Talk:McLaren Senna Festival Coin Pack/@comment-31458611-20200211131525/@comment-34918040-20200218071715

@ Non-VIP Forever!:

This is a very interesting approach and a puzzle much to my taste! In your three examples, I could not find a possible combination other than the one you suggested.

However, to generally accept data from TLE results, we should be sure that your method always delivers one and only one solution for every possible sum of coins. Unfortunately, I quickly found a counterexample that involves no 3-Coin results at all and has more than one possible solutions.

I therefore decided not to include data from TLEs as the probability that you or me overlook other possible combinations is to high, and verifying the calculations is simply too time-consuming.

But I'd like to thank you for making me dive deeper into the world of combinatorics, partitions and multiset coefficients until I found a much simpler solution that only requires simple algebra to find an infinite number of counterexamples. You can read my blog post for more details if you are interested: Is it possible to deduce the exact distribution of 3, 5 and 8 Coins from TLE results?

@ Tobias mann:

It's right that we don't know if the game does not simply multiply the number of Packs by an arbitrary rate, but thinking in terms of programming efficiency makes this possibility very improbable:
 * You'd have to take integer closest to the product and then calculate if it is possible that the resulting number is a combination of the summands 3, 5 or 8. To be honest, the example of the ARSE that would have required astronomical amounts of to build it during the very first Festival makes me doubt that the devs have deeper knowledge of combinatorics or probability theory.
 * On the other hand, the random process for opening a Coin Pack is already there and does the job within fractions of a second. It's a lot easier just to use it instead of additional calculations.

Therefore I'm quite sure that the results from TLE Coin Packs have exactly the same mechanism as all other Coin Packs. Besides, Non-VIP's other two results show different factors which would make it even more complicated for the programmers.