Say someone wanted to solo mine with a very cheap setup with hopes to find a block themselves.

What would the odds of finding a block be over a certain amount of time? I'm just trying to compare it to winning the lottery with a similar sized jackpot. I want to compare the odds for fun. If any probability / math experts want to chime in that would be great.

With a typical 13 TH/s Antminer/Avalon you have a ~ 1/3000 chance to hit a block next week, decreasing over time as difficulty grows.

Not sure how that compares to an actual lottery. You would probably need to figure out how many tickets is equivalent to the cost of ~250 kWh (roughly one week of power consumption for the miner), and account for the cost of the miner itself.