N/A
I did get a lot of Assassin's Vambraces in my last game, I mean like three or four of the darned things in the first 100 turns. Random number generator issues are notoriously hard to prove though, people forget that rolling 1, 1, 1 on three dice is not impossible, just unlikely. 1/216 is not even close to "never".
I would be curious to understand the mechanics for loot drops in Legendary Heroes, you do seem to get a lot of the same stuff sometimes. It's possible something is pre-seeded, or the same random number affects a lot of different results. It may just be that there is a relatively small list of "Uncommon armour", so if that was the loot drop you kept getting then chances of a duplicate or three are quite high.
It could just be observers' bias; it's doubtful that you've got a record of loot drops from *every* game that you've played, just the ones that seemed unusual.
That said, in the current game I'm playing I just got 5 weathered shields (3 in a row, even) from the early goodie huts...but I don't really recall any particularly unexpected strings of duplicate items from earlier games.
This has been a problem for me for several versions now. I'm still on 1.4, but I find that quite often in a game I will get 3-5 copies of a random item. I don't know if that's because the pool of available items is so small, or if it's a seed issue with the RNG, but it's persistent enough from game to game that I'd like to see it get addressed.
gs
Agreed with Primal_Savage. I've noticed this too. Each play session is a different item, but I get multiple copies of it to the point where something doesn't feel right about the randomizer.
Yes, this issue has persisted since at least 1.1.
I think the problem is that there isn't a lot of different items in each category as Merlinme said.
Major issue imo. Landmarks and monsters also tend to be distributed in pairs.
I'd say there is something definitely wrong with the randomizer and it isn't from lack of items. Take for example the uncommon drops, using the search function in the core files for armor, weapons and items, there are respectively 19, 61 and 44 matches for a total of 124 items. And this is without adding DLC or mod items. Recently I found 3 legendary broadswords (uncommon item) in the space of about 20 drops. In another game, there was a sudden shower of rusty armors (also an uncommon item) and several of the AI players were wearing them too. These are just examples, each game yields such repeat drops. So yes, in theory, it is possible to get four copies of one of these items in a single game but seeing this phenomenon in each game simply defies the laws of probability. It's four times one chance in 124 out of what? 30 or 40 uncommon drops on a huge map? I know there are different "likelihood" definitions, namely 200 or 250, but these don't seem to bear any significance for these repeat items.So yes, I believe the dice are loaded
Probability is confusing. If I have three dice, the chances of rolling a 1, a 1, and then a 2 are 1/216. But if I don't care about the order as long as I get a 1, a 1 and a 2 (so in other words 112 and 121 and 211 are also valid) then the chances treble to 3/216.
If there are 19 Uncommon armour drops and I have two drops, what are the chances both will be Assassin's Vambraces? 1/361. But if I have three drops, what are the chances at least two will be Assassin's Vambraces?
19 / 19/ any
19/ any/ 19
any/ 19/ 19 are all valid.
In other words, (1/19 * 1/19 * 1/1) + (1/19 * 1/1 * 1/19) + (1/1 * 1/19 * 1/19). So my chances are actually 3/ 361 (assuming my maths is correct.).
If I have four drops, what are the chances at least two will be Assassin's Vambraces?
19 / 19/ any/ any
19/ any/ 19/ any
any/ 19/ 19 / any
any/ 19/ any/ 19
19/ any/ any/ 19
any/ any/ 19/ 19
So I reckon that's 6/361. Still doesn't seem very likely. But we've been looking for a specific item; what are the chances of any item showing up at least twice in four drops?
In other words it doesn't matter what the first drop is; what we're interested in is whether there will be a duplicate in the next three drops.
What are the chances there will be no duplicate in the next three drops? On the second drop there are 18 items it can be which are not duplicates, then there are 17 items it can be which are not duplicates, and finally there are 16 items which are not duplicates to any of the previous three items. (18/19)*(17/19)*(16/19)=4896/6859. So the chance that there will be a drop of two identical items is (6859 - 4896) / 6859, i.e. 1963 / 6859. Or to put it another way, about 29%. Doesn't seem so unlikely now, does it? In fact if I played two games my chance of getting two duplicate Uncommon armours in the first four drops in either game are now slightly better than half (1-(0.71*0.71), i.e. 51%.
