...I knew this would happen when DNA mentioned the Monty Hall problem...
At least the Monty Hall discussion is friendly learning and not overly laden by conspiracy theories with no support. So that's pretty cool.
"I got 5 goats in a row, Monty is definitely rigging the pulls. That player who spent pulled the car first time! I heard that Monty took out a patent that alters the odds of pulling the car depending on how much you spend.
When you guys open your door do you spin or pop it? I half open, then shut it, then open again and twist the doorknob a few times and then open it. It definitely gets me better odds, even if people say it makes no difference."
I pick one, Another door is opened to be nothing I can stay or switch.
Both options are 50/50 now. Where am I wrong?
If someone replies to this please @SkyLord7000 I don’t wanna miss this.
your odds are locked in once you choose your first door. It’s 1/3 then, and removing the other option doesn’t suddenly make it 50/50 just because there’s only two options now.
To demonstrate this, imagine there were 100 doors, 1 with the prize and 99 with nothing. You randomly pick one, the host then opens 98 doors showing you nothing. He then asks you whether you want to swap.
The chances of you randomly picking the one door with the prize out of 100 is so low, that the host revealing 98 doors without a prize means that the final door he didn’t reveal likely has the prize in it.
The odds were locked in at 1% chance when you selected the first door. So the odds now that the other door contains the prize is 99%. Even though there are two options, it’s not 50/50.
I’m still confused, with 98 empty doors you would have a 50 / 50 shot if you hadn’t chosen prior. So why would choosing something in an event unrelated change the odds.
Tried to italic the parts that confused me the most.
The simplest way to explain this I think is to ask a different question. Suppose there are 100 boxes, and Monty is going to open 98 empty boxes. Do you want to pick *before* he does that, or *after* he does that?
Well, obviously you want to pick after, right? So your intuition is telling you that Monty opening those boxes gives you an advantage. But if the odds are 50% whether you pick before he opens or after he opens, there's no advantage. So your odds of picking the right box *before* he opens the other boxes must be low, and stay low no matter what he does after you pick.
When Monty opens boxes, he's giving you information. He's telling you where the prize is not. That's very valuable information, but that information is only useful if you know it before you pick. Knowing it after you pick cannot help you. Switching choices in effect is picking after he opens. Switching boxes *before* he opens offers no advantage. Your first pick is just as likely to be the right one as your second pick. But switching *after* he opens offers a huge advantage, because now you *know* where the prize is definitely not. The odds of you picking one of those other 98 boxes incorrectly is zero, because of course you aren't going to pick those empty boxes.
popped 8 crystals 3 of those were white mags 3*... the odds of that per crystals drop rate is insane and not sure how its possible. people that understand basic math should understand how it shouldnt be happening this often in game
to me, i see at least 2x 3x dupe pulls in stacks of 10 popped crystals, every other week. in the alliance feed of crystal openings a lot more often. even to the point where 2 separate accounts pull the same champ back to back of the same star lvl. knowing that i wouldnt put it past kabam to probably just being another bug with coding and people pulling duplicates within the same stacks.
Except the pool of champs is smaller than dates in the year, so the probability of finding a pair will be even higher in a given group size.
Dude,brithday prolem is so cool
If you want a cool one, @danielmath here's another one for the honors class. This is one where I think either you know it, or you don't. I don't think I've met anyone who's actually got the right answer directly through deduction or calculation, unless they were previously exposed to the technique. Suppose you start opening crystals, one after the other. How long before you get three in a row?
Let's simplify a bit. Let's assume the crystal contains one of 250 options, equally likely. How many crystals do you have to open before you get three in a row of identical choices? For the honors class, let's simplify even further. Suppose we're flipping a coin. How many flips before we get three heads in a row (always assuming a 50/50 coin).
The naïve calculation would say: the odds of three coins being all heads is one in eight. So the average number of flips to get three heads in a row is about 24 = three flips times eight attempts.
This number is off by about a factor of two. If someone in the honors class gets this one right, they get an official DNA No Prize, because when I learned this one back in high school it was a revelation (it was a math competition, by the way).
