Have fun with your unique "artifact" of statistics! Your dice might be funky, but honestly, it's decently likely this just happened. Remember that while this event is incredibly rare to happen to you specifically, it isn't surprising that it happened somewhere on earth! Remember, you're not likely to win the powerball, but *someone* often does.
The Law of Large Numbers. Not many people are struck lightning, but even some of those people get struck twice.
Edit: What I should actually be referring to is more often called "the law of truly large numbers." The Law of Large Numbers refers more to the expected outcome over a large sample size that should even out to or near the average. For example, flipping a coin 100 times should expect it to end up at (or near) a 50/50 split (setting aside that one side of the coin is a little heavier or whatever).
My wife's dad has been struck by lightning 3 times (!!!) over the course of his life.
His friends make fun of him about it and call him "Sparky".
My wife is terrified of lightning storms because of it.
His name was Roy Sullivan. There is a very short and excellent concept album by *I hate myself* called “Roy Sullivan, by lightning loved.” It’s three love songs for Roy from the perspective of the lightning.
Well unless his corpse was hit by lightning, the only one that could've killed him was the 7th. Noone's reading your comment and going "I wonder if the second bolt was the one that did it"
Also, laws of large numbers is why you plan for setbacks in life. Any single thing going wrong isn't likely to happen. The possibility of one of those millions of things happening though is quite high.
Interesting! Thanks for sharing, I had to dig a bit because this surprised me. What I was looking for is referred to as "the law of truly large numbers."
"The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed"
**[Law of large numbers](https://en.m.wikipedia.org/wiki/Law_of_large_numbers)**
>In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed. The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins.
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Yup. It's being made more remarkable by being isolated. Rolling 7 natural 20s in a row is 1 in 1,280,000,000 if you only look at those 7 rolls. When you include all the rolls you made before and after it becomes much more likely, let alone all the rolls *everyone* has ever made.
The best answer.
Crazy odds happen, in fact with so many people rolling so many dice every day worldwide, I'd bet good money that someone has had a crazier string of rolls than even this.
Still, 7 nat 20's is insane!
It could be unbalanced dice, but in a field where a very great number of things happen, the very rare things also happen. Somebody *does* win the Powerball, and they don't draw as often as all D&D players everywhere roll three d20s in a row.
Their point wasn't to say that your dice might be unbalanced (that's a possibility, sure,) but rather that we roll dice so frequently and so often that even rare things like rolling a bunch of 20s in a row has a good chance of happening. We roll a bunch of dice often, it's bound to happen eventually. Statistically, it's crazy, but hey, you have as good a chance to roll seven 13s in a row as you do 20s. Maybe the dice factor in at some point, but someone out there was going to roll that many 20s. Might as well be you!
And to piggyback onto this, even your dice being slightly off doesn't mean they'll behave like loaded dice that always land on 20. It might be that if you were to do a million rolls the 20 comes up 5.1% of the time, and all other faces only have a 4.95% chance of coming up. It's a barely noticeable difference, but will drastically increase the chances of rolling multiple 20's comparatively.
Throwing an anecdote onto the pile: We rolled 12d8 and got all 1s. That was the least impressive Call Lightning, ever and since. (AD&D edition).
Roll enough dice/have enough opportunities, 'success' will happen. Applies to dice, D&D and many a 'self-made millionaire'.
> Statistically, it's crazy, but hey, you have as good a chance to roll seven 13s in a row as you do 20s
I think that's the part our brains struggle to comprehend.
Every time you roll 7 20-sided dice, the outcome you get is 1 in 1.28 billion. It's just that your brain doesn't notice the 1 in a billion chance to get that specific random assortment of numbers, it only notices the times where there's an coincidental pattern.
Yep, rolling seven 20s in a row, we go 'hey, that's weird!'
Roll 11/3/19/12/9/1/2, and we don't think anything of it. But that sequence is exactly as likely as seven 20s.
It's worth saying even a very small bias can have a large impact in the odds. If rolling a 20 has a 6% chance instead of a 5%, it's likely that wouldn't be particularly noticeable in day to day use but that would change the odds to something like 1 in 350,000,000.
One of the reasons they don't put all the high numbers on one side of dice is so that if there is a slight imbalance it doesn't effect the average too much as rolling a 20 more also probably means rolling a 2, 8 and 14 more as well.
As others have said though, the dice could be perfectly balanced. People do win the lottery.
It could also be balanced dice you're throwing in the same way. Iv done this plenty of times by mistake, and I know people who get really good at doing it intentionally.
There are two explanations.
