Interesting stats. thank you for taking the time to research this. I do still have a few potential discrepancies however:

* Not all Android devices are ARM. However it's fair to say the x86 builds of Android are the exception so unlikely to affect the figures in any meaningful way

* Cuthbertson's figure is a sales pitch and hasn't been independently verified. Companies often inflate their figures to sound good (like when Apple included MacBook sales as part of their iPhone and iPad figures). Cuthbertson's figures do seem high (based on the napkin maths I presented earlier but also how Android has been growing faster than the growth of the population and smart phone market), so I'd be interested to know what Cuthbertson defines as "active". If someone upgrades their phone and sticks the old one in the draw, is it still classed as "active" for 1 month? 3 months? 12 months? Is it ever deprecated from the "active" list even though it's technically not in use any longer? If that's the case, we are back to my earlier point that deprecated Linux servers should also be in scope.

* Lastly not all Linux servers are sold as servers. There's quite a few examples of this:

1) Some of the larger hosting providers are known to build their own servers,

2) Some smaller or medium sized companies are known to buy second hand hardware for on-prem gear

3) ditto regarding hobbyists and home labs

4) It's not uncommon for desktops to be provisioned as makeshift Linux servers when requirements don't demand a rack-mountable enterprise solution

5) Also Linux doesn't have to be running bare-metal to be running an AMD64 kernel. There's plenty of instances of virtual machines in the world. Getting accurate figures of running Linux VPSs et al would prove impossible

6) Not all Linux AMD64 instances will be traditional servers. eg Elemental build their own Linux-based machines for transcoding. These wont be off the shell servers either. Then you have all manor of other black boxes out there from set top boxes, networking hardware, etc. Many of which wouldn't be AMD64 but many also will

7) Lets also not forget desktop Linux :)

Once you account for all of these edge cases I think non-AMD64/Android and AMD64/Linux become a lot more comparable. So I'd still be very surprised if non-AMD64/Android does outnumber AMD64/Linux by an order of magnitude.

Ultimately this an impossible argument to prove either way. However I think we do all agree on the overall point that both Android and Linux (in the more general sense) are hugely successful these days -- irrespective of their success relative to each other.