LABYRINTH ENCHANTS ARE RIGGED

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ScrotieMcB wrote:

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dudiobugtron wrote:

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Summoner wrote:

It's not impossible, but a brief simulation suggests it's unlikely. According to this, there're 362 possible helmet enchantments (2 levels each). I used excel's random function to generate 110 values between 1 and 362, and the frequency formula to bin them by value. In 5000 trials I got a max of 6 repeats once (0.02%), a max of 5 repeats 31 times (.62%), a max of 4 repeats 476 times (9.52%), a max of 3 repeats 3275 times (65.5%), and a max of 2 repeats 1217 times (24.34%).

All of the 5000 trials had at least one repeat; but if the odds of all results are equally likely, Umbra_the_Wolf's results are extremely improbable.

That is really cool. I thought 9 was unlikely, but it looks like it is far more unlikely than I originally thought. Even though the OP clearly plays fast and loose with words like 'everyone' and 'impossible', the claim about it being rigged is a bit less far-fetched than I originally thought.

...except that if you read the OP carefully...

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Umbra_the_Wolf wrote:

I've run the Lab on merciless 110 times now and I've seen Glacial Cascade 4x, Minion APS 6x, Split Arrow 4x, Mirror Arrow 9x.

He didn't say he got the same Mirror Arrow enchantment 9 times; he said he got Mirror Arrow enchantments 9 times.

So 1/181, not 1/362. Roughly double the chance each roll, to the power of 110 rolls. Which means Umbra's experience is several billion times more likely than Summoner's math would imply, if he would have ever calculated it out past 6 repeats.

This is correct, I've received variations of power for the arrow enchants but the same enchants for minion aps and glacial cascade damage

Hmm... seems I really was a bit hasty, sorry about that. Okay, let's think about it a bit more.
What do we have:
-N tries (110 in our case)
-k different result for each try (be it 362 or 181)
-assumption that their distribution is even (or w/e it is called in English)
What do we want to know: probability of getting exactly p results with some value "X" while all other results are whichever value except "X".
So... total number of possible combinations is k^N.
Number of desired combination is a bit trickier:
-first, our p results can be rolled in C(N,p) = N!/(p!(N-p)!) ways;
-second, for each of that combinations we have (N-p) "leftover" values which give (k-1)^(N-p) variations.
So number of desired combination is N!(k-1)^(N-p)/(p!(N-p)!)
And the probability is (number of desired combination)/(total number of possible combinations), or N!(k-1)^(N-p)/(p!(N-p)!k^N)
For OP's values it will be 0.000034, or 0.0034%. Looks like you are right, OP, this must be rigged. Maybe it is unintentional, though, who knows?

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silumit wrote:

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Summoner wrote:

It's not impossible, but a brief simulation suggests it's unlikely. According to this, there're 362 possible helmet enchantments (2 levels each). I used excel's random function to generate 110 values between 1 and 362, and the frequency formula to bin them by value. In 5000 trials I got a max of 6 repeats once (0.02%), a max of 5 repeats 31 times (.62%), a max of 4 repeats 476 times (9.52%), a max of 3 repeats 3275 times (65.5%), and a max of 2 repeats 1217 times (24.34%).

All of the 5000 trials had at least one repeat; but if the odds of all results are equally likely, Umbra_the_Wolf's results are extremely improbable.

omfg... excel simulations to solve elementary problem... just use your brain, dude!
Look, let's take one enchantment.
Probability of NOT rolling it once is 361/362 (if we consider different levels of same enchantment as different enchantments).
Now probability of NOT rolling it X times is (361/362)^X.
And then if you want to know the probability of rolling it, say, 6 times of 110(not necessarily consequentially, just 6 hits), it is the same as probability of NOT rolling it 110-6=104 times, or (361/362)^104 = approx.75%.
Note to OP: Seventy-five percent is way way way far from "impossible".
PS. Even if we consider different level enchants as one enchant, then it will be (359/362)^104=42%
or (358/362)^104=31%, depending on if there are 3 or 4 levels of the enchant. Still far from "impossible".

If there are 362 equally weighted options for helms, the chances of getting any one of those mods 6x out of 110 trials would be a binomial probability.

If I remember this stuff correctly:

There's a 22% chance that any given enchant will be doubled.

Three percent chance any given enchant will be tripled

0.3 percent chance of quads

0.024 % chance of 5 repeats

0.00140% chance of getting 6 of the same enchant (1/71,428)

I'm not certain - but I think the chance of getting two other enchants with quads, would be an included subset of the non-specific six success binomial.

(using 109 trials, as any given enchantment would count as a success on its first roll, and just needs to be repeated n-1 number of times)

DalaiLama, see my post above, the post you are quoting is totally wrong :)

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ScrotieMcB wrote:

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dudiobugtron wrote:

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Summoner wrote:

It's not impossible, but a brief simulation suggests it's unlikely. According to this, there're 362 possible helmet enchantments (2 levels each). I used excel's random function to generate 110 values between 1 and 362, and the frequency formula to bin them by value. In 5000 trials I got a max of 6 repeats once (0.02%), a max of 5 repeats 31 times (.62%), a max of 4 repeats 476 times (9.52%), a max of 3 repeats 3275 times (65.5%), and a max of 2 repeats 1217 times (24.34%).