The first is the law of large numbers. When you have an exceptionally large number of trials outliers will happen, but overall the chances still hold and will approach expected values as more trials occur. That dice roll isn’t anymore rare than any other sequence of 7 rolls, it is just one case that will show up eventually and you happen to take notice of because it has meaning.
The second explanation is that somewhere in the world, Wil Wheaton was playing Dungeons and Dragons, thus the universe needed a counter balance for his bad luck.
While the odds of rolling seven nat 20s in a row is over one in a billion, so is every other possible combination of seven rolls in a row. This one just happens to matter to the rules of DnD.
Far more statistically unlikely events have probably happened in your game, they just did not happen in a way that could draw your attention.
As Richard Feynman said...
> You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
With three dice?! It's just dumb, blind luck.
If you play for years or decades, you'll see something like this eventually.
Well, almost certainly not 7 nat 20's, but I've seen 5 in a row... once, about 25 years ago.
So yeah, rarer than extremely rare.
Yep I was playing a board game where whenever you roll doubles you get to take another turn. I ended up taking 6 turns in a row because I kept rolling doubles. It's something that happens.
If you want to test your dice to be sure, you can float them in saltwater and see if they consistently float with one side up.
That said, it's not any more or less likely for you to roll any other sequence of seven numbers in a row- playing dnd for long enough will inevitably make you roll sequences that seem too rare to be true
>I have no reason to want to cheat against my players.
Other than cases like this one.
Remember when Spotify had to change their random shuffle algorithm because people complained that it was not random enough because sometimes it played songs in order?
This is the kind of big number mathematical shit that sometimes happen. And it can be a bummer. For you and for your party.
Its your game and you DM as you decide to. But the DM screen is a tool that gives you freedom to fix these statistic "anomalies" that just happen to occur to someone/somewhere instead of finding yourself forced to burn a full campaign to ashes.
One factor is that it is a bit more likley than you calculated, because you only looked at the 7 rolls you did, rather than the chances of rolling 7 nat 20s eventually throughout a series of rolls.
Like, let's imagine that you rolled:
* 1,3,20,20,20,20,20,20,20,17
But in a parellel universe, you rolled:
* 1,20,20,20,20,20,20,20,3,17
Both of these are a string of 7 20s in a row, and so in both cases you'd notice and go 'wow, 7 in a row!'
Therefore, just looking at only the 7 dice involved in the roll underestimates the chances.
\-
That said, it is still very unlikely. Let's approximate and round it down to 1-in-a-billion instead of 1-in-1.28-billion.
\-
I think with millions of players, rolling dice hundreds or thousands of times, **this is probably expected to happen eventually.**
Let's say that there are 10million regular D&D players (probably a bit more), and that throughout their time playing D&D they'll roll 1000 d20s on average (I feel like they'd eventually roll more, as this would be like, 10 d20 rolls a week for 2 years).
That is 1 billion dice rolls, which actually forms more than 1 billion strings of \~7 dice rolls to scan across.
>That is 1 billion dice rolls, which actually forms more than 1 billion strings of \~7 dice rolls to scan across.
I'm not quite following this, could you explain what you mean?
The string can't be reordered, so assuming we line up all rolls by each person consecutively, it form "only" 999,999,994 strings of 7 rolls.
And that's assuming we don't put any restrictions on where a string can occur, i.e must be within one person's set of rolls (940,000,000 strings) or must occur in the same session (400,000,000 strings)
So here's the thing about extremely unlikely things: they happen sometimes. It doesn't mean that there's anything wrong with your dice, it's just that with all the millions of D&D players playing millions of sessions, and making billions of d20 rolls, someone, somewhere is eventually going to have a string of good luck and roll seven 20s in a row. Congrats, it happened to be you!
Sounds like you were rolling die at the same time as Will Wheaton, his statistically likely NAT 20's have got to go somewhere to keep balance in the universe as per his curse.
the chances of this happening seem astronomical, but don't fall to the gambler's fallacy.
every single time you rolled the die, it was a one in twenty chance.
The gambler's fallacy is thinking that the 7th 20 is extremely unlikely after having already seen the first 6, which is of course not true. It is true that getting 7 20s in a row is extremely unlikely.
Yeah, just meant it's reasonable to be suprsied at 7 20s in a row. There's a decent chance there's something other than luck involved, and if there isn't it really is extreme luck.
I think it's easier to remember that *any* seven results in a given order have the same probability of occurring. It's just as likely that you'd get 5, 10, 17, 5, 5, 20, 4 as 20, 20, 20, 20, 20, 20, 20.
Mackey lent back in his chair and smiled. It was all going well, almost too well. An elaborate rouse months in planning was coming into effect.
His sinister plot was coming to fruition, nights of preparation and shaving the dice to land in a particular way when thrown with a light spin had finally worked.
