I'm pretty sure you are complicating things for no reason.Don't even try to understand stochastic

Their is a certain formula I'm trying to find to calculate how many tries you need with a set probability to get at least one hit you have to use here. You can't simply use 1/.45=2.22..

As an example: The chance of rolling a 6 with 6 dice is only about 62%

The equivalent of what you say with dices would be us looking the chances of "having a RE proc while using 10 FS/DS/RS". But what we're looking are simple probabilities : if we do 1000 FS, we'll have a number of proc close to 450.

And I'm pretty sure that's why the efficiency of RE is actually 0.45 : when you launch one RP-ability, you have 0.45 chance of having a proc, same for the next RP-ability (a launch are independant). In a 10 minutes long fight, you'll have 45% of your RP-ability giving a rune (again : launches are independant).

The bottom line being : I don't want to know what my chance of having ONE RE proc on many rolls is, but just how many RP ability, in average, I have to use to gain one rune.

Edit : In other words "I cast say X rp-abilities, I wanna know with which one I gain the highest amount of runes".