As I think I’ve mentioned before, I run a regular D&D game on Sundays. Both I and one of the players are physics graduates, and we have a sort of running joke whereby every time somebody had a run of good or bad luck I’ll say “what are the chances of that happening” and he’ll reply “about one in [probability], assuming they’re independent random events.”
Tamarind has already talked about what a horrid troll-infested hellpit Heroic Gundrak is (seriously Slad’rann *fuck you*). Heroic Gundrak has been the Daily on our server four days running.
The chances of this happening are one in twenty-eight thousand, five hundred and sixty one. There’s thirteen dungeons, so the odds of the same dungeon coming up four times in a row are 13 x 13 x 13 x 13 = 28561
Except of course actually it doens’t work like that. I made the mistake of counting the first occurrance of the dungeon as a one-in-thirteen chance, when in fact it was a one-in-one chance. I only started counting the number of times Heroic Gundrak came up after the first time it came up, so the probability drops to one in two thousand one hundred and ninety seven.
And then of course there’s the large number of servers to take into account. The number of severs is so large that the chances of one of them, at any given time, being in the middle of a long run of identical dailies is actually extremely high.
This gets even more interesting (well, if you find elementary statistics as it relates to independent random events interesting) when you apply it to quest drops.
Suppose you take Repetitive Gathering Quest #247, which requires you to acquire 10 Generic Animal Organs. Suppose these organs have a 50% drop rate. How many Generic Animals do you have to kill to get them?
If you said “twenty” you are about sixty percent right.
On the other hand, it is entirely possible to kill twenty mobs and get precisely no drops. The odds of this happening are extremely low – one in one million, forty eight thousand five hundred and seventy six in fact, but remember that this game has over eleven million players. Every time there’s a quest drop with a 50% drop rate, you’d expect roughly eleven people to kill fully twenty of the damned things without getting a single drop. This is why old-world-style “kill the monkeys for monkey parts” quests have such a poor reputation. There’s so many of the damned things that everybody has had, at least one experience where – seemingly against all probability – a quest item has just plain refused to drop.
I understand that things are currently set up so that the chance of a quest item dropping increases the more mobs you kill without a drop. The thing I find really fascinating about this is that it has the knock-on effect of making quest drops behave the way people intuitively expect random systems to behave when they in fact don’t. Intuitively we assume that “random” means “balanced” but this is untrue – Gundrak, Gundrak, Gundrak, Gundrak is no less probable than any other string of four dailies, just as in a quest you are as likely to get two drops in a row as you are to get a drop immediately following a kill with no drop. What’s interesting is that in the case of quest drops Blizzard is artificially interfering with probabilities, and I can’t help but wonder if dailies will follow suit – if they will, in essence, set them on shuffle so that you get a cycle through every instance before they start repeating.
Obviously some randomness is necessary in a game, but in a game with as many players as WoW, you’ll find that the outliers you get in all large random systems start throwing up serious problems for actual players, and it’s interesting to see the ways Blizzard has reacted to this.
Well, it’s interesting to me, but I’m a math geek.
I understood the first three paragraphs. Yay for me!
All we ever get on Barthilas is Nexus, Azjol Nerub, Nexus, Azjol Nerbub… Halls of Stone.
That used to annoy me. But I concede you have it worse. I wonder if there’s a server out there stuck permanently on Heroic Oculus? That’d be hell.
If we got stuck on Heroic Oculus I’d … well I don’t normally bother with the daily anyway, so it probably wouldn’t affect me at all…
Once you start widening the net to groups of three or four, the chances of getting into a pattern get even higher – particularly once you throw confirmation bias into the mix, you notice things that fit the pattern more than things that don’t.
We are currently having a run of heroic Occulus, I keep meaning to do it to look at the gear scaling of the drakes but I keep finding other things to do (anything else really).
I never ran Oculus before they fixed the scaling, but from what I heard from other guildies who have, things are much better now.
I personally kind of like the instance, but only if I am dpsing. Healing that instance is a bitch.
My server (Bloodhoof US) routinely has the same daily for both heroic and regular every week. If we get lucky it will change. I think we had Oculus as the daily for 2 weeks at one point. Our recent one that we had for 4 days in a row was Old Kingdom.
My guild is now good at running that instance lol
I’ve still not done Oculus, even on normal. I just can’t be fucked to ride dragons. I can pretty safely say I’ll never do Malygos either. As somebody (Shay? Think it was a new rules thing) observed, if those freaking dragons can take the guy out, they don’t need us sitting on them.
I was a math major as well and I have always found the RNG fascinating.
I tell myself that a .1% doesn’t mean that if I kill 1000 then I should have gotten the drop. Because I am well over a thousand Barrens creatures for that stupid Savory Deviate recipe and I refuse to pay the 600g that it is going for on Aerie Peak.
I tell myself that every kill has a .1% chance and that it may never drop for me.
That’s what I tell myself, but it doesn’t stop me from thinking ‘it’s HAS to drop soon’.