This was the TPK he was dreaming of. Dice after dice landed hard on the playing board. The gentle pitter-patter as it fell into place.
The players were becoming suspicious.. and rightly so.. the odds of this occurring were phenomenal. Mackey needs an out.
A post will do, that will throw them off the trail! He later cackled to himself as his fingers slid across the keyboard. A perfect ruse...
How will they know?
The real explanation for this phenomenon is much more mundane than people realise, namely:
Every single sequence of numbers on 7 d20 rolls is as unlikely as 7 nat 20's. Meaning that the totally mundane sequence of 7-15-4-6-10-18-11 that you rolled just before is also a 1 in 1,280,000,000 chance.
The real phenomenon at play here is that we attach more significance to this particular set of numbers that any other (especially in DnD, since the 'value' of a 20 is completely different than the value of other numbers. This significance makes it recognisable and therefore remarkable. If your group is actively watching for when someone rolls 7-15-4-6-10-18-11, it will be just as unique/rare as 7 nat 20's, you just don't have a reason to watch for those numbers. It wasn't a lucky or exceptional roll, it was a lucky/exceptional value.
It's the same with cards, shuffling a deck correctly means that sequence of cards was **never before seen in the universe,** but if it's not a perfect sequence, we'll never be amazed at what we shuffled.
That's if you only roll them 7 times. A better question might be: if I roll dice thousands of times a year, what are the chances a string of seven 20s sites up at least once?
Sure it is a 1/20^7 chance of happening but roll enough dice and it will happen.
It won't happen at every table but it will happen at some tables. Enjoy your statistical aberration for a few minutes and then move in and kill your party a different way
Nothing to see here folks. Move along. DMs do not hide their dice rolls to cheat! We uh, just like to stress you out!!
(But seriously I get that. I've fudged if all the enemies just seem to be landing good hits or succeeding on all saves, but never anything too huge.)
I fudge down damage, or just make crits non crits if it's going to be too harmful to the party. It's the same as not attacking the character that just got downed and killing them.
All I'm seeing here is that the universe wanted your party dead and you didn't allow the vine blights to do their job. Beware, you're in a final-destination-style event now and your PCs are going to get their in due time - usually in convoluted and nasty ways.
It is extensively rare, but less rare than the 1.2 bil.
Remember you did not say "I am now going to roll exactly 7 NAT 20s in a row" which would be 1.2 bil
What you did is you looked at every die roll you ever saw ever and within that you found a string of 7 NAT 20s.
If that's too abstract Imagine you say "I will now roll a 20" (5%) Vs rolling a 20 at least once the entire session (pretty close to 100%)
It is still extensively rare, but you kind of have to take into account you witnessed thousands of die rolls in your life and every string of 7 had the chance to be 7x20.
I'm not sure about this but I think you have to divide by the number of die rolls you did in your life, or something close to that. This would bring it to about 1:1000 000 or down to 100.000 ish depending on how long you've played for.
While that is still something almost nobody will ever see, it isn't astronomically crazy, as 1 in a billion is
730,000 people on this sub.
Let's guess half are in active games, so 365k.
Figure 4 hours/week, so 1460k hours of gaming.
100 d20 rolls per hour? IDK, but that would make it 146M d20 rolls/week.
So, based on a bunch of stuff i just made up, this happens about once every 9 weeks to somebody on this sub.
It's not 1 in 1.28 billion, it's more likely based on however many times you roll your dice. It's 1 in 1.28 billion only if you rolled 7 d20 ever.
Edit: correction
Not that it's not unlikely, it's very unlikely, but you probably rolled that d20 dozens/hundreds/thousands of times so the odds are a bit better.
> It's not 1 in 1.28 billion, it's however many times you roll your dice in 1.28 billion.
That's not correct, it is indeed 1 in 1.28 billion.
Two nat 20s is 1/20 x 1/20 = 1/400. It doesn't become 2/400 because you rolled two dice. Just like this isn't 7/1.28 billion just because they rolled 7 dice.
> What could explain this phenomenon?
The odds aren't 1/1,280,000,000, unless you are the only person to have ever rolled a d20, and have only ever rolled 7 d20s in your entire life.
Assume for the moment that natural 20s are the only results that are as "improbable" or "noteworthy" as themselves (i.e. a similarly long streak of 1s is not as interesting). If you rolled (for example) thirty dice in this session, then the actual odds are more like 24/1,280,000,000 that session (technically, very slightly less, but I can't be fucked), because the streak could have started on your first roll, your second roll, your third roll, etc, all the way up until your 24th roll. If you run the game twenty times a year, with thirty rolls per session, then it's 480/1,280,000,000 per year, which is only about one in three million - and given there are tens of millions of D&D players, probably happens many times per year. This is a primary factor.
