There have been a few discussions about the Pink Floyd .moar file in the light of suggestions by some that some pieces of the file are particularly rare and by others that having a high level of luck will mean that you’re more likely to end up getting pieces of the file that you haven’t already got.

I wanted to put this to the test and compare the number of unique pieces of the file that people have got with the number that they would have if a random piece of the file dropped each time they received a single piece of the .moar file. If people with high luck have more unique pieces than they would if it were totally random, this would suggest that you really are more likely to get missing pieces with higher luck. If everyone has less unique pieces than they should then this suggests that some pieces really are more rare than others.

For this reason, I’d like to use this thread to pose two questions. Firstly, is there a formula to work out how many unique pieces a player “should” have once they’ve collected a certain total number of pieces (if the pieces were random)? Secondly, how many total and unique pieces has everyone got, and how does this compare with the number they “should” have? Does their luck make a difference to this answer?

In reference to the first question, it’s been too long since I finished school for me to remember much of my Maths A-Level, so I’m no good at formulating formulas (formulae?) any more. Instead, I set up a spreadsheet. For each piece that was dropped, I bumumed that the chance of a unique piece dropping was (50-u)/50 where u is the number of unique pieces so far. I carried the number forwards each time with no rounding at all. After getting the first piece, the player is guaranteed to have one unique piece. After getting another piece, he has a 98% chance of getting a new unique piece, meaning that he will on average get 0.98 new unique pieces. I’m saying that he will now have 1.98 unique pieces and carrying that number forwards, meaning that he has a 96.04% chance of getting a unique piece when he gets his next piece.

Can someone who is good at Maths let me know whether calculating the numbers in this way is likely to work, or whether I’m getting this all wrong? Am I wrong to bumume that I can use these numbers without rounding them in any way? If so, what’s a better way of calculating the answer?

If these figures are accurate, then this is the number of unique pieces any player would expect if the piece number was totally random each time:

Total  Unique        Total  Unique        Total  Unique
1      1             30     22.73         100    43.37
2      1.98          35     25.35         110    44.58
3      2.94          40     27.71         120    45.57
4      4.8           45     29.86         130    46.38
5      5.71          50     31.79         140    47.04
10     9.15          60     35.12         160    48.03
15     13.07         70     37.84         180    48.68
20     16.62         80     40.07         200    49.12
25     19.83         90     41.88         250    49.68

As to the second question, I’ve had around 35 to 40 luck for most of my grinding and I’ve presently got 53 pieces of the .moar file and I’ve got 28 unique pieces. This is a bit lower than the figure I should expect to have, but not proof of anything more than bad luck in itself.

How about you guys? How many total pieces have you got and how many different pieces have you got? Roughly what has your luck stat been set at while you’ve been getting these pieces?