Loot pool of rings is large enough for you to waste a good chunk of materials to get the right one and yet you still expect the right item to be an ancient, with 1/10 rarity rate. That’s not impossible, but still require a hefty amount if you don’t share someone else’s luck.
That simply means you have around 3.5 to 4.1 in a thousand chance (0.357-0.416%) to roll an ancient ring you want and this is not considering item weights.
That’s less than 4% chance with another 1/10 rarity modifier for a ring you want to be ancient quality on top of it. There are 24-28 different ring outcomes that you can acquire from rare item upgrading depending on the class. Upgrading rare rings must be a desperate measure if nothing else works.
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