With 1,3Gh/s you would get every block (so around one block every 2 min) if the difficulty was still the same as it is now, but as you told difficulty would double, so with 1,3Gh/s you would get statistically a block every 4min.You need a lot less power to find a block per day solo mining.And as @SoapyFresh told if you have a log of your higher share and one of them is higher than the network difficulty when you found it, than you are the one that found the block, but of course the block is shared with all miners in the pool, so it is just a fun fact to know nothing else.
In the past we understood that when this big difference happens, there is a big problem in monero mining. For example asics.In this case i do not Belive that We have asics, but i strongly beleive that major miners are botnet and datacenter that both are the biggest cpu owners. Cpu price, expecially amd ryzen that are perfect for monero mining, is lowering. This means that the demand is low and We know from the past that when a hardware is mining profitable We have shortage and price take off soon.Don’t you agree?
Infact i strongly beleive that cpu mining is a stupid things because for sure it give lot of advantage to botnets and server farm instead of small home miners. Gpu mining is the best one, asic mining is for big player as well as cpu mining.