I've been playing a MMORPG recently and have learnt basic probability to figure out how much money I will realistically need for upgrading different items.
I have a sword to upgrade. Normally when you try to upgrade the item and it fails, it will break. For this sword, each stage of upgrading has a different chance of succeeding, the formula for which is 1-n*0.1+0.1. So to upgrade from +0 to +1, the probability of success of 1, from +1 to +2 it's 0.9 and so on up to the maximum upgrade which is from +8 to +9 which has a 0.1 chance. That's fair enough and I got 1*0.9*0.8*0.7*0.6*0.5*0.4*0.3*0.2 = 0.0036288 to upgrade from +0 to +9.
However, there is an item that is making my head hurt. The Blessing Scroll makes it so that if you upgrade with this item and the upgrade fails, the sword will go down by one level. For example, if you try to upgrade from +5 to +6 and fail, the sword will go down to +4.
An additional issue with working this out is that each upgrade stage has different costs associated with it. +5 to +6 will require different items than +8 to +9
How would I approach working this out? I have googled for dependant events but didn't come across anything like this. Decision trees become massive when there are so many stages and they all link to their previous one, and I don't know other techniques that could help.