A form of incentive for the miner who successfully calculated the hash in a block during mining. Verification of transactions on the blockchain generates new coins in the process, and the miner is rewarded a portion of those.
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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 solving a block. A "share" is awarded to members of the mining pool who present a valid proof-of-work that their miner solved. Mining in pools began when the difficulty for mining increased to the point where it could take years 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.