Infernal Pit SpecialChest runs: high probability of Zod and other HRs
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I'm trying to follow your math, which is a bit tricky, but where/how did you calculate that you should get exactly one rune every ten runs in expectation?
Kinda tough to calculate based on how multiple item checks are calculated (I don't really understand this myself) but it's covered in some detail in Urlik's Runefinding Guide since iirc Jarulf or someone explains item generation of special chests in there
I used the data from a Grisu' post. The chance for the game to choose a rune (Runes 17 TC) for the IP SC is 14/130 = 10.77%
I'll be off internet for quite a while, but will be glad to answer the questions (if any) after my return.
I see. It's just that using "15-17% above expected values" as a reason to accept your hypothesis (which the data doesn't support), when deliberately underestimating expected rune drops by 8% looks pretty comical. Either accuracy and precision are important, or they aren't, picking and choosing so it fits your conclusions the best is a pretty basic and serious statistics error that calls into question the rest of the methodology.
Like someone said upthread, I appreciate your enthusiasm, but nothing in these initial numbers (both from the original post and from the more recent runs) indicate anything other than someone finding a number of runes that are slightly higher than the long-term average over a very small sample size, completely consistent with the way randomness and distributions work. Occam's razor would suggest that "completely normal result, nothing crazy going on" is more likely than "completely normal result, hidden unknown hard-coded secret bonus rune drop parameter found".
Like someone said upthread, I appreciate your enthusiasm, but nothing in these initial numbers (both from the original post and from the more recent runs) indicate anything other than someone finding a number of runes that are slightly higher than the long-term average over a very small sample size, completely consistent with the way randomness and distributions work. Occam's razor would suggest that "completely normal result, nothing crazy going on" is more likely than "completely normal result, hidden unknown hard-coded secret bonus rune drop parameter found".
"which the data doesn't support" - false statement #1
My whole conclusions were based on the received data. My guess is you just have not read my posts or have not understood them.
"when deliberately underestimating expected rune drops by 8%" - false statement #2
[UPD] Ok, let us see. First, it is not 8% but 7% (if "accuracy and precision are important"): (10.77-10)/10.77 = 7%, if you mean this value. Second, my calculations of IP SC were based on 10.0% rune drop THAT I HAVE OBSERVED for 6,000 IP runs. Thus, there is no manipulation of the obtained data. Third, do the math for theoretical expected values with 10.77% for HRs! For a Pul it will be 2.64 instead of 2.45 (for 6,000 runs). Does such a difference for the smallest HR allow you to accuse an opponent of manipulating the data? I tell you, it is an insult. Even in a soft form that you have chosen.
And, all my reasons why I started this thread were stated several times above. You have the whole right to be skeptical or do not agree with my theory. That is normal for people to have different opinions. You can blame me for not providing 500.000 runs or so that should be statistically enough for seeing the whole picture before writing the OP, but we both know it is impossible for ONE person to do that! So, you prefer that I would NEVER publish my findings because I am unable to prove it. All right, I see your point. But I have another opinion on this subject, and that's why I invite everybody who got interested to participate in finding the truth. It was my choice, and you have to live with that even if you don't like it.
Good luck!
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maareek
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A comment on the data or idea is not the same as a comment on the researcher. The purpose of Fabian's post, from the view of an outsider, was to comment on the situation objectively and give advice to the researcher about the pitfalls exciting data can create instead of as an attack or insult directed at the researcher.
Posting your findings is a good thing. Sparking discussion is a good thing. Giving reasons to test for additional data is a good thing. Nobody wants anyone to avoid doing those things. However, enthusiasm should be tempered with patience. The existence of a Zod pattern in a drop from the chest is enough to spark interest and runs from at least some members of the community, waiting for further data allows a more robust pool of information to gain an understanding from. Your experience doesn't need to be defended or validated, it speaks for itself.
Posting your findings is a good thing. Sparking discussion is a good thing. Giving reasons to test for additional data is a good thing. Nobody wants anyone to avoid doing those things. However, enthusiasm should be tempered with patience. The existence of a Zod pattern in a drop from the chest is enough to spark interest and runs from at least some members of the community, waiting for further data allows a more robust pool of information to gain an understanding from. Your experience doesn't need to be defended or validated, it speaks for itself.
I'll add that since the chests aren't 16-bit the existence of a zod pattern is virtually guaranteed (4 billion drops).
