[Math] Probability of entering Beta

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Fourier wrote:

[DISCLAIMER]This post is outdated, and reflects values from 2 weeks ago, when the beta began.[/DISCLAIMER]

Why, hello there!

I calculated a few probabilities for your enjoyment.

Assuming there are 50,000 registered accounts, ...
- Probability you will be picked on the next tick:
1/95,000 if you don't post of the forums;
1/9,500 if you do.

- Probability you will be picked today:
0.9% if you post on the forums;
0.1% if you don't.

- Probability you will be picked this week:
7.1% if you post on the forums;
0.6% if you don't.

- Probability you will be picked in the next two weeks:
13.74% if you post on the forums;
1.34% if you don't.

- Probability you will be picked this month:
25.6% if you post on the forums;
2.65% if you don't.

- Probability you will be picked in the next 3 months:
58.81% if you post on the forums;
7.75% if you don't.

This is, of course, assuming the 15-minute timer won't change over the next 3 months, which is highly unlikely.

The underlying math:
I'll explain how I obtained the values for the probability of getting picked today, if you're a forum poster.
We have a series of 96 trials, with a 1/9,500 probability of success on each trial. Then we are looking for the probability of NOT having 0 successes. In other words, let X be the number of times you will be picked today. Then we are looking for P(X>0). X follows a binomial distribution of parameters 96 and 1/9,500. So we're looking for 1-P(X=0), which, in this case, is 0.9%.

[Edit] Changed the base probabilities from 1/5,000 to 1/9,500 for forum posters and 1/50,000 to 1/95,000 for forum lurkers based on:

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FinalParagon wrote:

Let's go with [the] assumption at any given time there are 50,000 accounts...
The pool of names they pick from actually contains 95,000 names, even though only 50,000 of them are
unique.
timer.

Where did the other 45000 names come from? There are only approximetly 59000 accounts at this time?

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stanleyxd1 wrote:

i received an invite to test SWTOR... i dont want SWTOR damnit i want PoE!