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 [I apologize in advance for this wall of text, but I wanted to do my best to be thorough.]

Assuming both miners are being run at full power:

A Bitaxe running for a full day would generate 60,480 TH and consume 0.384 KWh. At my ~$0.14/KWh, this would cost me $0.048/day.

To generate 60,480 TH, I would need to run an S9 for 1.244 hours each day, consuming 1.711 KWh. At my cost/KWh, this would cost me $0.23 per day ($0.182/day more than the Bitaxe.

At presenr, I am able to find the Bitaxe on sale for $200, and am able to find an S9 in decent condition for $75, the price delta between these is $125.

Were I to purchase both miners today at the prices I found and listed above, I would need to run the both (the Bitaxe 24/7, and the S9 1 hour/day) for 686 days before the increased power efficiency of the Bitaxe made up for its greater initial capital expense.

Bear in mind that in this model, the Bitaxe is running 24/7, and the S9 is only running 1 hour a day to match the TH output of the Bitaxe. 

If I wanted to, I could opt to pool those 686 cumulative hours the S9 would require, and run them consecutively, immediately after acquiring the miner. I could then leave it off for the remaining 657 days in this model, betting on network hashrate increasing and my rewards/TH dropping over time.


https://image.nostr.build/24944b63862fc068a3c58a77b59718154f6893adce100bc5d15cb9f3eb72bd56.jpg

 
 nostr:nevent1qqs23sjxyw26mj4ceh0w29p4yhr49exen288y5mkqkzxseplf00mlvgpzamhxue69uhky6t5vdhkjmn9wgh8xmmrd9skctczyp3ra5scm6qnz9urv4nc84kwdy94yx5fcnwqnu5fvtjml4862jfyjqcyqqqqqqgrep20e 
 S9 vs s19... 

I would suggest you look at how many ASIC chips are on the board.  
 S19 is roughly 3x the cost of an S9, uses roughly 150% more power, but has around 7.5x the TH.

It would perform even better in this model than the S9.

I just went with an S9 as it is a cheap and approachable miner, is often used for underclocked "pleb-heater" builds, and seemed like the base case for arguing against novelty miners like the Bitaxe.

I cannot argue with the fact that novelty miners represent an easy entrance for newbies, and offer a simpler and less infrastructure-intensive introduction to mining. All I argue is that they are hardly the most economical method for gaining this educational experience, despite often being marketed as such. 
 yeah I didn't read your note fully when I responded - s9 is a better comparison for sure.

"All I argue is that they are hardly the most economical method for gaining this educational experience, despite often being marketed as such." - this, this is my gripe. If you ordered the parts yourself from aliexpress and PCBexpress, you'd be paying 200 in total including shipping for about 5 units. Now you'd still have to fabricate it but still...  
 Thank you for that clarification on pricing. 

I hadn't been aware that one could assemble their own, and had only seen them for sale as fully assembled units with a seemingly uneconomical price tag. 
 nah it's open source and here is the repo: https://github.com/skot/bitaxe

Everything you need is there, step by step. 
 But yes, you're work seems right on 
 Here a model using the Bitaxe and the S9. I opted to use KWh over J, as no one is using Bitaxes for heat, so I though just focusing on energy efficiency was a better angle.

nostr:nevent1qqs23sjxyw26mj4ceh0w29p4yhr49exen288y5mkqkzxseplf00mlvgpr4mhxue69uhkummnw3ezucnfw33k76twv4ezuum0vd5kzmp0qgsxy0kjrr0gzvghsdjk0q7kee5sk5s638zdcz0j393wt075lf2fyjgrqsqqqqqp7rvmq7