The reason the Act 1-4 superchests are interesting other than their density (like in LK) is that a lower total number of drops (65k) means that variance is much more likely to produce a significantly better or worse rate of HRs than the expected value. For 4 billion drops, even 10 more zods than expected isn't significantly good enough to be worth running. For LK, 11 vs 10 HRs (a difference of only one) is a HUGE deal, and this is the magnitude we're talking about, too. 10-20 HRs is the realm that we're talking about for 1.13 superchests.
The reason the Act 1-4 superchests are interesting other than their density (like in LK) is that a lower total number of drops (65k) means that variance is much more likely to produce a significantly better or worse rate of HRs than the expected value. For 4 billion drops, even 10 more zods than expected isn't significantly good enough to be worth running. For LK, 11 vs 10 HRs (a difference of only one) is a HUGE deal, and this is the magnitude we're talking about, too. 10-20 HRs is the realm that we're talking about for 1.13 superchests.
vm,
I didn't mean to insult you, and I apologize for saying you deliberately underestimated the expected drops if it was truly just a non-deliberate mistake. From reading your posts, at the time it seemed clear to me you understand enough about statistics to know that an "expected" value is a theoretical expectation, and not an empirical estimate, so at the time it seemed clear to me that you chose the incorrect number because it would best agree with your hypothesis. I'm more than happy to concede that's not the case though, and it doesn't change my overall points about the conclusions you draw from your numbers.
I would encourage you to perform some basic statistical testing on these numbers you've obtained; to look at the theoretical drop numbers and your observed drop numbers, and see if they are consistent with each other. I think you will find a very large p-value, which is the equivalent of saying that your results are entirely consistent with the null hypothesis (that is to say, that your results are consistent with the way these chests would behave without an unknown hard-coded secret bonus rune drop parameter).
Even if that p-value was reasonably small, I would still make the Occam's razor point I made in the post above and suggest it doesn't mean much of anything, but that would be an interesting case, and one where more data would definitely be interesting and needed. In either case, I think it would be very interesting to see more data and drop numbers either way, and I think you are quite wrong in your last paragraph to suggest that I'm not interested in that. I love d2 data, as people on this forum who know me will attest to, I'm sure
Edit: I'd be happy to do the statistics test for you if you post all the theoretical drop odds and your empirical results in an easy-to-parse way below.
I didn't mean to insult you, and I apologize for saying you deliberately underestimated the expected drops if it was truly just a non-deliberate mistake. From reading your posts, at the time it seemed clear to me you understand enough about statistics to know that an "expected" value is a theoretical expectation, and not an empirical estimate, so at the time it seemed clear to me that you chose the incorrect number because it would best agree with your hypothesis. I'm more than happy to concede that's not the case though, and it doesn't change my overall points about the conclusions you draw from your numbers.
I would encourage you to perform some basic statistical testing on these numbers you've obtained; to look at the theoretical drop numbers and your observed drop numbers, and see if they are consistent with each other. I think you will find a very large p-value, which is the equivalent of saying that your results are entirely consistent with the null hypothesis (that is to say, that your results are consistent with the way these chests would behave without an unknown hard-coded secret bonus rune drop parameter).
Even if that p-value was reasonably small, I would still make the Occam's razor point I made in the post above and suggest it doesn't mean much of anything, but that would be an interesting case, and one where more data would definitely be interesting and needed. In either case, I think it would be very interesting to see more data and drop numbers either way, and I think you are quite wrong in your last paragraph to suggest that I'm not interested in that. I love d2 data, as people on this forum who know me will attest to, I'm sure
Edit: I'd be happy to do the statistics test for you if you post all the theoretical drop odds and your empirical results in an easy-to-parse way below.
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I took some time off this thread in order to gather more evidence for my theory by doing extra runs. Then, having a decent amount in hand, I could calculate the statistical values as Fabian had suggested.
However, now the whole concept is a subject to change. My recent findings show that the accepted belief that the LK chests are UNIQUE in terms of 16-bit programming is false. In fact, Infernal Pit and Pit of Acheron special chests, that were postulated to have 2\32 = 4.3 billion combinations, also possess the same behavior as LK chests! Moreover, I suggest that ALL chests in D2 including “sparkling” and “super-special” perform a similar model.
