a simple test about trophy drop rate in single-player

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RyougiShiki
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misscarriage wrote:I'm confused about the logic in this thread. You are never granted getting a trophy, no matter how many times you run the uber. Just like you're never granted to get tails when you flip a coin. Mathematically speaking, you will get it eventually, but 100 or 200 or 300 runs don't prove anything at all. The odds will always be 2%


emmm, thats the law of large numbers grantee me.
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RyougiShiki
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whist wrote:"hi buddy, its me again"

Your previous thread was locked because it was getting out of hands. As for my reply, it wasn't meant to mock you, but rather to close the thread on a humoristic tone. You were already told by several moderators and two admins that the drop works as intended, and yet you kept going on about how THE GAEM IS BR0KEN PLS FIX USING OBJECTIVE LAW OF M4TH, providing absolutely no scientific evidence that it is broken other than "3 people had to kill the boss several times to get a trophy and I can't get one after 100 kill".

And now here you are, creating another thread, and this time providing pseudo evidence that was generated by altering the game's code, which renders your sample completely irrelevant. And as it was already mentioned by Swineflu, your data set is way too small to provide real insight, if you take a look at recognized probability research, you'll see these kind of values are often measured against several tens of thousands samples.

Had you done a few more runs instead of spamming the forums with your conspiracy theories, googling random wikipedia articles and hacking the game to generate "proof", you'd probably have your trophy by now :roll:

And for tinfoil hat enthusiasts that are watching this thread, the chances are the same for single player and multi player.


i have to say sth about "data set is way too small" ,since 2% is not a very small number there is no need to test for 10000 or more times.

SP MODE test is irrelevant? but how can i make it in MP MODE with 1000 still said to be "small" ?Should I try 10,000 times at TSW and get about 200 trophies? i cant, sorry, From this point of view, I can never prove myself.

one more thing, its not a conspiracy theory. plz dont make me to stand against you.
"it wasn't meant to mock you, but rather to close the thread on a humoristic tone" what you post you can say humoristic but i can have other ideas.i think it is offense to me but, hey, it doesnt matter. since you have made a reply to this i dont have to care it more.
i can trust you and all others but i need a more specific and reasonable explanation, instead of just RNG or bad luck. But if you think it's normal, for 4 people include me to run hundreds of times , i dont have much to say.
why don't we confirm the guys' word ? if they are false , the whole thing is meaningless . i can take it as "bad luck " for my own experience, but if more people went though I do have an incentive to doubt.
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SwineFlu
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OP, have you ever noticed that unique upgrade lottery recipe chance isn't the same that was mentioned in the docs for quite a long time? Does anyone else who's hunting the trophies ever noticed this change? It makes no sense that person with such a keen eye as you never noticed that. Well, you see that's the problem, it's hard to miss the difference in 2 percent, yet the chance for that recipe was downed to 3% from 5% and this change was committed somewhere in between MXL 17 iteration. What's your excuse would be this time? And what would be an excuse for any other local expert in drop rates and rng mechanics? How comes that this nerf went unnoticed for a few seasons? It was never mentioned in the patch notes as well iirc.
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Nahuatl
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whist wrote:"hi buddy, its me again"

Your previous thread was locked because it was getting out of hands. As for my reply, it wasn't meant to mock you, but rather to close the thread on a humoristic tone. You were already told by several moderators and two admins that the drop works as intended, and yet you kept going on about how THE GAEM IS BR0KEN PLS FIX USING OBJECTIVE LAW OF M4TH, providing absolutely no scientific evidence that it is broken other than "3 people had to kill the boss several times to get a trophy and I can't get one after 100 kill".

And now here you are, creating another thread, and this time providing pseudo evidence that was generated by altering the game's code, which renders your sample completely irrelevant. And as it was already mentioned by Swineflu, your data set is way too small to provide real insight, if you take a look at recognized probability research, you'll see these kind of values are often measured against several tens of thousands samples.

Had you done a few more runs instead of spamming the forums with your conspiracy theories, googling random wikipedia articles and hacking the game to generate "proof", you'd probably have your trophy by now :roll:

And for tinfoil hat enthusiasts that are watching this thread, the chances are the same for single player and multi player.

If we trust uberelite’s 354 streamed runs for a single trophy we get the following chi square:

1|353
7|347

(Observed 1 trophy in 354 runs, expected 7 trophies at 2% in 354) we get a p-value of 2.2% (2.1% if you don’t round the expected results)

In layman’s terms we’d expect a 2.2% chance that random chance picked that outcome with a 2% rate.

So there are possibilities here. One is that the data is flawed (I’m not checking 354 runs). One is that this was super unlucky. One is that there’s something fishy going on.

This does not need to be tested 10s of thousands of times. If the rate was actually 1%, for instance, 750 trials would give us 95% confidence it isn’t 2%.

