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How Does a Pool’s Luck Factor Influence the PPLNS Payout Model?

A pool's luck factor is the ratio of the actual number of shares submitted to find a block versus the statistically expected number of shares. In PPLNS, if a pool is "lucky" (finds a block with fewer shares than expected), miners receive a larger reward relative to their effort.

Conversely, if a pool is "unlucky," miners may have to submit many more shares before receiving a payout, leading to high variance.

How Does a Pool’s Payout Method (E.g. PPS) Utilize the Share Count?
Does the Market Maker’s Capital Base Influence the Required Minimum RFQ Size?
How Does “Luck” Factor into the Profitability of a PPLNS Mining Pool?
What Is the Financial Risk a Solo Miner Undertakes Compared to a Pool Miner?