Pool hopping is a mechanism by which certain miners may exploit the payment mechanisms of pools to dramatically increase personal profits.
The original mechanism by which funds were distributed to miners is the simplest and most obvious: Each miner submits "shares" of work and when the pool finds a block, the divide the block reward based on the proportion of the shares - if you did 50% of the work you get 50% of the reward, if you did 3% of the work you get 3% of the reward. Simple.
Unfortunately this creates an imbalance wherein blocks solved in less than average time are worth more per share than blocks that took average times or longer to solve. This makes proportional pay systems inherently exploitable.
To simplify the concept, imagine you're at the world's strangest casino. The only game in the house is rock-paper-scissors and you're playing against the other patrons. If you win the first game after you sit down at a table, they pay you 10 times your bet. The second game pays 9 times, the third pays 8 and so on until eventually you're not even earning your bet back. It seems obvious that the optimal strategy is to hop from table to table taking advantage of the 10x payout rule as many times as possible without every hitting diminishing returns.
Pool hopping is much the same. Mathematically it works out that diminishing returns begin when all workers combined have submitted a number of shares approximately equal to 43% of the current difficulty. After this point, your shares aren't worth any more than average and it becomes more profitable to hop to another pool with fewer shares. This strategy produces, on average, about 28% more income for a pool-hopping miner.
The effect of pool hopping on the other users of the pool comes from a shift in one factor of mining without a corresponding shift in the other: time vs. hashrate. Without hoppers, the value of shares in a proportional pool differs with time - shares submitted early in a round are worth a great deal more than those submitted later, but as long as hoppers are not present, the value of shares average out to a fair value. While hoppers do not change the average number of shares per block or the number of shares an honest miner submits, they do decrease the duration of the higher-paying portions of a round. With the most profitable portion of the round taking significantly less time to complete than the remainder, a miner submitting shares at a constant rate will have far more shares on average in the less profitable parts of a round than in the most profitable, thereby reducing their overall average share value. The more hoppers are present, the shorter the profitable span becomes and therefore the more dramatic the effect.
Preventing pool-hopping is simple: When creating a pool, simply choose an algorithm for funds distribution that has been proven immune or even hostile to hopping - i.e. anything but proportional. When choosing a pool to mine in, one should similarly choose a pool which has chosen a fair payment schema.
