Sharpe ratio decreases, the risk-reward ratio becomes unattractive. There comes a point when it becomes more profitable for miners to invest in the stock market than to try to mine.

The largest miner benefits from a higher Sharpe Index than its competitors. Therefore, they are incentivized to invest additional money in mining, pushing down the margins of others.
down), and then squeeze competitors out of the market.

Does this mean that the mining industry is destined to be dominated by monopolies? Not necessarily. The solution is to let miners outsource the risk instead of outsourcing the mining. This is what p2p mining can achieve. p2p mining acts like a decentralized underwriter, providing a swap between miners’ expected returns and actual returns.
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