The probability of a miner finding a valid block in the bitcoin blockchain is assumed to follow the Poisson distribution. However, simple, descriptive, statistical analysis reveals that blocks requiring a lot of time to find — long blocks — are won only by miners with a relatively higher hash power per second. This suggests that relatively bigger miners might have an advantage with regard to winning long blocks, which can be understood as a sort of “within block learning”. Modelling the bitcoin mining problem as a race, and by means of a multinomial logit model, we can reject that the time spent mining a particular block does not affect the probability of a miner finding a valid version of this block in a manner that is proportional to her size. Further, we postulate that the probability of a miner finding a valid block is governed by the negative hypergeometric distribution. This would explain the descriptive statistics that emerge from the data and be aligned with the technical aspects of bitcoin mining. We draw an analogy between bitcoin mining and the classical “urn problem” in statistics to sustain our theory. This result can have important consequences for the miners of proof-of-work cryptocurrencies in general, and for the bitcoin mining community in particular.