Not sure solo mining with this setup would be beneficial... even at 20TH you would have 683 years between blocks, according to solochance.org
A lot of people are buying small miners now just for this. It's of course a lottery. There was a single BitAxe that found a block back in July with only 500Gh/s.
https://cointelegraph.com/news/tiny-500gh-home-bitcoin-mining-device-produced-a-block-earning-over-200k-btc
Interesting. They could have bought a real lottery ticket instead. Why waste time and resources on mining if all they want is a lottery ticket? Playing in a casino is a better idea too. It is hassle free and still luck based.
Again, the shovel sellers are making the real money here while the adventurers dream on getting rich but we are all gamblers in the end. Some of us are just smarter and know math better than the rest.
Some people just want to run something to potentially hit the jackpot. It helps with decentralisation too instead of letting the large pools have the monopoly over the network.
You'll spend more buying lottery tickets than you will buying a miner like a BitAxe or the Avalon Nano 3. Plus the odds are way better mining solo. For instance, the odds of winning the lottery here in the UK is about 1 in 15-30 million depending on which lottery you play. Mining with 6.5Th/s is about 1 in 756k daily.