Mining pool

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 ${\displaystyle R=B\cdot p}$.

Miners earn shares until the pool finds a block (the end of the mining round). After that each user gets reward ${\displaystyle R=B\cdot {\frac {n}{N}}}$, where ${\displaystyle n}$ is amount of his own shares, and ${\displaystyle N}$ 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 (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.[5] This reduces the ability to cheat the mining pool system by switching pools during a round, to maximize profit.

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 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 (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.[5][6]

Geometric Method (GM) was invented by Meni Rosenfeld.[7] 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.

The method goes as follows:

• Choose parameters ${\displaystyle f}$ and ${\displaystyle c}$ (fixed and variable fee).
• At the start of every round, set ${\displaystyle s=1}$. For every worker ${\displaystyle k}$, let ${\displaystyle S_{k}}$ be the worker's score for this round, and set ${\displaystyle S_{k}=0}$.
• Set ${\displaystyle r=1-p+{\frac {p}{c}}}$, where ${\displaystyle p=1/D}$. If the difficulty changes during the round, ${\displaystyle r}$ needs to be updated.
• When worker ${\displaystyle k}$ submits a share, set ${\displaystyle S_{k}=S_{k}+spB}$, and then ${\displaystyle s=sr}$.
• If the share is a valid block, end the round. For every worker ${\displaystyle k}$ pay ${\displaystyle {\frac {(1-f)(r-1)S_{k}}{sp}}}$

Generalized version of Geometric and PPLNS methods.[7] It involves new parameter: ${\displaystyle o}$ ("cross-round leakage"). When ${\displaystyle o=0}$ this becomes the Geometric method. When ${\displaystyle o=1}$ this becomes a variant of PPLNS, with exponential decay instead of a step function.

• Choose parameters ${\displaystyle f}$, ${\displaystyle c}$, and ${\displaystyle o}$.
• When the pool first starts running, initialize ${\displaystyle s=1}$. For every worker ${\displaystyle k}$, let ${\displaystyle S_{k}}$ be the worker's score, and set ${\displaystyle S_{k}=0}$.
• Set ${\displaystyle r=1+{\frac {1}{c}}p(1-c)(1-o)}$. If at any point the difficulty or the parameters change, ${\displaystyle r}$ should be recalculated.
• When worker ${\displaystyle k}$ submits a share, set ${\displaystyle S_{k}=S_{k}+(1-f)(1-c)spB}$ (where ${\displaystyle B}$ is the block reward at the time it was submitted), and then ${\displaystyle s=sr}$.
• If the share is a valid block, then also do the following for each worker ${\displaystyle k}$: Give him a payout of ${\displaystyle {\frac {1}{c_{s}}}(1-o)S_{k}}$, and then set ${\displaystyle S_{k}=S_{k}\cdot o}$.