Out of 45 total screenshots with HRs I’ve done in both PoA and IP SC areas I found 4 (four) pairs of the same patterns. Obviously, that is improbable for 4 billion combinations, as it was presumed. Actually, even one pair is enough for a proof – that is just not possible to happen.
Here it is:
1. Pul rune, PoA SC, p7
View attachment 12384
View attachment 12385
2. Pul rune, IP SC, p7
View attachment 12382
View attachment 12383
3. Gul rune, IP SC, p7
View attachment 12378
View attachment 12381
4. Gul rune, IP SC, p7
View attachment 12379
View attachment 12380
The main conclusion is that we have a finite amount of patterns (presumably 2\16 = 65,536) for the Infernal Pit (or PoA) Special Chest. Thus, by finding all patterns, as it was done for LK, we can see the whole picture of this place in terms of efficiency for rune hunting. For example, if there would be at least another one Zod pattern – the Infernal Pit should give better chances for finding Zod in game (in general, 1 out of 5170 for a dropped rune), as I have suggested in the title of the OP. By now we already have screenshots of one pattern for Zod and two for Cham.
Other mini-conclusions:
1. PoA and IP chests have different patterns (until proven otherwise). All my experience (around 8K runs in both areas) shows that IP SC is much more profitable than the PoA one.
2. Unque, set, rare, and magic qualities are decided by another mechanism after the pattern is chosen (analogously to LK magic/rare).
3. The quality of an item is preset in the pattern.
4. Etheral/socketed quality is preset in the pattern (one example – bardiche).
Hope, we will eventually find the truth!
However, now the whole concept is a subject to change. My recent findings show that the accepted belief that the LK chests are UNIQUE in terms of 16-bit programming is false. In fact, Infernal Pit and Pit of Acheron special chests, that were postulated to have 2\32 = 4.3 billion combinations, also possess the same behavior as LK chests! Moreover, I suggest that ALL chests in D2 including “sparkling” and “super-special” perform a similar model.
Out of 45 total screenshots with HRs I’ve done in both PoA and IP SC areas I found 4 (four) pairs of the same patterns. Obviously, that is improbable for 4 billion combinations, as it was presumed. Actually, even one pair is enough for a proof – that is just not possible to happen
.Here it is:
1. Pul rune, PoA SC, p7
View attachment 12384
View attachment 12385
2. Pul rune, IP SC, p7
View attachment 12382
View attachment 12383
3. Gul rune, IP SC, p7
View attachment 12378
View attachment 12381
4. Gul rune, IP SC, p7
View attachment 12379
View attachment 12380
The main conclusion is that we have a finite amount of patterns (presumably 2\16 = 65,536) for the Infernal Pit (or PoA) Special Chest. Thus, by finding all patterns, as it was done for LK, we can see the whole picture of this place in terms of efficiency for rune hunting. For example, if there would be at least another one Zod pattern – the Infernal Pit should give better chances for finding Zod in game (in general, 1 out of 5170 for a dropped rune), as I have suggested in the title of the OP. By now we already have screenshots of one pattern for Zod and two for Cham.
Other mini-conclusions:
1. PoA and IP chests have different patterns (until proven otherwise). All my experience (around 8K runs in both areas) shows that IP SC is much more profitable than the PoA one.
2. Unque, set, rare, and magic qualities are decided by another mechanism after the pattern is chosen (analogously to LK magic/rare).
3. The quality of an item is preset in the pattern.
4. Etheral/socketed quality is preset in the pattern (one example – bardiche).
Hope, we will eventually find the truth!
hmm better start up a table and tabulate at least um+. I suspect it's just luck, though and it is 4 billion drops
I will try to show my point not mathematically but from the life perspective.
Jeanne Louise Calment was the oldest person on Earth, she died being over 122 years old. If you calculate how many SECONDS she lived the result will be close to 4 billion. Let us assume that the total amount of seconds of her whole life (days and nights) equals the amount of drops from this chest. Now, what you suggest that if you take RANDOMLY any 45 seconds from her remarkable life (from the first breath to the last moment) and 2 seconds should turn out be the same (I am not even talking about 4 pairs of "coincidence" out of 45, like I have) - that will be just luck???
No! That is just impossible
Jeanne Louise Calment was the oldest person on Earth, she died being over 122 years old. If you calculate how many SECONDS she lived the result will be close to 4 billion. Let us assume that the total amount of seconds of her whole life (days and nights) equals the amount of drops from this chest. Now, what you suggest that if you take RANDOMLY any 45 seconds from her remarkable life (from the first breath to the last moment) and 2 seconds should turn out be the same (I am not even talking about 4 pairs of "coincidence" out of 45, like I have) - that will be just luck???
