How many solver runs before we should technically find a block
Finding a block is a matter of chance. To figure out your odds, compare your sol/s rate to the global rate at https://explorer.zcha.in/ Odds are, you should be mining in a pool if you want to find a block more than once/bluemoon at this stage. zcash is quite popular at the moment.
Good luck 
I understand that it’s really just a matter of chance, but I’m trying to better understand what that chance is. If I’m solving at about 4.8 Sol/s and the network is at about 4.8M Sol/s, that means that my chances are literally about 1 in million, correct?
So does that mean that I would need to complete 1 million equihash solver runs, on average, to solve one block?
I created a statistic on my pool that calculates this for you.
You can get an idea from that persons sol/s vs time expected or point your miners there and have my stats run for you.
Or you can just do the math real quick. Geometric distribution with Bernoulli trials will work. 1 / (your sols / total sols) = num er of expected blocks till you find one. Each block ~ 2.5 minutes each.
whole network finding block not per second but per few minuts… so avarage you will need about 11 miliards, but if you unlucky then you would never find block
Correct…
What is 11 miliards? Is this the number of sols/s?