Probability an honest node finds the next block vs. probability the attacker finds the next block
No one has an upper hand in this process. So shouldn't p and q be equal to each other?


The chances of finding a valid block header that meets the target requirement increases proportionally to the number of tries. This means that it is proportional to the hash power that you have. Even if there are two miners, one could be using a huge datacenter (the size of United States), while the other might be mining on his 10 year old laptop. Their hash power would not be the same, and hence p and q will also not be equal to one another. Hash rate is the metric to be used to find out the probability of a miner finding the next block.


  Then all an attacker needs to do is to form a pool whose compute power is greater than max(p_i). Am I missing something? In other words, the pool with max compute power can attack the blockchain already.


What you are describing is a 51% attack. With the current hashrate of the Bitcoin network, it would require HUGE investments (billions of dollars) from the entity who is planning to do such attacks. At that investment level, the economic incentive to launch such attacks may be tiny, unless it's a state actor who is trying to annihilate the confidence of the network. Even if a fraudulent miner amasses >50% of the hash rate of the network, full nodes MAY try to patch themselves to reject such blocks (for example: if that attacker tries to broadcast a longest chain that is > 6 blocks different than the original chain, to prevent double spends).