I’m all for doing 750 runs and recording the data transparently. If there is an issue, it’s better to know it. That said, I’m not a fan of the way this is combative instead of data-driven exploration.
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RyougiShiki
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Nahuatl wrote:
whist wrote:"hi buddy, its me again"

Your previous thread was locked because it was getting out of hands. As for my reply, it wasn't meant to mock you, but rather to close the thread on a humoristic tone. You were already told by several moderators and two admins that the drop works as intended, and yet you kept going on about how THE GAEM IS BR0KEN PLS FIX USING OBJECTIVE LAW OF M4TH, providing absolutely no scientific evidence that it is broken other than "3 people had to kill the boss several times to get a trophy and I can't get one after 100 kill".

And now here you are, creating another thread, and this time providing pseudo evidence that was generated by altering the game's code, which renders your sample completely irrelevant. And as it was already mentioned by Swineflu, your data set is way too small to provide real insight, if you take a look at recognized probability research, you'll see these kind of values are often measured against several tens of thousands samples.

Had you done a few more runs instead of spamming the forums with your conspiracy theories, googling random wikipedia articles and hacking the game to generate "proof", you'd probably have your trophy by now :roll:

And for tinfoil hat enthusiasts that are watching this thread, the chances are the same for single player and multi player.

If we trust uberelite’s 354 streamed runs for a single trophy we get the following chi square:

1|353
7|347

(Observed 1 trophy in 354 runs, expected 7 trophies at 2% in 354) we get a p-value of 2.2% (2.1% if you don’t round the expected results)

In layman’s terms we’d expect a 2.2% chance that random chance picked that outcome with a 2% rate.

So there are possibilities here. One is that the data is flawed (I’m not checking 354 runs). One is that this was super unlucky. One is that there’s something fishy going on.

This does not need to be tested 10s of thousands of times. If the rate was actually 1%, for instance, 750 trials would give us 95% confidence it isn’t 2%.

I’m all for doing 750 runs and recording the data transparently. If there is an issue, it’s better to know it. That said, I’m not a fan of the way this is combative instead of data-driven exploration.


thats my point.
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Marco
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SwineFlu wrote:(lotto) ... yet the chance for that recipe was downed to 3% from 5% and this change was committed somewhere in between MXL 17 iteration.


Even more actually, it's been 3% for 6 years :D
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Rishab
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Bruh this thread...
I cant facepalm enough without breaking my face.

It is literal random, each time you do boss it resets to 2%, each time!
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Marco
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Nahuatl wrote:I’m all for doing 750 runs and recording the data transparently. If there is an issue, it’s better to know it. That said, I’m not a fan of the way this is combative instead of data-driven exploration.


Fully agreed but a lot of this "data" is really questionable.

Lets say you do 100 runs and get a trophy on run 7 and run 39. What are the odds you would get the trophies in these exact runs? 0.04%? Anything can be made to sound impressive with probabilities. Literally everything ever has a really small chance to happen, it all comes down to how you present it. Me writing this exact message here at this time was 1 in trillions but look, it just happened.

Trophy chance is 2% and this is a fact.

For anyone who still doesn't want to believe it,
https://en.wikipedia.org/wiki/Gambler%27s_fallacy
https://en.wikipedia.org/wiki/Independence_(probability_theory)
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Anything that has a low chance happening, will happen eventually. That includes not getting a trophy in 300+ runs. There are theories about how the world was born, and scientists calculated that there is a (ill just throw a random number) 10^(-9999999999999999999) chance that a new big bang would happen due to random quantum fluctuations at a given second. We might be here because that happened.
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SwineFlu
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Marco wrote:Even more actually, it's been 3% for 6 years :D

That's even better, it's not some plain 2% it's almost 2 times worse and nobody noticed it for such a long time, perfect example.


Drop chance is determined by the seed value from the monster that you've killed (e.g. Laz), however this seed is not some fixed value, in fact it's constantly changing during the game time (it might change after a few game ticks/frames). If anyone is willing to experiment with d2 pseudo random number generator here is the actual code which is used by d2 engine (C++):

Code: Select all

void RandomTest()
{
   using UINT32 = unsigned int;
   using UINT64 = unsigned long long;

   // Pretty much the same function used by d2 engine
   auto Random = [](UINT64& Seed, UINT32 Range) -> UINT32
   {
      if (Range == 0)
         return 0;

      Seed = 1791398085 * (Seed & 0xFFFFFFFF) + (Seed >> 32);
      return (Seed & 0xFFFFFFFF) % Range;
   };

   // Set initial seed value (could be anything)
   std::srand(std::time(nullptr));
   UINT64 RngSeed = (static_cast<UINT64>(std::rand()) << 32) + std::rand();

   // Trophy drop change = 2/100
   if (Random(RngSeed, 100) < 2)
      std::cout << "Success!" << '\n';
}