I should put in a disclaimer that I am not a mathematician and I do make mistakes. However I'm fairly confident in my broad point that the chances of getting a duplicate in something over a certain number of drops are actually quite high if there were only 19 items to choose from to start with. I don't therefore think there is a problem with the random number generator. I think the solution (if it really bothers people that much) would be to add more items. If there were, say, 30 uncommon pieces of armour then I believe the chance of getting two duplicates over four drops would be about 10% rather than about 29%. Each of those items would need artwork and a description though, so quite a lot of work for something which is mainly an illusion.
I was basing my calculations on this. If I got four Uncommon armour drops, what are the chances two would be duplicates? The example given was actually any four out of twenty (when the sample is all uncommon items, i.e. 124), you can work that out but it's a lot harder. Intuitively I would actually expect four out of twenty to be more likely than two out of four, even with the increased sample size, but I'd have to work it out. Feel free to work out the maths for larger numbers!
But the point remains that you can get duplicates quite quickly even if the sample size is large. It's the birthday problem: from a sample of 365 days, how many "drops" do you have to get before you will probably have two people sharing the same birthday?
The answer is 23, which is far lower than most people guess. https://en.wikipedia.org/wiki/Birthday_problem#Calculating_the_probability
Regarless, the issue is you can get multiple duplicates which shouln't happen.
I would like to see code built into the randomizer that says once an item has been been dropped, it is excluded from the remaining list of available drops for the remainder of the game.
You don't want a randomizer then, you want want a shuffle algorithm, which is entirely different.
I strongly disagree. This would also greatly skew the rarity weighting factors in the items lists, since after each "find", the chance for every other type of item would be greatly boosted. Personally, the idea that you'll only see certain items once in a blue moon is kind of appealing.
Besides, no one has actually confirmed a random number generator bug yet - it's merely suspected.
Whatever you call it, there needs to be a way to prevent duplicates. As for increasing the chance for the remaining items to be found..For that there is another simple solution, SD should significantly increase the number of magic items available for the drop. 32 additional items apparently wasn't enough to minimize the chance of getting multiple duplicates.
Given the relatively low number of items, I'm dubious whether there is a bug. This is exactly the same as the itunes shuffle "problem", and Apple came up with various solutions, including (for example) "without repetitions". "Without repetitions" is not random at all, but it may be more what people expect.
So two solutions spring to mind for legendary heroes:
1: add more items;
2: add a world option for "no repetitions" for loot drops.
Erm. I can't remember maths I never had, like I said I'm not a mathematician. It looks a bit simple to me though. See;
http://math.stackexchange.com/questions/25876/probability-of-3-people-in-a-room-of-30-having-the-same-birthday
Given that one answer uses an approximation and the other refers to an academic paper, I don't think it's that simple a problem to solve.
One of the answers suggests that the chances of having three identical drops out of 100 drops from a universe of 365 is 70%, so your answer sounds low to me. If you actually understand what a Poisson approximation is then maybe you can use it to get the correct answer with our actual problem, i.e. four identical drops out of 20 with a universe of 124 (or five identical drops out of 100 with a universe of 124).
The joys of probability distributions... from my memory on the matter you have to ensure what you are considering does in fact satisfy the conditions of the particular distribution.
The birthday problem does in fact create an interesting example for this particular problem. The binomial distribution leads to a miss conception here, when you say 5 identical items, you are speaking about getting 5 of the same thing, not 5 of exactly described one particular item.
Take the birthday problem the question what is the probability that 3 people have the birthday June 9. It is asking what is the probability that 3 people have the same birthday.
The binomial distribution is correct, if you want to calculate what is the probability one gets Assassin Vambraces. The real question is what is the probability that you get 5 of the exact same item. After 20 tries (suppose you haven't got the same item), but the next 80 items need to duplicate at least these first 20, not a specific one of the first twenty items. This is where the probability game gets interesting.