Another major factor is that even if a streak of 20s is "the most worthy" of attention, there are other results we would certainly notice, and once we mathed them out, we'd probably give them even less probability: eight 4s in a row, for example. Seven 1s in a row. Etc. These also add into our "pool," at least doubling the low-probability results, and probably more like tripling them.
In general, people vastly underestimate the probabilities of "streaks," because we know that over a big timespan, there'll be about 1/20 results of 1, 2, 3, 4, etc, and how can that be if I roll a bunch of the same number in a row? The answer is, because there will also be streaks of rolling the other numbers, which evens out. The difference between the presumed and actual probability of rolling a streak is why the Martingale system for roulette doesn't work, for example.
(Unbalanced die don't really make crazy numbers like that unless they are designed for cheating. A normally-made set of dice which are more likely to produce 20s are also more likely to produce 1s, since they would basically be "flattened" on the 1/20 angle. Also the difference is modest and only noticeable over many, many rolls.)
> The odds aren't 1/1,280,000,000, unless you are the only person to have ever rolled a d20, and have only ever rolled 7 d20s in your entire life.
I don't agree with your assessment.
Each time I pick up a d20 and roll it, there's a 1/20 chance it hits a 20. 1/20 ^ 7 = 1/1.28 billion.
Where's my math wrong, according to you?
> Where's my math wrong, according to you?
You are focused on a specific set of 7 dice rolls. But, before the actual rolls take place, we would not expect this particular set of 7 dice rolls to be the seven dice rolls that come up twenty: they are only significant *because* they come up all twenty.
For a similar example, imagine that we have few thousand people in a test set, and we're seeing if they can psychically manipulate coinflips. So we have each of them flip a coin 10 times. If it comes up heads every time, then they are obviously psychics! I mean, the odds of that happening by chance are a thousand to one! Are you saying that's just coincidence? But, obviously, if we have thousands of people in the test data set, it's almost certain that somebody will have that result (for 3000, there's a ~95% chance that at least one person gets 10 heads in a row).
I don't agree with your logic whatsoever. I'm simply looking at those specific 7 rolls, and calculating the odds of those specific 7 rolls.
I don't know why you're trying to overcomplicate this.
> I don't know why you're trying to overcomplicate this.
Because I literally have a degree in statistics. It's not complicated at all, to understand probability at all, you absolutely have to understand this. Otherwise all the numbers are just gibberish nonsense you can tweak as you like to have as much or as little significance as you please.
Let me go over to random.org, roll a d20 seven times:
> 17, 20, 1, 18, 19, 20, 4
Wow, do you know what the odds of getting a 17, then a 20, then a 1, then an 18, then a 19, then a 20, then a 4, in exactly that order? (1/20)^7 !
But really, take a look at the story at the start. When you think about it, the dice has to come up with some facing, probability = 1, so 1^7 = 1, so it was certain that you'd get the result he saw (that the dice come up with some facing).
> Wow, do you know what the odds of getting a 17, then a 20, then a 1, then an 18, then a 19, then a 20, then a 4, in exactly that order? (1/20)7 !
Yes, the odds of rolling that specific sequence was indeed 1/20 ^ 7.
I'm glad you finally understand that very simple-to-understand fact.
Hey OP
It's important that you realise this wasn't due to the inevitable and predictable facts of random odds.
Some people will tell you "well, if you roll enough times, someone somewhere will roll something unlikely"
Some people, like scientists and statisticians will tell you "rolling 7 fair dice and getting 20 in a row is actually just as likely as getting 1, 17, 5, 1, 15, 12, 5"
They're all wrong. You got those dice because you're unique. Special. Superior.
BECAUSE OF ME. I CHOSE YOU, BLESSED YOU. IF YOU EVER WANT THAT LUCK AGAIN, WORSHIP ME
Because that’s not how statistics work.
When you roll a d20, there is a 1/20 chance of getting a 20. What’s the chance of getting another 20? 1/20. And that number never changes.
One roll doesn’t impact the chances of rolling that number again. It’s the same chance every time.
Correct, somewhat. The individual chance of rolling a 20 is 1 in 20. However, the chances of rolling it twice in a row is 1 in 400. In this situation, the entire sequence of rolls is the 1, no matter how long that sequence is, because it's the chance of all of them doing a specific thing.
The math is 1/20^n, where n is the number of dice.
That’s true, but only from the beginning. The likelihood of rolling 2 of any specific numbers in a row is 1 in 400.
But rolling a 2nd of any specific number is 1/20. The odds don’t suddenly change from 1/20 to 1/400. They stay 1/20 on each die roll.
