Thanks Lobo, but are you absolutely sure it's not a supported card?

If I go to the OpenCL tab, I get pretty much the same as you see on the CUDA tab, and RX580 is the listed GPU and selected, just as you have your 980Ti selected. I can't imagine why AMD, who actively support Blender, don't have their new cards supported when nVidia, who do not support Blender, do work. I know that CUDA cores are different to the cores on an AMD card, but the point is, they are cores, and even EEVEE uses them.

From what you say, you sound very confident and you are probably right, but I hope not, cause the reason I bought this card was mainly for Blender, and it was a top recommended card for Blender on some website out there. I know AMD have released their own Renderer for Blender (called ProRender) that is supposed to outperform Cycles on an AMD card, so maybe that's why it was recommended, but nevertheless I am shocked that AMD, who support Blender, have not yet gotten Cycles development team to support AMD's cores as well as nVidia's.

I'm surprised Ton even stands for Blender supporting a proprietary thing like CUDA, while something open like AMD is not supported yet, seems absolutely backward to me, and even more so considering AMD are kinda friendly with Blender, and nVidia are not.

I'll try it in AMD's "ProRender for Blender" mode when I get it back out, and if the recommendations were true then it should be fully supported and blisteringly fast. If not, I suppose I could change the card for an nVidia card, but I don't like nVidia and their arrogant proprietary way of doing things, and I intend to be using Linux, where again, AMD are open about drivers and nVidia are not.

That said, it does use the AMD cores when using EEVEE, and the CPU is so fast I thought I were using the GPU anyway, so I don't suppose it matters. I'll just have to check out "ProRender for Blender" mode on YouTube, give it a try later, and bloody-well hope it is as good as they say it is.