I believe you cannot see God but you can know He is there by the effects He has on people and your experiences. I have experiences of God all the time. Have you experienced fellowship with loving Godly Christians? if not then how can you say what the experience is like. It is nothing like the feeling of false hope (such as your lottery example).
Let me explain something to you. I really do believe you when you say you "feel" God, and have all these experiences of well being. I believe you, because I have had these experiences too. I felt them when I was a teenager, and had just spent an hour on the phone with my crush, and then just lie in bed imagining what it would be like to have her as my girlfriend, and I would review the conversation in my head, looking for hints that she liked me, and everytime I found a hint that she really did like me, I simply began floating and got excited about the fact that we would soon get together and become boyfriend and girlfriend. I also had a similar experience the first time I saw my favorite rock band on a stage. I was speechless, I felt an intense feeling through my body. I had goose bumps. I literally could not speak for the first five minutes after they came out. I was just about to cry like a little girl (just like those girls you see crying in old Michael Jackson concert footage). Another good example, for me, is Apollo 11 mission. Everytime I see a documentary about it, and see that video of Neil Armstrong steping onto the moon and saying those words, I have goosebumps just thinking about that great advance for humanity. It's intense! Oh, the list goes on, you get the idea.
What I'm trying to say here is that "feeling" you have that you think is God, is simply a series of biological and neurological functions acting up, when you
believe you are in the presence of something great. That is common to every human being. That is why you feel that way when you pray to the christian God (because you
believe you are in front of something great), but wouldn't feel it if you prayed to Buddha. Likewise, a muslim feels it when he prays to the muslim Allah (because he
believes he's in front of something great), but wouldn't feel it if he prayed to Jesus. How do you think that dozens of other religions have been able to last several centuries, including the really primitive religions of the mayans and aztecs, which even Christians recognize to be extremely primitive? They all are able to last because the human body is capable of "feeling God", as long as they truly believe in what they are praying, or doing, or when feel they are in the presence of something great (like I felt when I was front row seeing my favorite rock band). As you can see, everyone "feels" this, regardless of who they are praying to, or who they admire or have strong feelings about. And there is one simple explanation: this "feeling" is caused by the human body itself, it's part of its biology and neurology. There's a whole science behind this (look it up). This "feeling" is not caused by "God", because, if it were, only followers of the christian religion (or whichever the "right" religion was) would feel it, and the rest wouldn't. But everyone feels it, that's why everyone else sticks by their religion throughout their lives, unless they attempt to rid themselves of all the barriers that tradition, authority and dogma have put onto them. Once you begin thinking on your own, without believing that someone is watching you, without feeling guilty that He might be offended and therefore punish you, without thinking you will let your mom down.... once you are able to do that, you will begin realizing all of the nonsense you used to believe.
I would suggest you read this page http://www.godisimaginary.com/i7.htm
titled "Understanding religious delusion", and watch its accompanying video http://www.godisimaginary.com/video7.htm.
If you read this and see this video with a truly open mind, you should be able to build-up enough doubt to investigate a little further. Once you do, you will quickly realize what we already know, that believing in God is just as primitive and nonsensical as believing in Zeus.
Only then you will become a truly free human being. Best of luck!