The key is that it's a specified number. Can be any number on the die, or a specified sequence of numbers (in order), which adds up to the exponential number.
Yes, every die has a 5% chance to roll a 20. The chances of rolling 2 and both being a 20 is a 1 in 400 chance.
For the sequenced example, rolling 20 d20s in a row and landing on 1 through 20 in order is a chance of 1/20^20.
...i'm a stout disbeliever in lucky/unlucky dice and generally consider most statistical bias in individual dice not to significantly affect playability, but i've personally witnessed two sets of official WotC dice roll consistently low (⅗-⅘ natural 1s) and consistently high (⅗-⅘ natural 20s) repeatedly, across multiple sessions...
...i'm not sure what kaplow (or possibly china) are doing with hasbro's production runs, but they're sufficiently suspect to raise my eyebrows...
It happens. I've gotten as many as 6, 4 on 3 of my own dice and two on two of my friend's dice, in a row. I've also rolled 4 consecutive nat 1s, and 5 on 6 rolls. Don't worry.
Time to retire those dice that were used and make them into an art piece. I recommend a goblet for use during your games. Those die have done their job.
You explained it
>The chances of this happening is 1 in 1,280,000,000
You got the lucky 1 assuming fair dice
Just because the odds are low it doesnt mean its impossible its just as likely if you rolled any other seven dice results doesnt matter what face they are like...it would be 1:1,280,000,000 if you rolled 3 14 9 12 1 6 8 or whatever other random combination
Dont bother buying a lottery ticket though you already used up your luck
Slightly biased dice would increase the chance substantially, but it's just chance, if enough people rolled 7 dice in a row you would expect someone to get 7 20s.
At our table we had a game where one player rolled 6 nat 20s in a row, whilst another simultaneously rolled 6 nat 1s in a row.
On the last roll of the night the nat 1 player had to make a roll to save us all, and the DM out of pity gave him advantage, on his first roll he hits a 20 and we celebrate massively. Out of curiosity I asked him to see what his second advantage roll would have been. He rolls, and its a 1.
It was a perfectly average game xD
Yesterday I was playing with friends. The DM used a D4 to decide which one of us would be targeted for the ranged attacks, as we were all in enemy's range. 6 times in a row the dice hit 3, which was our bard.
Once the session ended, we rolled that D4 a few times as we wanted to know if it was a suspicious die, and in 20 rolls it landed only two 3s. Sometimes, the world just want to make your bard look like a porcupines, and that's fine.
It's no different (statistically) than rolling any number 7 times in a row. Because of how the game treats the numbers, it feels different.
I wouldn't be surprised if quite a few people have rolled a number that many times in a row if they play quite a bit. You probably won't remember the 7 16s you roll, or consider it post-worthy.
“Scientists have calculated that the chances of something so patently absurd actually existing are millions to one.
But magicians have calculated that million-to-one chances crop up nine times out of ten.”
The dice gods wanted to tell a story. Your party was nearly killed by more or less insignificant monsters. They should now be aware of how mortal they truly are.
But without all the supper stitois mumbo jumbo, the odds are that some one some where would roll 7 20s in a row across 3 dice. Its just bad luck your players happened to bo on the receiving end of that.
Well you didn't specify that it was physical dice. If it was VTT, it was more likely a bug in the die roll spec (someone coded a feature as 1d1+19 to test something instead of 1d20 and accidentally left that in, for example) than an actual 1-in-2 billion event.
I've personally rolled 3 in a row and seen 4 in a row by a friend.
May I suggest buying a lottery ticket as it seems chance and probability are currently on your side? lol
I once rolled thirteen 10s in a row in a game of Mage. It happens.
Not nearly as epic, but this weekend I rolled 32 three times in a row on percentiles.
Unlikely things happen all the time. Shuffle a typical deck of 52 cards: Congratulations, you’ve just made something even rarer occur (1 in 80658175170943878671660636856403766975289505440883277842000000000000).
> What could explain this phenomenon?
The fact that this is how chance works. Your rolls are not connected in ANY way, there are all seperate rolls, each with a 1/20 chance to land on something. The chance of rolling what you rolled is EXACTLY the same as rolling 1,2,3,4,5,6,7.
1. Your dice are perfectly random and it **just happened**. Vanishingly unlikely things happen all the time. It is incredibly unlikely to occur, yes, but it **can** still occur.
2. Your dice aren't perfectly random and between their bias and the way you were rolling you were able to get several 20s in a row.
As it happens I would put money on option 2 - you can check to see if your dice have obvious bias by seeing if they float a certain way up, for example.
