There are a lot of good ideas in this thread, but I feel like some concrete advices might be helpful.
1.) Usually, your first relic is better than gold.
You have one coin less, but your opponent loses one card. The latter is usually more important. Unless ...
2.) You might favor gold over relic, if you want to hit a certain price point ASAP, but your opponent doesn’t.
If your strategy depends a lot on when you get that Forge/Inheritance/Pathfinding, and your oppenent does something where a missing card
is not similarly crucial, look at your own purposes and get a gold.
To be honest, this advice is theory-crafted, I haven’t had this situation yet. However, it seems legit to me.
3.) In a BM-Mirror, buy one or two relics before gaining gold.
In general, Relic is 1$ less than gold for you, and for your opponent the average loss is the product of his average money Density times the probability that your Relic didn’t collide with others. So, when does your opponent lose more than you? Examples given,
if his Money Density is 1.5$ per card, your Relic needs to be non-colliding with a likelihood of 2/3;
if his Money Density is 2$ per card, your Relic needs to be non-colliding every other play.
That being said, it seems logic that a third Relic is usually weaker than a Gold, because the risk of collision is often closer to 1/2, whereas your opponents Money Density is rarely above 1.5$. Whether a second Relic is better than Gold is more complicated; I assume that simulators will tell us more about the perfect number. In doubt, a late game Relic is stronger than an early one, both because of the lower risk of collision, and the higher money density.
Btw, I have absolutely no idea if a second relic is good when your opponent goes engine. One day, logs will let us know.
4.) Get X instead of your first relic, if you prefer X over a grand market without +buy.
Grand Market nets you +2$ + buy, Relic nets +2$, „-card“ for you, „-card" for opponent. Unless there is some evidence that „-card“ is considerably more impactful either for you or for your opponent, Relics relative effect is like a Grand Market without +buy. I feel like this concept can be helpful in both directions: On the one hand, Grand Market is really good for engines, if there are costy components, and so is Relic; on the other hand, there are more powerful $5-cards in many kingdoms, e.g. Junk Attacks or strong trashers like Junk Dealer.
5.) If you plan to draw your deck, buy exactly one relic.
Simply put, the advantages of a second Relic are outweighed by its disavantages. With increasing likeliness to draw your deck, your second Relic tends to become a silver. And asides being too expensive at 5$, Silver is usually bad in a drawing engine.
6.) With Borrow on board, Relic is more like silver than grand market.
Once you’ve purchased your Relics, your opponent will use Borrow on a regular basis, which sabotages your attack.