For every unit of hash power, the user gets to draw one ball from an urn. There is a predefined number of balls in every urn which may be winning or losing balls.Within a system that is perfectly memoryless, every time that a losing ball is drawn it is then put back in the urn, which is then shuffled, and the participants try again. In that sense, there is no “unfair” learning, and the relationship between effort (hash power) and success, is linear. Hence, other than smoothing the frequency of winning, there are no incentives for miners to pull their resources together and increase their size.
But what happens with blockchain is that once a losing ball has been picked, it is thrown away. This means that in the next round, the probability that a miner picks a winning ball has increased as there is one less losing ball in the urn.
Let’s say that there are 100 balls in an urn, 99 of them are black and one is white. Players are looking for the single white one. A smaller participant can remove one ball at a time while larger players can remove two.That means that the initial probability of a smaller player winning a round is 1 in 100 and for a larger player, it is 2 in 100. The relative advantage of the larger player compared to the smaller player is (2/1).
But if after 10 rounds, the white ball has still not been found, the probability that the smaller player will find the ball has dropped to 1 in 90, while that for the larger one has dropped to 1 in 80. This is the key problem. The relative advantage of the larger player is now (2.25). Hence, the relative advantage of the larger player increases over time without this advantage being accompanied by an additional effort.
The longer that the game progresses, the more it becomes tilted in the favor of the larger players. In other words, there is learning in the mining process within each of the blocks.