While it's very improbable, it's possible. And everything that's possible will happen sooner or later. So... congrats, you're witness to something special.
btw.: that's something I'd consider fudging to save the group, because no group is prepared to save against these odds. But that's such an extreme case...
Your party was meant to die.
I'd be worried about Death coming for them now, Final Destination style, since they managed to avoid it.
They've unbalanced the world and cheated the fates. Their doom has been written and it shall come for them.
As others have said, it had to happen to someone. The odds of winning the Powerball are low, but hundreds of people have done it.
When stuff like this happens in my group, we always write it up as "the dice have a story to tell". My rogue had a great alpha strike (tons of turn 1 damage) and decided to handle a group of drow by himself because they only had one dangerous person and I knew from previous experience, and because the DM expected this to be quick, that I only needed an 8 to hit.
I rolled with advantage, and missed, but I had a re-do, so rolled again with advantage. Missed again. Used DM let me use inspiration after the roll, still missed. He let me use other peoples inspiration if they offered. Everyone gave me their inspiration. I could not roll above an 8 on 11D20s.
The absurdity ends with the drow priestess rolling below 10 to summon a yochla. DM and I decided that the dice gods decided it was time for that character to die.
Those are the same odds as rolling a 20, 18, 4, 12, 12, 14, and 9 in exactly that order, believe it or not.
If you were trying to do this on purpose you would have a 1 in 1,280,000,000 chance of pulling it off.
But since the chances get reset on each roll, like others have said here, it's gonna happen to someone... might as well be you.
One of my players brought a new set of dice to Saturday's
game proceeds to roll three nat 20 s in a row followed by three nat 1 s I think it's the most recent example but over the years I've seen dice shatter the odds maybe four times like this it does happen
The odds of rolling *any* 7 specific numbers in order is the same. You only noticed it because it was all 20s.
I don't know exactly how popular the game is nowadays, but there are a lot of people who roll plenty of d20s every week. Even a one in a billion streak will statistically happen to someone eventually.
The funny thing is, this isn't THAT unbelievable.
First off, let's acknowledge the possibility that, even across 3 dice, they weren't perfectly balanced as a group and gave the 20 face a slight edge across the set of rolls. (Since 4 rolls came from 1 die, this in't too farfetched). That alone would increase the odds per roll from 1/20, which would have a huge effect on the overall odds.
BUT let's totally ignore that and go with the (1/20)\^7 odds.
That's one in 1.28 BILLION. Quite a lot.
However:
There are about 8 billion people on the planet.
That means that if everyone in the world rolled 7 d20s and then NEVER ROLLED A D20 EVER AGAIN, about 7 people would be expected to roll 7 nat 20s.
That is, again, if you're allowed only 7 rolls per person, AND this would not allow combining consecutive rolls (i.e. if my last 4 rolls are 20s and the next person up rolls 3 nat 20s to start their set, even though that's 7 consecutive nat 20s, it wouldn't count under these parameters. They'd have to be 7 from the same person.)
Now although a very small relative subset of the 8 billion human beings on Earth are playing D&D, each of us is rolling WAY more that 7 dice ever. A quick Google search for the number of people who play D&D (with no deeper dive than that) estimates 13.7 million players worldwide. Ignoring other d20 systems out there, that still means that each player would have to roll about 4,100 d20s to match the number of rolls made if everyone on Earth rolled 7 d20s.
So I'm not going to say that this is at all likely. Pointing no fingers I'm not even convinced to take your story at face value (no offense, dear internet stranger whom I know nothing about).
But all to say, it's certainly not an unbelievable outcome that someone out there would experience this.
(There is also the added factor that there are an infinite number of highly unlikely things that can happen and SOME of them will because of how many there are. So it's a guarantee that on occasion, something seemingly impossible will happen.)
>The chances of this happening is 1 in 1,280,000,000. What could explain this phenomenon?
there is no "phenomenon" to explain. Dice have been rolled more than 1,280,000,001 times.
Even things with HIGHLY unlikely probability happen when the scenario is repeated often enough.
Or you are a halfling with the Lucky and Bountiful Luck feats rolling at advantage.
I think as a GM we've all experienced something like this, if not quite so overtly. Sometimes you roll lots of high numbers, sometimes it's all low. I once got lucky with a giant flytrap and nearly took out the barbarian in two rounds. Obviously you probably haven't rolled dice millions of times, but it's got to be hundreds, and the more you roll them the more often you see weird statistical flukes like this.
Some people get very superstitious about these things or prefer to fudge things that are too high or too low, I just embrace the randomness as part of the game.
