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Mining pool
In the context of cryptocurrency mining, a mining pool is the pooling of resources by miners, who share their processing power over a network, to split the reward equally, according to the amount of work they contributed to the probability of finding a block. A "share" is awarded to members of the mining pool who present a valid partial proof-of-work. Mining in pools began when the difficulty for mining increased to the point where it could take centuries for slower miners to generate a block. The solution to this problem was for miners to pool their resources so they could generate blocks more quickly and therefore receive a portion of the block reward on a consistent basis, rather than randomly once every few years.
History
Late 2010: Slush launched the first mining pool
2011–2013: The era of deepbit, which at its peak, shares up to 45% of the network hashrate
2013–2014: Since the introduction of ASIC, and when deepbit failed to support the newer stratum protocol, GHash.IO replaced deepbit and became the largest
2014–2015: Rise of China. F2Pool which launched in May 2013, replaced GHash.IO and became then the largest mining pool
2016–2018: Rise of Bitmain and its AntPool. Bitmain also controls a few other smaller pools like BTC.com and ViaBTC
2019–2020: The launch of Poolin. Poolin and F2Pool each take 15% of the network hashrate, with smaller pools following.
2020: Binance launches a mining pool following Huobi and OKex. Luxor launches a US-based mining pool.
Mining pool share
Share is the principal concept of the mining pool operation. Share is a potential block solution. So it may be a block solution, but it is not necessarily so. For example, suppose a block solution is a number that ends with 10 zeros and, a share may be a number with 5 zeros at the end. Sooner or later one of the shares will have not only 5, but 10 zeros at the end, and this will be the block solution.

Mining pools need shares to estimate the miner's contribution to the work performed by the pool to find a block. There are numerous miner reward systems: PPS, PROP, PPLNS, PPLNT, and many more.

Mining pool methods
Mining pools may contain hundreds or thousands of miners using specialized protocols. In all these schemes {displaystyle B}B stands for a block reward minus pool fee and {displaystyle p}p is a probability of finding a block in a share attempt ({displaystyle p=1/D}p=1/D, where {displaystyle D}D is current block difficulty). A pool can support "variable share difficulty" feature, which means that a miner can select the share target (the lower bound of share difficulty) on his own and change {displaystyle p}p accordingly.

Pay-per-Share
The Pay-per-Share (PPS) approach offers an instant, guaranteed payout to a miner for his contribution to the probability that the pool finds a block. Miners are paid out from the pool's existing balance and can withdraw their payout immediately. This model allows for the least possible variance in payment for miners while also transferring much of the risk to the pool's operator.

Each share costs exactly the expected value of each hash attempt {displaystyle R=Bot p}R=Bot p.

Proportional
Miners earn shares until the pool finds a block (the end of the mining round). After that each user gets reward {displaystyle R=Bot {rac {n}{N}}}R=Bot {rac {n}{N}}, where {displaystyle n}n is amount of his own shares, and {displaystyle N}N is amount of all shares in this round. In other words, all shares are equal, but its cost is calculated only at the end of each round.

Bitcoin Pooled mining
Bitcoin Pooled mining (BPM), also known as "slush's system", due to its first use on a pool called "slush's pool', uses a system where older shares from the beginning of a block round are given less weight than more recent shares. A new round starts the moment the pool solves a block and miners are rewarded Proportional to the shares submitted. This reduces the ability to cheat the mining pool system by switching pools during a round, to maximize profit.

Pay-per-last-N-shares
Pay-per-last-N-shares (PPLNS) method is similar to Proportional, but the miner's reward is calculated on a basis of N last shares, instead of all shares for the last round. It means that when a block is found, the reward of each miner is calculated based on the miner contribution to the last N pool shares. Therefore, if the round was short enough all miners get more profit and vice versa.

Solo Mining Pool
Solo pools operate the same way as usual pools, with the only difference being that block reward is not distributed among all miners. The entire reward in a solo pool goes to the miner who finds the block.

Peer-to-Peer Mining Pool
Peer-to-peer mining pool (P2Pool) decentralizes the responsibilities of a pool server, removing the chance of the pool operator cheating or the server being a single point of failure. Miners work on a side blockchain called a share chain, mining at a lower difficulty at a rate of one share block per 30 seconds. Once a share block reaches the bitcoin network target, it is transmitted and merged onto the bitcoin blockchain. Miners are rewarded when this occurs proportional to the shares submitted prior to the target block. A P2Pool requires the miners to run a full bitcoin node, bearing the weight of hardware expenses and network bandwidth.

Geometric method
Geometric Method (GM) was invented by Meni Rosenfeld. It is based on the same "score" idea, as Slush's method: the score granted for every new share, relatively to already existing score and the score of future shares, is always the same, thus there is no advantage to mining early or late in the round.

Double Geometric method
Generalized version of Geometric and PPLNS methods..

Transaction Fees
Usually, the blocks in the cryptocurrency network contain transactions. Transaction fees are paid to the miner (mining pool). Different mining pools could share these fees between their miners or not. Pay-per-last-N-shares (PPLNS), Pay-Per-Share Plus (PPS+) or Full Pay-Per-Share (FPPS) are the most fair methods where the payouts from the pool include not only the block subsidy but also the transaction fees.

Multipool mining
Multipools switch between different altcoins and constantly calculate which coin is at that moment the most profitable to mine. Two key factors are involved in the algorithm that calculates profitability, the block time, and the price on the exchanges. To avoid the need for many different wallets for all possible minable coins, multipools may automatically exchange the mined coin to a coin that is accepted in the mainstream (for example bitcoin). Using this method, because the most profitable coins are being mined and then sold for the intended coin, it is possible to receive more coins in the intended currency than by mining that currency alone. This method also increases demand on the intended coin, which has the side effect of increasing or stabilizing the value of the intended coin.