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Nvidia 10 series and newer will now work with freesync too. A 1060 mini will be about the same performance as your 570
I'd decide on the case first as you may find you don't need to downsize it.
Good luck with the build.
I'm not sure but you should be able to find out if an 8 gb versions available from the manufaturers website.
If it's Gigabyte I'd avoid it, I bought their ITX sized single fan RX560 last year and it was a horrible card that got very hot and very loud under load, Gigabyte do not make good AMD cards that often & if a 560 can be so bad imagine what the more demanding 570 will likely be like, one to avoid if you ask me.
My mistake, it was a small dual fan model but the point still holds, it was a horrible card.
That's the best thing to do, It looks like it'll fit to me.
The game is either badly coded or your settings need sanity checking.
VRAM is less likely to be a problem, a 1060 or 570 is more likely to be cpu bottlenecked at the resolution. Running at a higher resolution (e.g. at least 1080P), aggressive AA and AF are needed less and you can dial them back which will likely reduce VRAM usage as well
Most of the time texture quality can be lowered from "ultra" to "high" for example and the difference is imperceptible, but can make a huge difference to vram usage due to ultra being uncompressed vs high using high quality compression.
Some stats for VRAM usage with Antialiasing here:
https://www.tomshardware.co.uk/graphics-card-myths,review-32882-6.html
Sapphire pulse rx580 8gb is a mini card. Think it's about 230mm long dual slot.
That's a shame. especially with the cable connectors being in the way, I have an M-ATX Corsair Cube case, I managed to shoehorn a Vega 64 Nitro plus in to it but I had the same issue with the psu cables, I grabbed some extensions that didn't have the extra cable out to an additional 2+6 and with a little cutting fixed it, Although I managed to get it all in the air flow wasn't good enough so I moved back into my C70 midi tower case.
I don't think I'll bother trying to go small again for my main PC but I'd like to build something really small when we finally get an APU that handles gaming well.
I have a lot of 550/560 cards and imo the best value for money one you can buy is this one, its a baffin based 550, so rx460/rx560 core which you can unlock shaders and compute units on with a different bios, there are more sku's of this card than I can remember but only one in this configuration:
Next best one is the xfx single slot 550:
Forget the asus cards (I have 5 of these 4gb ones) and the gigabyte cards (Have 7 a mix of 4gb and 2gb) as build quality is really poor, I ended up doing this to all my asus cards because the stock cooler is worthless: