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The palette and tools you have are very limited so an algorithm purely based on a neural network is pretty much out of the picture. A neural network could easily learn more colors with little to no extra work. If any at all. I wouldn't however dismiss it entirely. There might be a neural network in the background doing certain tasks.
The next thing are concrete algorithms. I doubt that it creates layers so the picture is always judged "as is." One of the easier ones is color. It definitely counts how many different colors you used in a sort of "is this a colorful picture" kind of way. I also wouldn't put it beyond them to simply count strokes that you made in a way and use that kind of information for evaluation.
It also probably looks at the canvas as a two dimensional pixel array iterating over the whole thing to determine these neat little things like "is every pixel the same color code?" if so "You made a one color canvas" and it triggers the corresponding responses.
I wouldn't put it beyond the algorithm to make every part of the array that has a distinct color to be approximated as one of many shapes and run every single "shape" through a neural network to determine things like "size" and "shape." Like this it can approximate things like "You drew 3 shapes total" "1 is recognized as a line." "2 are recognized as rectangles" "The overall complexity is low." This can be teached to a neural network with sample sizes as small as 100.
Lastly, I think time spent 'actively' painting does account for something, because, currently I am pursuing the ending with the castle, the ladies like very complex pictures and although I sometimes end up with pictures that lack a lot of complexity in some parts of it (because I was really busy fleshing out a person or so, that is the foreground of the picture) it nets more money than a more "complex appearing" picture simply because the character took so long to draw. Going over lines over and over again. Painting fine lines because I intercepted an outline... stuff like that.
So. Yeah. I think the money is dependent on time spent drawing as well.
___
What I am getting at is: While I can't be certain there are a lot of ideas I have had on how it's probably done but ultimately you'd have to ask Niklas Lindblad from Flamebait games as I suspect that he's had the biggest chunk of fun with figuring this out 'just right,' only for people to complain about the minimalists wonky AI. Haha.
General speaking though:
If you just want to beat the game go for other peoples "advices" they'll net you the achievements/endings.
Thinking the algorithm through does little besides ruin the charm of the game.