Pay-Per-Last N Shares (PPLNS)

Pay-per-last N shares (PPLNS) is a payout method used by a mining pool in which each block the pool finds is divided among the last $N$ shares submitted before it, regardless of when the previous block was found. Miners are paid only when the pool actually earns a block reward, so their income rises and falls with the pool's luck. In exchange, PPLNS pools usually charge lower fees than pay-per-share pools.

PPLNS was developed in the early years of Bitcoin (BTC) pool mining as an answer to "pool hopping", a strategy that exploited simpler proportional schemes. Meni Rosenfeld's 2011 paper "Analysis of Bitcoin Pooled Mining Reward Systems" described it and its properties. It is the main alternative to pay-per-share (PPS) and full pay-per-share (FPPS), where the pool rather than the miner carries the luck risk.

Picture a sliding window over a queue of workers. Whenever the team wins a prize, it is shared equally among the last thousand units of work done, whoever did them. If you worked steadily, you are always in the window and get your fair share of every prize. If you only turned up for a moment, most of your work slides out of the window before the next prize arrives.

That is why PPLNS rewards loyalty. Miners who stay with the pool receive, on average, the full value of their work, minus a modest fee. Miners who jump in and out lose part of what they contributed.

When the pool finds a block, each share inside the window receives the same amount, so a miner's payment for that block is:

• $R_{\text{miner}}$ is the miner's payment for that block.
• $f$ is the pool fee as a decimal.
• $R$ is the full reward of the block: subsidy plus the actual transaction fees in it.
• $n$ is the number of the miner's shares among the last $N$.
• $N$ is the window size, often set as a multiple of the network's mining difficulty (for example $N = 2D$ difficulty-1 shares).

Worked example: a pool finds a block worth 3.2 BTC (a 3.125 BTC subsidy plus 0.075 BTC in fees). The window is 1,000,000 shares, of which a miner submitted 20,000, or 2%. With a 1% fee, the miner receives $0.99 \times 3.2 \times 0.02 = 0.06336$ BTC. If the pool finds no block for a long stretch, older shares slide out of the window and earn nothing; if it finds several blocks quickly, the same shares are paid more than once.

Early pools used a proportional scheme that split each block among all shares submitted since the last block. Because a short round meant fewer shares to share with, the expected value of a share was highest early in a round, and some miners hopped into pools just after a block was found and left as rounds grew long. This cost loyal miners money. PPLNS removes the round boundary: a share's expected value depends only on the chance that a block is found while it remains in the window, which is the same at any moment. Hopping therefore gives no advantage, provided the pool implements the window correctly.

Under PPLNS the miner, not the pool, carries the variance of block discovery. Expected earnings are similar to PPS before fees, but actual earnings over a week can differ widely, especially at small pools that find blocks rarely. In return:

• Fees are lower. PPLNS pools have commonly charged around 0% to 2%, because the operator does not need reserves to cover bad luck.
• Fees are passed on in full. Miners share the actual transaction fees in each block, including spikes when the mempool is congested.
• Solvency risk is smaller. The pool only pays out what it has earned, so it cannot be bankrupted by a losing streak.

The trade-off suits miners who can absorb uneven cash flow and plan to stay with one pool. Industrial operators that need steady payments to cover electricity contracts and financing for their mining rigs often prefer FPPS.

Several variants modify the basic window. Some pools weight recent shares more heavily or count shares by difficulty rather than number. PPS+ combines approaches, paying the subsidy on a PPS basis and fees on a PPLNS basis. Ocean, a Bitcoin pool launched in November 2023, uses a PPLNS-style system it calls TIDES. PPLNS remains common on pools for smaller proof-of-work coins such as Monero, Litecoin (LTC) and Ethereum Classic (ETC), and on pools that let miners keep more independence from the operator.

Because PPLNS pools pay only on real blocks, they are sometimes seen as healthier for decentralisation than FPPS, which favours large, well-funded operators. Payouts land at the miner's wallet address only after the pool's payout threshold is reached and, on most pools, after the block has gained enough confirmations to be safe from a reorganisation. For background on the wider business, see crypto mining and hashrate.

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