2015-02-07, 03:26 AM
The cost for 5 star at least seems consistent with my own experience and testimonies of a few of my old alliancemates. That said, your calculations seem a generalized or incorrect to describe the expected cost (if there is one). Moreover, the average cost doesn't mean much without a variance. I aced a probability course last semester, but describing the distribution of this system seems very complicated. It's quite similar to a random walk problem, but restricted to positive integer values. The changing probabilities and chance of returning to the start (booming) severely complicate it as well :\
My issue with the calculations for stars 1-5 is that you're dividing by the probability of getting x successes in a row when there are more alternatives. For 5 stars, for example, you could fail any number of times at the beginning, pass 4, fail 2, then pass 3 in a row and get to 5 stars. To get to x stars in general, you'd need to get x more successes than failures in N attempts where failures from 0 stars can be ignored. The problem is fixing x and calculating the expectation of N where N can take values from x to infinity.
This is kind of interesting, so I think I'll build some code to test this with fixed probability values.
My issue with the calculations for stars 1-5 is that you're dividing by the probability of getting x successes in a row when there are more alternatives. For 5 stars, for example, you could fail any number of times at the beginning, pass 4, fail 2, then pass 3 in a row and get to 5 stars. To get to x stars in general, you'd need to get x more successes than failures in N attempts where failures from 0 stars can be ignored. The problem is fixing x and calculating the expectation of N where N can take values from x to infinity.
This is kind of interesting, so I think I'll build some code to test this with fixed probability values.