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So I already upgraded it to +3 and I want to know when it's best to stop Upgrading it? Because I don't want to grind for a long time just go down the floor after exploring it all. (I've won twice now, I don't know of this helps saying it incase it is helful)
The "basic" strategy for RoW is, imho, to upgrade it so much that you find your endgame equipment with it. Thus means upgdraded Tier-5 weapon and upgraded plate armor. To clarify: you find these items already upgraded. You also should hoard some scroll of transmutations because you then transmute the RoW when you no longer need it. The upgrades of the RoW scales similar as with weapons or armor. This means as wutg weapons that +1 reduces the strength requirement and then +3 again, as +6. This means the upgrades that are interesting for an RoW are +1, +3, +6, +10, +15, +22. Each if these levels may yield upgraded weapons or armor. As far as I remember (and it may have changed) a +1 RoW can drop +1 equipment, a +3 RoW can drop +2, a +6 can drop +3.
Let's assume you upgrade to +10. this should eventually drop +4 weapon and +4 plate armor and then still having +5 SoUs left to either upgrade tge weapon, the plate armor, another ring (+4 rings could drop as well). Just to finalize tbe example: We use the 5 SoUs to upgrade the weapon, then our final equipment is: +9 weapon, +4 plate (maybe the smith can upgrads to +5) and a +10 ring, that was the RoW before transmuted. This is a good enough equipment in my opinion.
So, tl;dr: +6 or +10 is what I would do. +15 for the fun of it.
A final reminder: The equipment still needs to drop, which is random. So you may just die before anything useful drops. And you need a lot of Scrolls of Curse Removal, since you usually fund a lot of stuff.
I found one early in a game today and was curious about the math. Thanks for breaking it down.