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The probability of 20 heads, then 1 tail is 0.5^20 × 0.5 = 0.5^21
The probability of 20 heads, then 1 head is 0.5^20 × 0.5 = 0.5^21
The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152. When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail. These two outcomes are equally as likely as any of the other combinations that can be obtained from 21 flips of a coin. All of the 21-flip combinations will have probabilities equal to 0.5^21, or 1 in 2,097,152. Assuming that a change in the probability will occur as a result of the outcome of prior flips is incorrect because every outcome of a 21-flip sequence is as likely as the other outcomes. In accordance with Bayes' theorem, the likely outcome of each flip is the probability of the fair coin, which is 1/2.
A friendly advice to all people like OP who can't understand this (which is perfectly fine, understanding probabilities isn't for everybody, it isn't an intuitive science) : never ever set foot in a casino, you risk losing all your money to gambler's fallacy.
yeah i'm learning about your ignorance of gambler's fallacy, and it's glorious
some good end-game content right here, keep it up please
Yeah that is big issue games RNG are known to be prone to all kinds of stuff. Yeah loot tables are pretty common way to save on system resouces.
I mean you can't really teach someone who's math level is primary school.
You are calculating joint probability calculation and not cumulative. In dumber terms sequencing of the prediction of a series that are independent. It's not even the same math problem. Also your math is incorrect.
The odds of what you said would be 4.768x10(to the power of -7) not 0.521.
You're not even remotely correct with your math.
https://study.com/learn/lesson/joint-probability-formula-examples.html#:~:text=Joint%20probability%20is%20the%20product,happening%20at%20the%20same%20time.
You are victim of gambler's fallacy, everything is explained in my post, including your mistake (literally a copy pasta of the gambler's fallacy demo, which is why a fair coin is used).
This isn't verbal jousting, simply verifiable facts. You could argue that you don't believe the 20% drop rate and you would have a point (i hear the company is known to lie on those) but saying that a coin toss is influenced by previous coin tosses is just plain wrong, it isn't debatable.
but whatever lmao.
There is a simple to use calculator repeatedly presented that explains how it works. I don't know why it's so difficult to use: https://www.danielsoper.com/statcalc/calculator.aspx?id=71
It literally can not be dumbed down further than a simple to use calculator.
Here's a few in case you think it's some weird conspiracy or hoax calculator that I some how made:
What is Cumulative Binomial Probability?
Cumulative Binomial Probability refers to the probability of achieving a certain number of successes or fewer in a given number of independent trials, each with the same probability of success. It is calculated using the binomial distribution, which is a probability distribution that describes the number of successes in a fixed number of independent trials. Cumulative binomial probability is useful in various fields, including biology, psychology, and finance, to name a few.
https://z-table.com/binomial-probability-calculator.html
https://www.gigacalculator.com/calculators/binomial-probability-calculator.php
I want to point out I didn't invent this math in this world. Johann Bernoulli did: https://en.wikipedia.org/wiki/Johann_Bernoulli
You can ask him about it but he's been dead for hundreds of years or you could go to college or you could learn it here: https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/binomial-mean-standard-dev-formulas/v/bernoulli-distribution-mean-and-variance-formulas
Everyone's allergic to just learn and given you guys are allergic to effort I'm not sure why you're still here pushing primary school math.
Lying about lootboxes yes, that you had to pay for, not drops from mobs. Not excusing Nexon, but the reason why they eventually got caught, is because things that were supposed to drop, did not drop, ever. However, with this game so far, everything has been dropping in spec.
After 5 runs there is a 32.76800000% of not getting it, after 10 there is 10.73741824% after 15 it's 3.51843721%, You might think, wow that number is so low, so I must truly be that unlucky huh? Except no, because now factor in 3.51843721% of total playerbase that has the valid chance of also grinding it out, but just for numbers sake I'll use 200.000 because that's the current playercount and there will be roughly 7036 people who will have to do 15 or more runs to get it, now in reality this number is much much larger, because the playerbase is much much larger and of course none of these numbers are guarantee because gamblers fallacy exists, and there is no such thing as a 100% chance to get something when the odds are not 100% However what does exist is Loss aversion and Confirmation bias. And the fact that people are more likely to post about not getting something than they are to post about getting other 20% 5% or even 3%, because how many times have you had a awesome drop and let people around you know about it? I bet you didn't even think of ever doing that. So there is a huge negative confirmation bias, that makes it looks like the odds are very low or even rigged, while in reality they are not.
Because it's extremely easy to have ♥♥♥♥ luck, look up others that have also ♥♥♥♥ luck, because people are more likely to post about their luck when its bad, and not when it's good, and boom you have a confirmation bias, because in your eyes you are only seeing the people that have the worst of luck but not all the people that get it within 1try, 2 tries, 4 tries and so on.
You have a sample of one toss ffs. your "given number of independant trials" is 1.
the fact that you are spending time looking for links all over the internet to try to hide your mistake instead of actually owning your mistake and moving on is worrying. You can't prove obviously false maths with actual calculators and mathematician, it makes no sense.
chill mate, it's okay to be wrong, as i said it's perfectly fine, probabilities aren't intuitive. you seem to be versed in maths, and able to use a search engine, so don't believe everybody on this thread, just search "gambler's fallacy' yourself and educate yourself on your own.
are you feeling ok, mate ? maybe think 30 seconds before posting such nonsense. ^^ I even said it's copy pasted from the GFD and not even from me lmao. i'm not responsible for steam failing to paste powers correctly nor for OP not recognizing such basic coin toss calculations(which tells a lot about their "understanding" of probabilities). you guys are being so ridiculous at this point, i mean i understand you're trying to be trolling or whatnot but i don't even get the point, you are just making fools of yourselves ?
the likely outcome of each flip is the probability of the fair coin, which is 1/2, keep raging lmao
I play a little more it not drop. Delete game....
It's a flat 20% chance on a single event so running it 20 times doesn't actually increase the probability as the probability is not additive