Hint: math students are first introduced to the guiding principle for solving this problem when they learn how to sum infinite convergent series, or else they learn it directly when they take an advanced probability class.
If you want a cool one, @danielmath here's another one for the honors class. This is one where I think either you know it, or you don't. I don't think I've met anyone who's actually got the right answer directly through deduction or calculation, unless they were previously exposed to the technique. Suppose you start opening crystals, one after the other. How long before you get three in a row?
Let's simplify a bit. Let's assume the crystal contains one of 250 options, equally likely. How many crystals do you have to open before you get three in a row of identical choices? For the honors class, let's simplify even further. Suppose we're flipping a coin. How many flips before we get three heads in a row (always assuming a 50/50 coin).
The naïve calculation would say: the odds of three coins being all heads is one in eight. So the average number of flips to get three heads in a row is about 24 = three flips times eight attempts.
This number is off by about a factor of two. If someone in the honors class gets this one right, they get an official DNA No Prize, because when I learned this one back in high school it was a revelation (it was a math competition, by the way).
Hint: math students are first introduced to the guiding principle for solving this problem when they learn how to sum infinite convergent series, or else they learn it directly when they take an advanced probability class.
I don't want to ruin the math for whomever comes along next, so I'll just say that it's about 15.69 alots.
The maths is beside the point, the point is that each crystal opening SHOULD have the same chance or probability as the previous opening. Much like lotto or powerball. However, if I'm not mistaken are there not some champs that are designed to be more rare? ( correct me if I'm wrong on that). Also, RNGs really aren't truly random. They still run on code written by someone. I have had a couple of the same openings in a row but have thought no more into it other than its a coincidence (annoying, but still a coincidence)
I don't want to ruin the math for whomever comes along next, so I'll just say that it's about 15.69 alots.
Hang on, I believe I just committed the same error that we've been chastising Glads for, and calculated the probability of getting 3 Hercs in a row, not of getting 3 of any champ in a row. It should be 62.75 much smaller denominations.
The maths is beside the point, the point is that each crystal opening SHOULD have the same chance or probability as the previous opening. Much like lotto or powerball. However, if I'm not mistaken are there not some champs that are designed to be more rare? ( correct me if I'm wrong on that). Also, RNGs really aren't truly random. They still run on code written by someone. I have had a couple of the same openings in a row but have thought no more into it other than its a coincidence (annoying, but still a coincidence)
Each opening does have the same probability as the previous opening. If certain champs are weighted, it's never been demonstrated, at least as far as I know. If it has been demonstrated, post it up. Read back to DNA's post on RNG implementation. It's not an area I know a ton about, but my understanding is very much that the belief that "RNG tools aren't truly random" are significantly overblown. They're random enough to not make a material difference in our situation.
Also, I meant that I didn't want to spoil the math for others who wanted to try DNA's problem above about how many openings/coin flips you'd need to get same result 3 times. That's not really the same as calculating the odds of a dupe.
The maths is beside the point, the point is that each crystal opening SHOULD have the same chance or probability as the previous opening. Much like lotto or powerball. However, if I'm not mistaken are there not some champs that are designed to be more rare? ( correct me if I'm wrong on that). Also, RNGs really aren't truly random. They still run on code written by someone. I have had a couple of the same openings in a row but have thought no more into it other than its a coincidence (annoying, but still a coincidence)
Some rarities (i.e. star rating) have different chance to drop in crystals with multiple rarities. Featured crystals can have specific featured champions with higher drop odds than other champs. Besides those difference and any explicitly listed in the crystals, there is no weighting towards or away from certain champions, even though there are persistent conspiracy theories that make this claim. To the extent that they can be tested at all, all such claims have either been demonstrated to be false, or demonstrated to be so weak of an effect that no human being could possibly see it.
In other words, while there's no way to prove that every champion has *exactly* the same chance to drop, it is possible to demonstrate that a difference big enough for a human being to just spot by opening tens or hundreds of crystals cannot evade statistical testing, and thus cannot exist.
