More math...

Assuming a Bitaxe uses 20 watts, thats about 3⅓ watts of power per block, or about 480 watts per day. Both powerball and megamillions appear to cost 2 USD tokens per play. If someones power costs are 15 cents/kWh, then 2 USD tokens would buy about 2 weeks of running a BitAxe.

So we can compare the winnings of a BitAxe over time with powerball tickets.

If one buys a powerball ticket every two weeks, with the odds of winning any prize at ~1 in 25, the overall typical loss through the year would be about $45 to $48 (based on a single win from 26 tickets purchased and that win resulting in low value $4 or $7 prizes)

On the other hand, a BitAxe will very likely lose $52 per year (its power cost is roughly 1 USD per week) unless its participating in a pool to get gradual payouts over time based on shares.

Assuming pool participation, and zero growth of the network, and ignoring pool fees, it would receive about 1/1,000,000,000 subsidy and tx fees per day. At 3.125 BTC per block the subsidy portion would be 3.125 * 144 * 100000000 sats per day. Thats 45 billion sats spread across the whole mining network. Knowing a BitAxe is currently 1/1000000000 of this gives us an expected earnings of 45 sats per day. Converted to fiat at a $100000 exchange rate for simplicity, this results in a loss of about 69 cents per week, or about $36/year