I understand that. But isn't the pool still dependent on probability to write the block first?
No.
If a smaller pool finished a block first it would still propagate around the network. The larger pool can't stop that. I mean having > 50% of the miners doesn't mean it controls > 50% of the clients receiving blocks.
So what. It just ignores the block found by the smaller pool.
Or maybe I'm still missing something about that. In which case, I don't really see how being slightly less than 50% is different from being slightly more than 50%. If the bigger pool has a lucky streak it could create blocks quicker even with less than 50% of the hash rate. And in that case the system is potentially in failure mode now, and would seem to be poorly designed.
With slightly more than 50%, you can simply ignore every other block. You will win eventually because your chain will eventually be longer. The only blocks on the public chain will be your blocks.
With less than 50%, you will fall further and further behind. You will be using up more and more resources with a lower and lower probability of success. You'd do much better to accept blocks found by other miners because it makes your chain longer and thus gives you a better chance of getting your own blocks into the chain.
(By the way, there is a fix to this attack that requires no change to the protocol. It has some issues though, but if this ever became a huge problem, it could be perfected and deployed.)