If a pool exists where the rewards are shared among participants based on the amount of hash power that they each contribute to the pool, BUT each participant gets to run their own software to choose for themselves which transactions are included in the block (and builds those blocks themselves), would you call that solo mining? Most wouldn't.
I wouldn't call it a solo mining.
Most wouldn't. But franky1 keeps saying that solo mining is when you create your own block headers and has nothing to do with how the reward is shared, so I assume he would disagree with you (however, he hasn't answered the question yet even though I've asked it of him in multiple threads now so we don't know for sure).
The scenario of the waitress in the restaurant seems that the miner is paid based on his hash power (working ability) just as an individual waitress. Let's assume the most hardworking waitress is thrown out of the restaurant to serve customers out of nothing, he will not make such money. The waitress is successful because a restaurant(pool) exists.
You've stretched the analogy too far. In that particular analogy, the restaurant isn't meant to represent the pool. It's meant to represent the Bitcoin mining process. You'll notice that ALL the participants in the analogy work in the same restaurant, just like all the participants being discussed participate in the Bitcoin mining process. I chose it specifically BECAUSE "tip pooling" is a concept that many people are already familiar with.
Let's see a scenario where there is a sea for fishing, and the target fish is dolphin. Individual fishers have small canoe that cannot penetrate the sea, then decided to join their canoes to build a big boat. Everyone of them climbs the boat for fishing and then one person catches the dolphin.
Is is correct to call him a solo fisher, because his hook caught the dolphin? Besides there would never be a scenario that two hooks from two fishers will catch the dolphin simultaneously.
Well, the first thing to understand is that in bitcoin mining the miner that solves the block does NOT increase his chances of solving a block by participating in a pool. In your analogy you indicate that the fishers "cannot penetrate the sea" individually, but that on the boat "one person catches the dolphin". This implies that he improved his ability to catch the dolphin because he was on the boat. That doesn't happen with bitcoin mining and mining pools.
Let's make your analogy more accurate...
There is a sea for fishing. This sea has VERY big fish that don't bite hooks very often, but if they do bite then they are easy to pull in. Catching a single fish will set a fisher up for decades of fishing costs. So, hundreds of thousands of fishers go out and try to catch fish in this sea. Every once in a while 1 fisher will catch a fish and be VERY happy. The money he will get for this fish will take care of his family for a VERY long time. Meanwhile, the other hundreds of thousands of other fishers will come home empty-handed again, and again, and again for their entire lifetime. You can fish from the shore, or you can fish from a boat that you own, or you can fish from someone else's boat. It doesn't matter, your chances of a fish biting one of your hooks are the same. You can, however, drop as many hooks into the water as you can afford to buy and maintain.
Eventually, someone with a very big boat comes along. This person states that anyone can fish from his boat. Everyone understands that fishing from his boat won't make them any more likely to catch a fish, so why should they fish from HIS boat? The owner of the boat tells everyone that he is offering 2 important things for those that fish from his boat. First, there is some effort involved in the fishing process and he is willing to assist in that effort. He personally will monitor the hooks and bait them if they no longer have bait on them, he'll also personally reel in the fish if they bite, The fishers just have to provide and maintain the functionality of all the fishing equipment themselves. ALSO, there is an important condition to be allowed to fish from his boat... If you catch a fish, you do not get to keep it all to yourself. Instead, he'll remove a small portion of the fish for himself as a fee and then all the remainder of ALL of the fish caught from this boat will be split up amongst all of the fishers on the boat with each fisher receiving an amount of fish that is proportional to the number of hooks they put in the water. Now everyone sees a good reason to participate. The chances for each individual fisher haven't increased at all, but the chances that they'll go home with SOME fish that day are much better since it's a pretty good chance that SOMEONE on the boat will catch a fish. Instead of fishing for their entire life hoping to maybe catch 1 BIG fish, they can fish on this boat and take home a small amount of fish regularly. This would be analogous to traditional "Bitcoin Pool Mining" where the boat owner is the pool operator and the hooks are the hash power.
Now, someone else comes along with another big boat (perhaps not quite as big). He also offers people the ability to fish from his boat. Again, everyone understands that fishing from his boat won't make them any more likely to catch a fish, so why should they fish from HIS boat? The owner of this boat tells everyone that like the other boat, he will monitor the hooks and bait them if they no longer have bait on them, he'll also personally reel in the fish if they bite. The fishers still have to provide and maintain the functionality of all the fishing equipment themselves. HOWEVER, if your hook is the one that catches a fish, then you don't share that fish with the others on the boat. He will remove a small portion of the fish as a fee for himself, and then just like when you were fishing all by yourself, you'll get to keep the rest of the fish for yourself. So, just like when you fish alone, if you're lucky and get a fish on YOUR hook, then you get a HUGE fish, but most end up fishing from this boat for their entire life and never going home with any fish. This would be analogous to CK Solo Pool where the boat owner is again the pool operator and the hooks are the hash power.
In the first scenario, you are "pooling" with the other fishers, sharing in the rewards. In the second scenario you are "partnering" with the boat owner (paying him a small fee to handle some of the work for you), but you are not "pooling" with other fishers. You are still keeping all the rewards for yourself (minus the small fee you paid to the boat owner). It seems that franky1 would call the second scenario "pooled" because the boat owner is handling some of the work for multiple people. Most people don't seem to consider that a "pool" since there is no increase in your chances of catching anything or with going home with anything.
Now there's another scenario that I keep asking franky1 about and he does answer:
A group of fishers see what's going on with the first boat and like the idea of getting a small amount of fish regularly, but they don't want to pay the fee, and they want to have control over their own bait. They form an organization. Anyone can join this organization, and you can fish from wherever and however you like. The only condition for being a member of this organization is that you agree that if you ever catch a fish you will split it up with everyone else that is a member of the organization. Each member will get a portion of the fish that is proportional to the number of hooks that they've put in the water. Note that there is no longer someone else handling the baiting and reeling in for you, but you get to share in all the fish caught by everyone in the organization. Is this a fishing "pool"? According to franky1's explanation, it would seem that it is not since you have full control over your own equipment, but I think most people would say that the point of the "pooling" is to increase the frequency that you get some fish.