Drop Statistics

[chocobochicken]

I've always had a good head for numbers, but I'm a bit of an amateur when it comes to statistics. This became apparant when I recently began attepting to calculate the odds of completing several consecutive Fake In Yellow runs without finding a single Rappy's Wing (my record so far is 13).

First, I reasoned the formula:

F(x) = 127^(47x)/128^(47x)

where x is the number of FIY runs and F(x) is the % chance that I will not find a single wing.

Now, I'm not exactly certain I have the right equation, but it intuitively feels right to me. This is assuming a drop rate of 1/128 and 47 rappies per run, with what I think is the total number of wingless outcomes divided by the total outcomes. If this is right, then this means I have about a 33% chance to come out empty-handed after 3 consecutive runs (with a 67% chance of finding one or more).

Unfortunately, I can no make calculations with this formula for x>3 because the exponential is too high for the abilities of MS Excel (my tools are limited). So is there a method using logarithms or other mathematical techniques that can simplify this equation, or do I just need to seek bigger number-crunching power?

Math majors, go wild. ^^

[Kirika]

Simplify it to (127/128)^47

You have about a 1% chance of getting none after 13 runs. Sounds small, but thats more than the chance of getting one from one individual rappy!

[chocobochicken]

*slaps self on the forehead*

For some reason, I didn't think the fraction could factor out like that. So my run of 13 was a 1 in 100 chance, huh?

Okay. Next up, I want to figure out the odds of how you managed to get 7 wings in 8 runs. :P

[Darkness fall]

whaat?

[Icelight]

Pfff only 13 runs?

When I first started Rappy Hunting I went 17 runs without finding a single wing. On the 18th and 19th, however, probability realized it had missed me and gave me 2 and 3 wings respectively.

Still though, it is quite unlucky to go even 3 runs without seeing a wing :D