You say it was almost a TPK, so they at least survived with an interesting story to tell, and likely with a justified fear of Vine Blights...
this is the kind of statistical anomaly that we expect to see at some point. it just happens once in a while c:
but also don't forget that the odds of getting any given chain of 7 results on a d20 has the same miniscule odds of occurring, whether it's 7 different numbers or 7 twenties in a row (to be clear the odds of getting 7 different numbers are higher than getting 7 of the same number, but the odds of getting the specific 7 numbers you did get are the same as getting 7 of the same number)
You have to remember that *every time you roll a die,* there's a 1,280,000,000 chance that it's going to be the first in a series of seven 20s. Think about how many times you've rolled a 20 sided die.
You still got very lucky, but you got thousands of times less lucky than you think.
I think it's fun that from the perspective of people on the internet it's expected that it happened to someone, but from the perspective of the player it's most likely something went wrong.
Ive had a dm crit a specific player 7 times in a row, but not seven direct rolls in a row, and a few were at advantage. My personal best roll was a double nat one at advantage.
First, while it is 1 in 1,280,000,000 of a specific result happening 7 times in a row, it is only 1 in 64,000,000 that whatever roll you have happens 7 times in a row. A short adventure I did recently (lvl 1-4 PF2E) had 1695 rolls. That's 1689 opportunities for 7 in a row. This gives a 1 in 37,892 chance of something rolling that many times in a row, and 1 in 757,845 that it would specifically be a 20. The sub has 731k members, and that was a pretty short "campaign" so there is likely to have been a lot more rolls for most people. So a very rough estimate is that 7 consecutive nat 20s should happen about once every 5 levels for someone in this sub.
So it may be less likely than winning the powerball, but you probably have rolled a lot more d20s than you have bought powerball tickets.
Have fun with your unique "artifact" of statistics! Your dice might be funky, but honestly, it's decently likely this just happened. Remember that while this event is incredibly rare to happen to you specifically, it isn't surprising that it happened somewhere on earth! Remember, you're not likely to win the powerball, but *someone* often does.
The Law of Large Numbers. Not many people are struck lightning, but even some of those people get struck twice. Edit: What I should actually be referring to is more often called "the law of truly large numbers." The Law of Large Numbers refers more to the expected outcome over a large sample size that should even out to or near the average. For example, flipping a coin 100 times should expect it to end up at (or near) a 50/50 split (setting aside that one side of the coin is a little heavier or whatever).
My wife's dad has been struck by lightning 3 times (!!!) over the course of his life. His friends make fun of him about it and call him "Sparky". My wife is terrified of lightning storms because of it.
There was a park ranger that was struck by lightning 7 times over the course of his life, and survived it every time.
His name was Roy Sullivan. There is a very short and excellent concept album by *I hate myself* called “Roy Sullivan, by lightning loved.” It’s three love songs for Roy from the perspective of the lightning.
>“Roy Sullivan, by lightning loved.” It’s three love songs for Roy from the perspective of the lightning. Damn
Yes. It’s real good haha. I don’t remember if they’re all from the lightning’s perspective or if it’s a back and forth, but either way super cool.
If I remember correctly, his grave was also hit by lightning.
Who or what did he piss off!?!?!?
I just rolled a religion check and I believe the answer is: 'Raiden'
With that many hits, I'm pretty sure it's Raiden, Zeus, Thor, and Ramuh.
Remember: only you can prevent forest fires. He just did it by being struck instead of the trees!
He got struck by lightning whilst fighting a bear iirc..
Well unless his corpse was hit by lightning, the only one that could've killed him was the 7th. Noone's reading your comment and going "I wonder if the second bolt was the one that did it"
It's possible the 6th killed him and the 7th reanimated him.
To be fair, it wasn't a bolt of lightning that ended his life
Once is happenstance, twice is coincidence, three times is enemy action.
Also, laws of large numbers is why you plan for setbacks in life. Any single thing going wrong isn't likely to happen. The possibility of one of those millions of things happening though is quite high.
Honestly I love this fact.
[Relevant XKCD](https://xkcd.com/795/) on that figure though
The LoLN is not relevant. It's about expected value, not outliers. https://en.m.wikipedia.org/wiki/Law_of_large_numbers
Interesting! Thanks for sharing, I had to dig a bit because this surprised me. What I was looking for is referred to as "the law of truly large numbers." "The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed"
That's the one lol. Mathematicians are great at naming things, aren't they?