No! That is just impossible
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Odds of finding pair(s) of matching drops in a pool of 4B drops with 45 samples is ludicrous.
Winning the Powerball is 1:300M not 4B.. Imagine playing 45 Powerball tickets (once per week for 45 weeks), and winning 4 times..
Edit: I guess that isn't fair. Sample size is ~8K runs. Just 45 that have been worth taking notice of..
Edit 2: If we take 8,000 runs and (assuming none were missed), 45 drops included hrs. That gives just over 0.5% rune drop rate. Out of 4B drops, we are looking at 22.5M that would include a hr?
Winning the Powerball is 1:300M not 4B.. Imagine playing 45 Powerball tickets (once per week for 45 weeks), and winning 4 times..
Edit: I guess that isn't fair. Sample size is ~8K runs. Just 45 that have been worth taking notice of..
Edit 2: If we take 8,000 runs and (assuming none were missed), 45 drops included hrs. That gives just over 0.5% rune drop rate. Out of 4B drops, we are looking at 22.5M that would include a hr?
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Sorry, didn't get to finish my thought:
So, let's play with a deck of cards instead. I show you one card, 2-clubs, and then shuffle.
What are your odds of NOT drawing the 2-clubs? 51/52
If we did this again and again 45 times? (51/52)^45 = 0.41
Odds of finding a SINGLE pair of identical results in a deck of cards with 45 attempts is 59%.. Now, imagine a deck with 20M cards, and matching FOUR times?!?
If we are talking about a 64K possible drop pool (assuming the same 0.5% rune rate), then we are looking at ~320 rune patterns. That sounds like a much more realistic number to draw four matching pairs.
So, let's play with a deck of cards instead. I show you one card, 2-clubs, and then shuffle.
What are your odds of NOT drawing the 2-clubs? 51/52
If we did this again and again 45 times? (51/52)^45 = 0.41
Odds of finding a SINGLE pair of identical results in a deck of cards with 45 attempts is 59%.. Now, imagine a deck with 20M cards, and matching FOUR times?!?
If we are talking about a 64K possible drop pool (assuming the same 0.5% rune rate), then we are looking at ~320 rune patterns. That sounds like a much more realistic number to draw four matching pairs.
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As you discover new rune patterns you would increase your odds of finding a pair:
With only one known pattern: 1/320 = 0.3%
With 41 known patterns: 41/320 = 12.8%
@vmiguli - do you have your screenshots numbered? We could see how many patterns you had before making first pair, second pair etc. The frequency should be increasing, and we could make guess at total rune patterns from this info.
With only one known pattern: 1/320 = 0.3%
With 41 known patterns: 41/320 = 12.8%
@vmiguli - do you have your screenshots numbered? We could see how many patterns you had before making first pair, second pair etc. The frequency should be increasing, and we could make guess at total rune patterns from this info.
T72on1
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I completely forgot about this thread, although I have actually leveled a Barb in the past mainly for the purpose of chest running (and to put a great 2/20 Barb circlet to use).
I'll leave the statistics and theorycrafting up to you guys. But I'll start doing some runs from time to time and provide screenshots here for every rune Pul+. @vmiguli I think it's best you add a table to the first post, similar to the one in the LK rune finding thread, which gives an overview of every pattern found, with a link to a post with a screenshot. I'll hopefully be able to provide some of those screenshots.
I'll leave the statistics and theorycrafting up to you guys. But I'll start doing some runs from time to time and provide screenshots here for every rune Pul+. @vmiguli I think it's best you add a table to the first post, similar to the one in the LK rune finding thread, which gives an overview of every pattern found, with a link to a post with a screenshot. I'll hopefully be able to provide some of those screenshots
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T72on1
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Some 60 initial test runs done. First observations:
- 24 sec average runs, but that's with a lot of misclicking (never done 200% fcr, boy that's fast !!) and a horrible 6 - 7 second S&E lag
- 2 set and 1 unique item so far
- hardly any runes, I think 4 in total, all low level
- Barb is perfectly suited for the task. 4600 life + Howl + fcr = win
I'm assuming it's p7 all the way, so how dangerous are those runs in relation to LK for example?
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