[Math] Probability of entering Beta

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Gildarts wrote:

Magnificent.

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Hmm... maybe, but I didn't see it official. Chris states that you had to use forums before August, 10th. I don't think that the veteran pool is growing anyhow.

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Fourier wrote:

Why, hello there!

I calculated a few probabilities for your enjoyment.

Assuming there are 50,000 registered accounts, that forum posters have ten times more chances of being picked for the beta and that new players are picked every 15 minutes, we have these basic probabilities:

- 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 not in the beta and 10% of those (from one of your posts a few pages back) have posted in the forum (so 5,000), with every person picked replaced by a new person of the same category over time. For the purpose of probability, the posters actually count as 10 people, or a total of 50,000 vs. the 45,000 who haven't posted. The pool of names they pick from actually contains 95,000 names, even though only 50,000 of them are
unique.

So the probability of a non-poster is 1/95000, where the probability of a poster is 1/9500 given the numbers [we're] using.

[Edit #2]
Adjusted values for the new 15-minute timer.