I'll give you some general advice and a phrase I was given by my teacher when I was learning gemmology and appraising.
Generally, we can't help you without a lot more information, if you were looking for more specific information like what is the dispersion of a diamond and how would we be able to try and figure it out then we would be happy to help. If you were an aspiring appraiser or gemmologist and had specific questions about the ring like how to test the gold or what an inclusion might be then we could try to help. The phrase I was always told to use when someone showed me a piece of jewellery and asked me what I thought was "it's a very beautiful ring."
The problem is a gemmologist, and more specifically an appraiser that would be able to potentially give you any help or ideas on "what do you think", will usually not just glance at something and give you an opinion or just look at photos and say anything about it. We would need to fully identify the stone, identify if there have been any treatments, identify the metal, the style, any provenance, etc. to help price the ring to be able to actually tell you what we think and none of that can really be done by pictures.
The only general information I'd start with is find out the metal that it's set in. Weigh the ring in grams and subtract 0.4g from it for the stone and then figure out how much the metal is worth and it'll give you a starting point. For an example, if the ring is 14KT white gold, you would find out the price of the gold by taking 14 and dividing it by 24 and then multiplying it by the cost of gold per gram (you can just google the cost of gold per gram and find it). The problem with using this method is that nobody will give you that price because that's a little higher than what you'd be selling the ring for as scrap, not what you'd find in a secondary market, like a private sale, and certainly not what you'd find in a retail market.
My best recommendation if you want to find out if the $800 is a good price is bring it to a local jeweller you trust and ask what they'd offer for it. Either that or get an appraiser to give you the most accurate number and explain to them that you are wanting an appraisal for a private sale and if they know what they're doing then they'll give you a more accurate price.
Hope that helps. If you do have more specific questions then please post them here and we'll try to help out.
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