The concept of solo mining with a fixed hashrate like 2 GH/s is intriguing, especially for those who want to dip their toes into solo mining without investing in expensive hardware. However, as you mentioned, the probability of actually finding a block with such a low hashrate is extremely slim. Bitcoin's network difficulty is incredibly high, and even with larger hashrates, solo mining is often more of a lottery than a reliable income stream.
I recently wrote an in-depth article about solo mining, How to Mine 3.125 Bitcoin at Home（https://yesmining.io/en/how-to-mine-3-125-bitcoin-at-home/）, and it’s a great resource for anyone interested in solo mining. The article covers key topics like the basics of solo mining, the challenges of low hashrates, the importance of mining pools, and whether it’s feasible to mine Bitcoin at home.
If you also think this lottery-like BTC mining is fun, you can start by learning about the Solo BTC Miner above. Solo mining requires patience, but the potential rewards make it a worthwhile venture for miners.