That doesn't sound right, judging from how many users tell you that the chance is only around 2% within a year. Not to mention the difficulty is going to fluctuate, and I bet it will increase and just lower your chance even further. Doesn't really matter whether you have free electricity or not if you will never get it in the first place. Can you show us the math?

Based on my experience, I only saw one post from a lottery miner in this forum, while the rest are just talking about probability, etc. Most of the time they are just doing it for fun, so if profit is your goal, mining with a pool is arguably more profitable & efficient. CMIIW.