I actually don’t have the math-fu necessary to prove this, but some simple “try it with big numbers” tests seem to show that actually the probability of a one-in-n chance coming up after n attempts winds up at a relatively stable 64% (1 – ((n-1)/n)^n).
It’s an interesting gap between what’s intuitive (if it’s a one-in-x chance, it should be very likely to come up after x attempts) and the mathematical reality, which is that it’s about a two-thirds chance, which of course means that killing a thousand mobs in the Barrens is a very poor way to get Savory Deviate Delight.
I understood the first three paragraphs. Yay for me!
All we ever get on Barthilas is Nexus, Azjol Nerub, Nexus, Azjol Nerbub… Halls of Stone.
That used to annoy me. But I concede you have it worse. I wonder if there's a server out there stuck permanently on Heroic Oculus? That'd be hell.
We are currently having a run of heroic Occulus, I keep meaning to do it to look at the gear scaling of the drakes but I keep finding other things to do (anything else really).
I think the worst part about killing all those extra mobs on a “collect 10 legs/eyes/ears” quest is knowing that somewhere out there is some git that only had to kill 11 mobs to get his quest done when 3 hours later I’m still killing the buggers for the last one.
Yeah, it’s infuriating. Tam has insane luck with drops – he got his Aged Gorilla sinew on his first kill.
A really good example of the RNG doing bad things to good players was the Valentine’s day event. I can’t quite remember the details, but one of the achievements required getting bags of candy hearts. There were something like 8 different kinds of hearts and you had to get them all to get the achievement. But there were enough passes through the RNG to get the candy that some people never got them all before the event was over. I thought this was one case where the Blizz engineers simply hadn’t considered the implications of the RNG when the wrote their code. They figured out what probabilities to assign each step along the way in order to guarantee that most people would have to spend at least X amount of time working on it. But the outliers were the people who got all the candies almost immediately, and the people who never got all the candies.
Yeah, that was a good example. Again it’s easy to see why they didn’t think of it – there’s only eight candy types so you’d expect people to get most of them within eight or ten pulls, but again some people will pull hundreds of times and not get that last damned candy.
I was a math major as well and I have always found the RNG fascinating.
I tell myself that a .1% doesn't mean that if I kill 1000 then I should have gotten the drop. Because I am well over a thousand Barrens creatures for that stupid Savory Deviate recipe and I refuse to pay the 600g that it is going for on Aerie Peak.
I tell myself that every kill has a .1% chance and that it may never drop for me.
That's what I tell myself, but it doesn't stop me from thinking 'it's HAS to drop soon'.
I never ran Oculus before they fixed the scaling, but from what I heard from other guildies who have, things are much better now.
I personally kind of like the instance, but only if I am dpsing. Healing that instance is a bitch.
My server (Bloodhoof US) routinely has the same daily for both heroic and regular every week. If we get lucky it will change. I think we had Oculus as the daily for 2 weeks at one point. Our recent one that we had for 4 days in a row was Old Kingdom.
My guild is now good at running that instance lol
I think the worst part about killing all those extra mobs on a "collect 10 legs/eyes/ears" quest is knowing that somewhere out there is some git that only had to kill 11 mobs to get his quest done when 3 hours later I'm still killing the buggers for the last one.
A really good example of the RNG doing bad things to good players was the Valentine's day event. I can't quite remember the details, but one of the achievements required getting bags of candy hearts. There were something like 8 different kinds of hearts and you had to get them all to get the achievement. But there were enough passes through the RNG to get the candy that some people never got them all before the event was over. I thought this was one case where the Blizz engineers simply hadn't considered the implications of the RNG when the wrote their code. They figured out what probabilities to assign each step along the way in order to guarantee that most people would have to spend at least X amount of time working on it. But the outliers were the people who got all the candies almost immediately, and the people who never got all the candies.
I play in an Exalted game every Saturday. We’re, like, kindred! ~_^
But you’re not on Archimonde, are you? Because we’ve had Gundrak for like three days in a row. Yesterday’s AN broke that streak. Strange how that all happens, eh?
No, we’re on Emerald Dream.
I’ve not played Exalted, but I’ve heard good things about it.
I play in an Exalted game every Saturday. We're, like, kindred! ~_^
But you're not on Archimonde, are you? Because we've had Gundrak for like three days in a row. Yesterday's AN broke that streak. Strange how that all happens, eh?
If we got stuck on Heroic Oculus I'd … well I don't normally bother with the daily anyway, so it probably wouldn't affect me at all…
Once you start widening the net to groups of three or four, the chances of getting into a pattern get even higher – particularly once you throw confirmation bias into the mix, you notice things that fit the pattern more than things that don't.
I've still not done Oculus, even on normal. I just can't be fucked to ride dragons. I can pretty safely say I'll never do Malygos either. As somebody (Shay? Think it was a new rules thing) observed, if those freaking dragons can take the guy out, they don't need us sitting on them.
I actually don't have the math-fu necessary to prove this, but some simple "try it with big numbers" tests seem to show that actually the probability of a one-in-n chance coming up after n attempts winds up at a relatively stable 64% (1 – ((n-1)/n)^n).