The maths is beside the point, the point is that each crystal opening SHOULD have the same chance or probability as the previous opening. Much like lotto or powerball. However, if I'm not mistaken are there not some champs that are designed to be more rare? ( correct me if I'm wrong on that). Also, RNGs really aren't truly random. They still run on code written by someone. I have had a couple of the same openings in a row but have thought no more into it other than its a coincidence (annoying, but still a coincidence)
Each opening does have the same probability as the previous opening. If certain champs are weighted, it's never been demonstrated, at least as far as I know. If it has been demonstrated, post it up. Read back to DNA's post on RNG implementation. It's not an area I know a ton about, but my understanding is very much that the belief that "RNG tools aren't truly random" are significantly overblown. They're random enough to not make a material difference in our situation.
Also, I meant that I didn't want to spoil the math for others who wanted to try DNA's problem above about how many openings/coin flips you'd need to get same result 3 times. That's not really the same as calculating the odds of a dupe.
Sorry, my comment about the maths was more directed at the thread as a whole. I'm no mathematician and the maths on probability and statistics makes my head explode. It is interesting I guess to try and work out that the probability of getting a 6* magneto (for example) 2 or 3 times in a row but it should be no more than that. If the OP is spending all their time on trying to this then their really not enjoying the game in the spirit in which it was intended. My comment about rarer champs was hearsay as much as anything. I thought I'd read it somewhere on the forums. There is still the fact that not all champs are available on the basic crystal and some such as Kang, Thanos and Weapon x aren't available in crystals at all. So i guess that also needs to be taken into account.
Comments
When you guys open your door do you spin or pop it? I half open, then shut it, then open again and twist the doorknob a few times and then open it. It definitely gets me better odds, even if people say it makes no difference."
Well, obviously you want to pick after, right? So your intuition is telling you that Monty opening those boxes gives you an advantage. But if the odds are 50% whether you pick before he opens or after he opens, there's no advantage. So your odds of picking the right box *before* he opens the other boxes must be low, and stay low no matter what he does after you pick.
When Monty opens boxes, he's giving you information. He's telling you where the prize is not. That's very valuable information, but that information is only useful if you know it before you pick. Knowing it after you pick cannot help you. Switching choices in effect is picking after he opens. Switching boxes *before* he opens offers no advantage. Your first pick is just as likely to be the right one as your second pick. But switching *after* he opens offers a huge advantage, because now you *know* where the prize is definitely not. The odds of you picking one of those other 98 boxes incorrectly is zero, because of course you aren't going to pick those empty boxes.
Let's simplify a bit. Let's assume the crystal contains one of 250 options, equally likely. How many crystals do you have to open before you get three in a row of identical choices? For the honors class, let's simplify even further. Suppose we're flipping a coin. How many flips before we get three heads in a row (always assuming a 50/50 coin).
The naïve calculation would say: the odds of three coins being all heads is one in eight. So the average number of flips to get three heads in a row is about 24 = three flips times eight attempts.
This number is off by about a factor of two. If someone in the honors class gets this one right, they get an official DNA No Prize, because when I learned this one back in high school it was a revelation (it was a math competition, by the way).
Hint: math students are first introduced to the guiding principle for solving this problem when they learn how to sum infinite convergent series, or else they learn it directly when they take an advanced probability class.
The use of the non-existent word “consequentive” jars my eyes to the point of nausea every time I see it.
Dr. Zola
Also, I meant that I didn't want to spoil the math for others who wanted to try DNA's problem above about how many openings/coin flips you'd need to get same result 3 times. That's not really the same as calculating the odds of a dupe.
In other words, while there's no way to prove that every champion has *exactly* the same chance to drop, it is possible to demonstrate that a difference big enough for a human being to just spot by opening tens or hundreds of crystals cannot evade statistical testing, and thus cannot exist.
My comment about rarer champs was hearsay as much as anything. I thought I'd read it somewhere on the forums. There is still the fact that not all champs are available on the basic crystal and some such as Kang, Thanos and Weapon x aren't available in crystals at all. So i guess that also needs to be taken into account.