In the process, I'm not sure exactly how the random generator chooses items or if there is a real problem in the first place. If they let me see the algorithm they use, I'd be glad to do some mathematical analysis on it and see if it does produce cluster points, but my time is limited in that regard.
Yes, I think that's what I was trying to get at. It's the point that in my example above, assuming my maths is correct the chance of getting two Assassin's Vambraces (i.e. one specified piece of armour) in four drops is only 6/361. However the chances of getting any two identical items in four drops is more like 29%.
With many drops and a specified number of duplicates, the problem gets very hard, but the principle remains that it's higher than people generally think. You are looking at the end result, e.g. four Assassin's Vambraces out of eight drops, but you would have found it equally odd if the game gave you four Weathered Shields (or whatever) out of eight drops. So it's the example where we're looking for any combination of four, we're not looking specifically for the example where we got four Assassin's Vambraces.
For five out of 100 you have the combination
1, 1, 1, 1, 1, (95 other numbers)
1, any, 1, 1, 1, 1 (95 other numbers) etc.
And then
any, 1, 1, 1, 1, 1, (94 other numbers)
etc.
"At least" is important, because if you calculate the chances of getting exactly four more drops of the first item in the next 99 drops you will get too low a probability. Getting 100 identical drops is a combination which matches "at least four matching the first drop".
It might be possible to write a computer program to do a brute force calculation of the combinations, assuming you could specify the problem correctly.
The web page which uses a Poisson approximation states that for three people out of 25 to share a birthday the chance is about 3%, but for three people out of 100 to share a birthday the chance is about 70%. What I take from this is that as you increase the number of drops the number of possible combinations increases massively; so if you increase the number of drops from 25 to 100, the chance of three duplicates is not quadruple, it goes up by 23 times.
If you apply this to the game, with a universe of 124 rather than 365, then I personally expect the chances of getting five drops to be quite high, perhaps even over 50% for 100 drops.
I've had a stab working out the Poisson approximation with a friend, assuming our maths is correct I believe the chance to get five duplicates out of 124 items with 100 drops is approximately 27%.
The chance of getting four identical drops out of 124 items with 20 drops is approximately 0.25%. The chance passes 50% after about 77 drops.
The problem by just multiplying by 124, you are making the assumption that the events are disjoint, which they are not disjoint. You are comparing a 124 different games where you would get 1 item 5 times. This is not the calculation you are trying to make.
For example, what is the probability you get a 4 duplicate items after 124 pick-ups.
Let us compute...
n = 124
k = 4
p = 1/124
Thus, the probability by the binomial distribution, (the probability of getting 4 of exactly the same item after 124 treasure pick-ups) would be roughly 1.5 percent.
Multiply this by 124 then we see that the probability of this occurring is 186%...
But probability can never be more than 100% and therefore, the formula you are using is incorrect. I've not done probability distributions in awhile and I'd have to look up the correct distribution for this problem. But as indicated before it may be a Poisson Distribution. If we avoid these predetermined formulas, we can come up with the direct calculation for the problem. But it may require some in-depth mathematics.
There's always the possibility that something in the game is not working as intended. I remember a while back there was a problem with Shattered Statue being a very common "loot" type, and there were only a few drops you got from it, e.g. Stone Mace, so the chances of getting lots of Stone Maces were actually quite high. I've yet to see anything to persuade me that what has been seen in the current game is not within the realms of normal probability though.
I don't remember seeing five drops of the same thing. I do remember seeing four duplicates, but the chances of that are above 50% for 77 drops with a universe of 124 items. Another problem is that we tend to remember the game where we got four duplicates in the first 20 drops, not so much the ten games where that didn't happen; and then there's lack of precision in what exactly we saw anyway. Was it really 25 drops rather than 20? Because the chances of getting 4 duplicates are a lot higher for 25 drops than 20 drops, not just a bit higher.
Problems do come up with incorrectly generated random numbers, but a lot less than people think they see them. Probability is not intuitive, especially as the numbers become large. In particular, duplicates happen a lot more often than people expect.
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