In this paper, the authors describe the various scoring systems used to calculate rewards of participants in Bitcoin pooled mining, explain the problems each were designed to solve and analyse their respective advantages and disadvantages.

Bitcoin is the world’s first decentralised digital currency. It relies, among other things, on a network of computers that synchronise transactions with a process called mining. Bitcoin pooled mining consists in repeatedly computing hashes of variants of a data structure called a block header, until one is found whose numerical value is low enough. When this happens it allows releasing a valid block, for which the miner is rewarded with bitcoins.

The authors introduce Bitcoin mining and explain why the high variance in the rewards for this activity creates the need for mining pools. They have explored several methods used by pools to distribute rewards, and have demonstrated how some of them fall short of the ideal of fair reward distribution – most notably due to the exploit known as “pool-hopping”. They have developed a general framework for hopping-proof methods which are immune to this problem, and analysed some specific examples. Finally, we have discussed some innovative ways pools could improve the service they provide going forward.