Automated cutting is used for less valuable stones, or when you need to have multiple stones of the exact same size and shape. Hand cutting is used when you want to maximize the yield, so you use the raw stone to guide the final size and shape.

Thanks, that makes sense, when you say 'you use the raw stone to guide the final size and shape' does that mean you might look for things like imperfections in the stone and try to remove those

Yes, finding a shape that excludes incursions is a big part of it. In the video he shows how he uses refractive fluids on the rough surface to make it less opaque so he can spot such inclusions more easily.

Like if the raw stone is elongated you probably don’t want to cut it into a square finished gem, something like an oval cut would have less waste. And instead of trying to decide on an exact size in advance (like, exactly 1 ct), the final gem is whatever it is when the cutting is finished, so if it’s a smidge over you don’t shave it down.

I understand that this is how it is, but why? How is not using computerized process giving better yields?

For example, computer optimization is used to cut pieces out of leather to maximize yield while avoiding flaws.

This video [1] shows laser cutting, 3D modelling, and hand grinding of diamonds in a diamond factory. They discuss when and why they use laser cutting machines a bit.

[1] https://www.youtube.com/watch?v=YMyPo-MEvMA