So, I'm trying to work on a tool that calculates the enhancement chances of an item and how many times it would mathematically take to reach a certain item level.
In the table below you can see the following:
- You have a $70\%$ chance to enhance a clean item to level $I.$
- You have a $40\%$ chance to enhance an item of level $I$ to level $II.$
- You have a $30\%$ chance to enhance an item of level $II$ to level $III.$
- You have a $20\%$ chance to enhance an item of level $III$ to level $IV.$
- You have a $10\%$ chance to enhance an item of level $IV$ to level $V$
|----------------------------------|
| I | II | III | IV | V |
|----------------------------------|
| 70% | 40% | 30% | 20% | 10% |
|----------------------------------|
I'm trying to figure out a formula that helps me calculate what the success rate is when I attempt to enhance a clean item to item level $V$
For example: if I try it $300 \times$, I'll be $65\%$ succesful.
I know that I can use probability maths to calculate what my chances are of making a $40\%$ enhancement work after $5$ times $1-((1-0.4)^5)$, but I don't think that'll help me here.