Pay-Per-Share (PPS)

Pay-per-share (PPS) is a method that a mining pool uses to pay its members. Each time a miner submits a valid "share", a piece of work showing that it is hashing honestly, the pool credits a fixed amount calculated from the expected value of that share. The miner is paid whether or not the pool actually finds a block, so its income is steady and predictable.

PPS is one of several reward systems used in proof-of-work mining. Its closest relatives are full pay-per-share (FPPS), which also passes on an estimate of transaction fees, and pay-per-last N shares (PPLNS), which pays only when blocks are found. Under PPS the pool operator, not the miner, absorbs the variance of block discovery, and it charges a higher fee for doing so.

Think of fishing boats. A crew member can either take a share of whatever the boat lands, which means big weeks and empty weeks, or take a fixed wage per hour on deck, paid even if the nets come up empty. PPS is the fixed wage. The boat owner keeps the catch, good or bad, and sets the wage a little below the average catch to cover the bad weeks.

For a small miner, waiting for a share of an actual block can mean long dry spells. PPS turns that lottery into a regular pay packet, at the price of giving up a slice of the expected earnings to the pool.

A share is a hash that meets an easier target than the real network target. A "difficulty-1" share is expected to take $2^{32}$ hash attempts, and a full block is expected to take $D \times 2^{32}$, so on average a pool needs $D$ difficulty-1 shares to find one block. The PPS payment per difficulty-1 share is:

• $P_{\text{share}}$ is the amount credited for one difficulty-1 share.
• $f$ is the pool fee, written as a decimal.
• $B$ is the block reward counted by the scheme; under plain PPS this is the block subsidy only.
• $D$ is the network's mining difficulty.

A miner's expected daily pay follows from its hashrate $h$ in hashes per second:

Worked example: take the Bitcoin (BTC) subsidy of 3.125 BTC that applies after the April 2024 halving, a round illustrative difficulty of 100 trillion ($10^{14}$), a miner hashing at 200 TH/s ($2 \times 10^{14}$ hashes per second) and a 2% fee. The miner performs $1.728 \times 10^{19}$ hashes a day, against $4.295 \times 10^{23}$ expected per block, which is about 0.0000402 of a block. Multiplying by 3.125 BTC gives 0.0001257 BTC, and after the fee the miner receives about 0.0001232 BTC, or roughly 12,300 satoshis, per day.

Under PPS the pool pays out the expected value of every share immediately, but its own income arrives only when it finds blocks, which happens at random. A run of bad luck can leave the pool paying miners for weeks of work that produced fewer blocks than expected. To survive such runs, a PPS pool must hold a cash reserve and charges a higher fee than pools using PPLNS or proportional schemes. Fees for PPS and its variants have commonly been in the range of about 2% to 4%, against 0% to 2% for PPLNS pools, though each pool sets its own.

The fixed price also removes the incentive for "pool hopping", where miners jump between pools to collect a larger share of rewards early in a round. Because every share has the same value at any time, there is nothing to gain by timing. The risk the operator carries instead is solvency: a thinly capitalised PPS pool can fail during a long losing streak.

As transaction fees became a meaningful share of Bitcoin miners' income, plain PPS, which leaves fees with the pool, lost ground to FPPS and variants such as "PPS+", which pays the subsidy on a PPS basis and fees on a PPLNS basis.

PPS concentrates risk in the pool operator, which tends to favour large, well-funded pools and adds to concerns about the concentration of hashrate and the Nakamoto coefficient of a network. Miners must also trust the pool's share accounting and its solvency, since credited balances are a claim on the pool until they are paid out to the miner's wallet address. Finally, because payment is fixed per share, a pool could in principle withhold found blocks without its PPS miners noticing, so transparency about blocks found is part of choosing a pool. Large miners that can bear variance themselves sometimes prefer PPLNS or solo mining to avoid the PPS premium.

• Meni Rosenfeld: Analysis of Bitcoin Pooled Mining Reward Systems (arXiv)