Quick question about how the probability of mining changes (or doesn't) in larger/smaller pools. From what I understand, all the miners in one pool, mine the same block until it is found. I think that the probability of the block stays constant. Let's say it's 1/1000000. In a smaller pool it would take a certain amount of time for us to compute the right answer for this block, while in a larger pool it would take less time. However, the probability of finding the block does not change, or in other words the "luck" doesn't increase in a larger pool. The larger pool just does more tries/second on the block. My friend argues that with more people, a sort of compound probability applies and the probability of finding the block actually does increase. Can someone please explain this properly please?
