Does anyone know how to translate the artefact rarities into a percentage as a function of the current depth? Let's assume no artefacts have generated yet in the game (since the more artefacts you've found, the less chance you'll find the next one).

Say I really want Angrist.

Angrist depth is 14 (700 feet) and rarity is 4. 4 is not very rare by artefact standards - in fact I think it's the least rare, but we have to look at how rare daggers are on 700 feet. Daggers are most commonly found at depth of 1 (50 feet), with rarity 2, and also at depth 10 (500 feet) with rarity 1. So daggers would have to spawn 4 levels away from its natural depth.

I'm sure there are a lot of calculations that go into this, but the question I want to ask is. Would it be worth it to scum 500 feet a few times for a better chance at Angrist? How many tries would it take on average? And would you have better odds scumming at 950 feet instead?

absolutego's post on artefact generation for reference:

http://angband.oook.cz/forum/showthread.php?t=6990
Clearly, artefact rarity number is not the sole determinant for its rarity. The lesser jewel of Finwe has only rarity 10, but because of how rare lesser jewels are in general (rarity 20), it's difficult to encounter this artefact. And Celeg Aithorn practically never spawns. It also has a mediocre rarity rating of 10. This is because its natural depth is 20 (1000 feet) , so even if you scum 950 feet, it would have to spawn out of depth. And mithril longswords are rather rare in general - 80 rarity at 250 feet and 10 rarity at depth 700 feet. So my guess is your best odds of finding a mithril longsword would be after 700 feet, by which point half the game is already gone and you've probably found other artefacts already to lower your chance of seeing a new artefact.