I have no interest in a small guaranteed payout.

I'm asking if I have $20 to buy Powerball tickets (with a chance to win $1 billion) or $20 to buy electricity for my i5-based mining machine, how do the odds compare?

I'm not sure what the exact house edge is on Powerball. But let's say it's 20%.

Due to dynamic difficulty adjustments, the profit for miners is just a bit more than the cost of electricity. However, this is only true for those who have the best specialized mining equipment and the cheapest electricity in the world. For an average person living in a typical area, even with dedicated equipment, you'd probably be far under breaking even. Most likely much less than 20%.

And that's with specialized equipment (costing thousands of dollars). With your home computer, it'll be hundreds of thousands of times less efficient per watt of electricity to mine bitcoin. Even for other cryptocurrencies that might be resistant to specialized equipment, you'd still most likely be over 10x less efficient.

Go with the powerball tickets.

You can still mine yourself and that might appeal to someone who likes buying lottery tickets. Mining yourself at least has the possibility of positive ROI as opposed to a guarantee of losing money.

I didn't say you can't do it - I said people don't really do it anymore. You can easily get a positive roi if you do it correctly, why do you think there are literal crypto factories built to mine coins?