It's an interesting gap between what's intuitive (if it's a one-in-x chance, it should be very likely to come up after x attempts) and the mathematical reality, which is that it's about a two-thirds chance, which of course means that killing a thousand mobs in the Barrens is a very poor way to get Savory Deviate Delight.
Yeah, it's infuriating. Tam has insane luck with drops – he got his Aged Gorilla sinew on his first kill.
Yeah, that was a good example. Again it's easy to see why they didn't think of it – there's only eight candy types so you'd expect people to get most of them within eight or ten pulls, but again some people will pull hundreds of times and not get that last damned candy.
No, we're on Emerald Dream.
I've not played Exalted, but I've heard good things about it.
“Lotteries are taxes for stupid people” was a favourite saying of one of my math teachers at uni, meaning that the chance of actually winning big was so infinitesimally small that you might as well just give the money you spent on lottery tickets of any kind to the government directly.
But some people do win big, don’t they, and that is why most of us do buy a ticket now and again.
And I am still hoping that the gods of dice and statistics will be benevolent and let me get my Raven mount from Sethekk Halls soon!
I always think that the “taxes for stupid people” description of the lottery actually misses a rather important step in the understanding of economics.
While from a purely statistical standpoint it’s true that the expected return on a £1 lottery ticket is significantly less than one pound (although not as much less as you might think – the average jackpot is several million pounds, so your expected return winds up being about 50p) people forget that the value of money doesn’t scale linearly.
For most people living above the poverty line, one pound has effectively no value. Buying a lottery ticket incurs no opportunity cost – it’s not like you’ll turn around later that day and say “crap, if I hadn’t bought that lottery ticket I’d be able to afford an extra chocolate bar”.
From an economic perspective, buying a lottery ticket is an extraordinarily good idea. You’re wagering what is effectively zero reduction in your present quality of life for a non-zero chance of a large improvement in your future quality of life.
Sorry, this kind of thing really fascinates me, so I tend to ramble on about it.
There is another saying, the one about that it’s 50% chance to win in any lottery, because, you know, either you win or you don’t.
And you should never underestimate the value of an extra chocolate bar in the afternoon!
"Lotteries are taxes for stupid people" was a favourite saying of one of my math teachers at uni, meaning that the chance of actually winning big was so infinitesimally small that you might as well just give the money you spent on lottery tickets of any kind to the government directly.
But some people do win big, don't they, and that is why most of us do buy a ticket now and again.
And I am still hoping that the gods of dice and statistics will be benevolent and let me get my Raven mount from Sethekk Halls soon!
I always think that the "taxes for stupid people" description of the lottery actually misses a rather important step in the understanding of economics.
While from a purely statistical standpoint it's true that the expected return on a £1 lottery ticket is significantly less than one pound (although not as much less as you might think – the average jackpot is several million pounds, so your expected return winds up being about 50p) people forget that the value of money doesn't scale linearly.
For most people living above the poverty line, one pound has effectively no value. Buying a lottery ticket incurs no opportunity cost – it's not like you'll turn around later that day and say "crap, if I hadn't bought that lottery ticket I'd be able to afford an extra chocolate bar".
From an economic perspective, buying a lottery ticket is an extraordinarily good idea. You're wagering what is effectively zero reduction in your present quality of life for a non-zero chance of a large improvement in your future quality of life.
Sorry, this kind of thing really fascinates me, so I tend to ramble on about it.
There is another saying, the one about that it's 50% chance to win in any lottery, because, you know, either you win or you don't.
And you should never underestimate the value of an extra chocolate bar in the afternoon!
There is another saying, the one about that it's 50% chance to win in any lottery, because, you know, either you win or you don't.
And you should never underestimate the value of an extra chocolate bar in the afternoon!
There is another saying, the one about that it's 50% chance to win in any lottery, because, you know, either you win or you don't.
And you should never underestimate the value of an extra chocolate bar in the afternoon!
There is another saying, the one about that it's 50% chance to win in any lottery, because, you know, either you win or you don't.
And you should never underestimate the value of an extra chocolate bar in the afternoon!
On a more serious note, and after having thought about it a bit, there is the question of when byuing a lottery ticket ceases to be a good idea and becomes something of a “tax for stupid people”. I think that is when you don’t play occasionally only, like once or twice a month or less.
If you play for say 10 pounds a week, with a standing weekly subscriptions or similar, you are not gambling zero for not-zero. 10 pounds a week adds up to 520 pounds a year, which is a not too shabby sum of money for most people I think.
On a more serious note, and after having thought about it a bit, there is the question of when byuing a lottery ticket ceases to be a good idea and becomes something of a "tax for stupid people". I think that is when you don't play occasionally only, like once or twice a month or less.
If you play for say 10 pounds a week, with a standing weekly subscriptions or similar, you are not gambling zero for not-zero. 10 pounds a week adds up to 520 pounds a year, which is a not too shabby sum of money for most people I think.