# Determining the validity of loot box drop rates

I have been playing a mobile game where the listed drop rate for a loot box prize is 1/3. I have opened 48 loot boxes and received 6 prizes (1/8). It has been so long since stats class, but can't I use a t-test with a 95% confidence interval to find if my H0 should be rejected? I know my sample size is small but RNG can't be that bad, can it? It seems that the drop rate is far less than 1/3.

I'd like to know how to set it up so that I can do it on my own in the future. I'm having trouble understanding my sample SD and using a chart.

• When did you decide you wanted to test? After seeing the data? see en.wikipedia.org/wiki/Testing_hypotheses_suggested_by_the_data Sep 23, 2018 at 8:36
• I started to keep track when it became apparent that I was not getting a 1/3 return. I'm aware of type 1 errors and plan on gathering more samples going forward. I did not want to invest money into a chance game where the return was no where near the posted rate. Sep 23, 2018 at 16:00
• How did you decide when to test it? Edit: sorry, that's unclear. How did you decide that now was the time to stop collecting data and try to test the hypothesis? Sep 23, 2018 at 16:27

What you are looking at is a Bernoulli variable, that is outcome 0 or 1 for one repetition. When considering many such repetitions you are looking at a binomial distribution. There you can calculate the 95 % CI for the null hypothesis (proportion is equal to 1/3) with

qbinom(c(0.025,0.975),48,1/3)

which get you [10,23], so your value of 6 is outside the 95 % CI. The probability of this event (6 out of 48 with true probability 1/3) is

pbinom(6,48,1/3)

which is 0.0009170562.

Edit: if you are not ready to use R then have a look at Wikipedia page where you have an approximate formula using normal distribution https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval

• Given OP doesn't study stats, I don't think he will know how to use R, nor any other statistical programming language Sep 23, 2018 at 8:59
• I do not know how to use R. If I use the equation from the wiki page (which I can do), do I recieve a z score that I can look up on a z table? I wasn't sure what [10,23] represented or what I use that with. Sep 23, 2018 at 16:08
• Yes, the z score can be obtained from a z table, although if you are going to use the 95 % CI you can always use the predefined value of 1.96 for z. [10,23] represents the 95 % Confidence Interval (CI), that is where you can expect 95 % of all values to lie, if your null hypothesis is true. Sep 24, 2018 at 6:09