All of the 5000 trials had at least one repeat; but if the odds of all results are equally likely, Umbra_the_Wolf's results are extremely improbable.

That is really cool. I thought 9 was unlikely, but it looks like it is far more unlikely than I originally thought. Even though the OP clearly plays fast and loose with words like 'everyone' and 'impossible', the claim about it being rigged is a bit less far-fetched than I originally thought.

...except that if you read the OP carefully...

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Umbra_the_Wolf wrote:

I've run the Lab on merciless 110 times now and I've seen Glacial Cascade 4x, Minion APS 6x, Split Arrow 4x, Mirror Arrow 9x.

He didn't say he got the same Mirror Arrow enchantment 9 times; he said he got Mirror Arrow enchantments 9 times.

So 1/181, not 1/362. Roughly double the chance each roll, to the power of 110 rolls. Which means Umbra's experience is several billion times more likely than Summoner's math would imply, if he would have ever calculated it out past 6 repeats.

No, it's 1/362. There are 724 possible enchantments, 2 each for 362 possible skills. That's 2/724 or 1/362.

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silumit wrote:

DalaiLama, see my post above, the post you are quoting is totally wrong :)

Hmm, sorry about that! I wonder if I had that browser window open for commenting while my attention was on something else for awhile. Your formula looks good. What numbers did you plug in? The 4,4,6 or did you include the 9 too?

I didn't notice the 9x when I was using a binomial calc. Even a single enchant with 7 repeats is about 1 in 1.4 million. Possible with hordes (tens of thousands) of people playing at 7 and maybe even 8. 9 sounds like something *might* be broken?

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Umbra_the_Wolf wrote:

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Qarl wrote:

Helmet enchants are evenly weighted. The repeats you report are certainly not mathematically impossible.

While getting that precise set of results again is not going to happen, getting a set of results with large number of repeats of things you don't want certainly can happen.

I'm calling B.S. on this flat-out, that's what this post is about. not math. It's about a slots-machine style game getting one more quarter from us, ie- more time in the game with less return than we invest to create a stable base. RIGGED.

By taking some assumptions we find something we don't like
1. If I'm right, then that means the game is set up to be able to mathematically cater to the house (to continue the gambling analogy)
2. If you're right, then still Random Number Generation is so evil it's almost a miracle it's used by POE in its base form, ie- raw numbers without filters. In which case it begs for some kind of filter like what we have for chromes on intelligence, dexterity, armor and mixed defense gear for changing colors.

No matter who is right or wrong, the entire LAB is a pile of steaming crap that was quite obviously created to keep people addicted by pouring as much time of their lives into it for as long as possible. One more quarter. One more level. One more enchantment. It's all the same in the end.

[Removed by support] Not even Diablo 2 was this horrible.

Ohhhhhhhhhhhhhhhhhhhhhhhhhh, so its just the basic RNG sucks kind of thread. I was almost fooled you were inventing new math here.

Hmmm, so yeah. Have you looked around, like, ever? Everything in this game is RNG. Like it or not, it is what it is.

There aren't 362 skills in the game. Just count them.

Whether it's mathematically likely or not these results are still crappy and unrealistic, which is very discouraging. I would have expected a greater variety of outcomes and only a few pairs.

When the results seem ridiculously skewed and unrealistic like this it's because it isn't rigged. The results are produced entirely by RNG without enforcement. Random number generators never produce even distributions. The system needs to be 'rigged' by forcing specific results to happen after a number of random results over an interval of outcomes to produce realistic results.

For instance, you're supposed to have a 78% chance to hit. That means precisely 78 hits and 22 misses in every interval of 100 attacks. But 100 is a big interval in which the results can vary wildly so, to produce a smoother outcome, I would use an interval of 10 attacks instead. That would leave an adjusted ratio of 7 hits and 3 misses per interval of 10 attacks. Truncate the fractional values and add them to an accumulator that adds +1 to the adjusted values whenever it's >1. I would use RNG at the beginning of each interval to decide hit or miss but only until the maximum number of hits or misses is reached. The outcomes of the remaining attacks must then be forced as either misses or hits, respectively. Game applications should employ something like this anywhere RNG is used.

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TheNightFly wrote:

For instance, you're supposed to have a 78% chance to hit. That means precisely 78 hits and 22 misses in every interval of 100 attacks.

You're mixing up "chance" with "rate". Big mistake.

In short&simple words: you can easily have 50 (and even more) attacks "miss" with 78% chance to hit.
Hence, "the chance".

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TheNightFly wrote:

But 100 is a big interval in which the results can vary wildly so, to produce a smoother outcome, I would use an interval of 10 attacks instead.

Second mistake.
If you're trying to describe probability theory (here) to someone who doesn't know anything about it - you're doing it seriously wrong.