As shown in the picture, music sheet #1 is more than doubled the number of music sheet #4. WHY??
I know some others lacks sheets other than #4, it varies among players.
It cannot be a programming error since implementing a uniform distribition is the easiest thing (easier than a non-uniform like it is now). So why? Is this some kind of psychological trick on gamers that I do not know?
Limiting tactics.
It’s coded like this to frustrate the players…
That’s indeed very interesting. I did a simple test to see how ridiculous it actually is.
In each iteration, I generated 522 random numbers (your total of verses) from 1 to 4 to simulate a verse. Then I check if any of those 4 has dropped 83 times or less (your brown verses). When it occurs, I register how many iterations it took to achieve that (= probability) and also the verse distribution.
Here are the results:
215.375 ==> [141, 165, 134, 82]
1.156.074 ==> [143,157,143,79]
257.604 ==> [154,80,145,143]
726.693 ==> [160,126,83,153]
276.750 ==> [122,83,167,150]
1.153.354 ==> [153,145,141,83]
484.747 ==> [79,153,140,150]
1.097.830 ==> [155,142,75,150]
1.057.209 ==> [179,126,82,135]
301.735 ==> [134,82,166,140]
204.876 ==> [83,145,153,141]
1.934.581 ==> [147,83,147,145]
1.196.335 ==> [131,139,83,169]
616.995 ==> [152,76,150,144]
920.357 ==> [145,144,152,81]
279.521 ==> [146,159,80,137]
1.669.933 ==> [164,141,83,134]
258.163 ==> [80,149,149,144]
76.204 ==> [159,151,83,129]
895.979 ==> [154,145,140,83]
1.306.173 ==> [137,80,149,156]
204.469 ==> [143,165,133,81]
1.258.673 ==> [146,139,82,155]
724.478 ==> [139,150,81,152]
154.376 ==> [149,81,157,135]
853.452 ==> [149,79,148,146]
195.404 ==> [81,152,143,146]
676.824 ==> [81,156,150,135]
14.264 ==> [144,167,82,129]
191.478 ==> [161,78,143,140]
134.715 ==> [162,128,152,80]
100.780 ==> [82,144,146,150]
533.105 ==> [168,140,131,83]
416.613 ==> [154,123,162,83]
822.370 ==> [150,137,152,83]
124.805 ==> [152,134,82,154]
3.847.579 ==> [82,152,151,137]
353.745 ==> [149,81,144,148]
1.320.181 ==> [139,157,83,143]
1.680.935 ==> [131,161,147,83]
On average, that is 1 in 742.368,35. That is based on 40 samples, but since the difference between the first 20 samples and second 20 samples didn’t differ awfully much, I think it gives a good idea.
Conclusion: Since it’s not the first time that someone complains about this and GoW definitely doesn’t have even close to 740k players there’s definitely something going on.
On average, that is 1 in 742.368,35. That is based on 40 samples, but since the difference between the first 20 samples and second 20 samples didn’t differ awfully much, I think it gives a good idea.
Conclusion: Since it’s not the first time that someone complains about this and GoW definitely doesn’t have even close to 740k players there’s definitely something going on.
You method has flaws. Your assumptions would be correct if OP never used any verses but he probably used a lot of them, so number of his overall collected verses is much bigger and difference in distribution between them is less.
Lets assume that he used X (for example, 200) sets of verses. Ratio of distribution between Verse#1 and Verse#4 isn’t 176:83, it’s (X+176):(X+83), in case of 200 sets of verses it’s 376:283 and it’s much more likely than 176:83
I was indeed assuming he never used (a lot of) them, given he has such an amount of verses 
With the assumption of 200 used GAPs in your example, it would be ~1 in 200 to end up with numbers like OP, which is ofc likely to happen. Thanks for noticing!
Why would you think this has been implemented? Players with number of verses that are (relatively) close to each other are content.
Players with number of verses that are wildly uneven will spend gems and/or money on offers to correct that imbalance.
They have zero incentive to make sure these verses even out, because player satisfaction has’nt been a consideration of theirs for years. It’s all about how they can monetize every single aspect of the game they can.
Apparently, the drops are not random and independent. They might be random and not independent, nonrandom and independent, or nonrandom and not independent, which all can be a result of conditional probabilities. If a uniform distribution provided by a pRNG generator on the server is transformed via multiple conditions set by the code, the result of the outcome may be not random and independent, which is probably the case.
If you want to go into detail, a wiki article provides good explanation of the mechanics of these deviations.
On a larger scale across multiple players, this whole conditional deviation is smoothed out due to the law of large numbers. However, the law is not applicable to individual players who may experience this deviation.
Basically, as the code grows and gets more and more complex, GoW is gradually becoming a mess resembling de facto a biased casino. A simplified case is described in another wiki article about fair coin:
Alas, the developers consistently fail to implement any standard means used by other software, including certified tools, to compensate for these anomalies, instead firmly sticking to “take it or leave it” approach.
This is not a conclusion that can be reliably drawn just from the information presented in this post.
It can indeed be applied to individual players as long as they have farmed enough verses, but the analysis is made complicated because such players are also using up these verses, leading to a deviation that may seem much greater than expected (as has already been discussed in this thread).
Again, this is not a conclusion that can be reliably drawn just from the information presented in this post.
In general, note that the deviation between your most and least common verses scales as sqrt(N), where N is the total number of verses you have farmed. Thus, people who have farmed more verses are expected to see the largest deviation in the verses they own, regardless of whether or not they have been using them up. This is somewhat ameliorated by the fact that verses can appear as daily offers which can be bought or dismissed as required.
I think you are confused as my post does not have have any conclusions, only hypotheses. If you can be bothered to check my posting history and accompanying discussions and clarifications, you may be able to find previous considerably more thorough evidence, indicating either actual not random and independent evidence or actual random and independent evidence, depending on what has been tested.
I had used a lot of verses, lost track of how many. But verses #4 has been the weakest link since day 1 and the gap just kept widening.
In a similar situation. Used a lot Verses, and verse 3 has been the lowest for months. Meanwhile, I have over twice as many verse 4s (Thirteen 3s & Thirty 4s).