you're telling me that a miner can supposedly mine forever and without getting his reward ever?basically he would turn in a full node
If you are solo-mining, the answer is unequivocally yes. Look at any pool's recent blocks to see how much variance there is in luck block to block, even with 10's or 100's PH/s of hashrate. Even if probability dictates that you should solve a block within 2500 days (again, making an unrealistic assumption that difficulty does not increase, which it will), if your effective "luck" was 50%, it would in fact have taken you double that timeframe. Just as possible would be your "luck" being 200% and solving the block within 1250 days. There is NO guarantee you will solve a block with almost any amount of hashrate, just better odds the more hashrate you have.
If you want your guaranteed income, mine in a pool. Solo mining comes strictly down to having an adequately good enough share for the current block given the current difficulty rating. The network doesn't care whether you are mining with a CPU, GPU, ASIC or you are antpool. Nor if you have 1 Hash per second or 100 PH/s, nor if you've ever solved a block or you solved the last one. All that matters are submitted shares and difficulty rating.
I'll say it again because it bears importance, but past performance has zero impact on your current probability of solving a block. Just like roulette, like lotteries, like anything involving probability.