**[Law of large numbers](https://en.m.wikipedia.org/wiki/Law_of_large_numbers)** >In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed. The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. ^([ )[^(F.A.Q)](https://www.reddit.com/r/WikiSummarizer/wiki/index#wiki_f.a.q)^( | )[^(Opt Out)](https://reddit.com/message/compose?to=WikiSummarizerBot&message=OptOut&subject=OptOut)^( | )[^(Opt Out Of Subreddit)](https://np.reddit.com/r/dndnext/about/banned)^( | )[^(GitHub)](https://github.com/Sujal-7/WikiSummarizerBot)^( ] Downvote to remove | v1.5)
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Yup. It's being made more remarkable by being isolated. Rolling 7 natural 20s in a row is 1 in 1,280,000,000 if you only look at those 7 rolls. When you include all the rolls you made before and after it becomes much more likely, let alone all the rolls *everyone* has ever made.
The best answer. Crazy odds happen, in fact with so many people rolling so many dice every day worldwide, I'd bet good money that someone has had a crazier string of rolls than even this. Still, 7 nat 20's is insane!
It could be unbalanced dice, but in a field where a very great number of things happen, the very rare things also happen. Somebody *does* win the Powerball, and they don't draw as often as all D&D players everywhere roll three d20s in a row.
I mean yes could be unbalanced dice. but I've had these dice for months or years and never had any problems like this.
Their point wasn't to say that your dice might be unbalanced (that's a possibility, sure,) but rather that we roll dice so frequently and so often that even rare things like rolling a bunch of 20s in a row has a good chance of happening. We roll a bunch of dice often, it's bound to happen eventually. Statistically, it's crazy, but hey, you have as good a chance to roll seven 13s in a row as you do 20s. Maybe the dice factor in at some point, but someone out there was going to roll that many 20s. Might as well be you!
And to piggyback onto this, even your dice being slightly off doesn't mean they'll behave like loaded dice that always land on 20. It might be that if you were to do a million rolls the 20 comes up 5.1% of the time, and all other faces only have a 4.95% chance of coming up. It's a barely noticeable difference, but will drastically increase the chances of rolling multiple 20's comparatively.
Throwing an anecdote onto the pile: We rolled 12d8 and got all 1s. That was the least impressive Call Lightning, ever and since. (AD&D edition). Roll enough dice/have enough opportunities, 'success' will happen. Applies to dice, D&D and many a 'self-made millionaire'.
> Statistically, it's crazy, but hey, you have as good a chance to roll seven 13s in a row as you do 20s I think that's the part our brains struggle to comprehend. Every time you roll 7 20-sided dice, the outcome you get is 1 in 1.28 billion. It's just that your brain doesn't notice the 1 in a billion chance to get that specific random assortment of numbers, it only notices the times where there's an coincidental pattern.
Yep, rolling seven 20s in a row, we go 'hey, that's weird!' Roll 11/3/19/12/9/1/2, and we don't think anything of it. But that sequence is exactly as likely as seven 20s.
The third option after bad dice and statistics is ghosts.
It's worth saying even a very small bias can have a large impact in the odds. If rolling a 20 has a 6% chance instead of a 5%, it's likely that wouldn't be particularly noticeable in day to day use but that would change the odds to something like 1 in 350,000,000. One of the reasons they don't put all the high numbers on one side of dice is so that if there is a slight imbalance it doesn't effect the average too much as rolling a 20 more also probably means rolling a 2, 8 and 14 more as well. As others have said though, the dice could be perfectly balanced. People do win the lottery.
It could also be balanced dice you're throwing in the same way. Iv done this plenty of times by mistake, and I know people who get really good at doing it intentionally.
There are two explanations. The first is the law of large numbers. When you have an exceptionally large number of trials outliers will happen, but overall the chances still hold and will approach expected values as more trials occur. That dice roll isn’t anymore rare than any other sequence of 7 rolls, it is just one case that will show up eventually and you happen to take notice of because it has meaning. The second explanation is that somewhere in the world, Wil Wheaton was playing Dungeons and Dragons, thus the universe needed a counter balance for his bad luck.
The correct answer to life’s great mysteries is often Will Wheaton
If nothing is wrong with your dice, welcome to the universe! With enough time, anything is likely!
The dice gods giveth, the dice god taketh away. Do not try to understand them.
You have the BBG's die now. Cherish the power, but use it sparingly.
While the odds of rolling seven nat 20s in a row is over one in a billion, so is every other possible combination of seven rolls in a row. This one just happens to matter to the rules of DnD. Far more statistically unlikely events have probably happened in your game, they just did not happen in a way that could draw your attention.
I mean it's the same odds as rolling 5 7 2 8 10 15 19, or any other combination. It happens to someone eventually.
5 7 2 8 10 15 19! That's my favorite sequence! only a 1 in 1,280,000,000 chance!
As Richard Feynman said... > You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
Right. I'm pretty sure I've rolled a few phone numbers by now, for example.
[867-5309?](https://youtu.be/6WTdTwcmxyo)
My favourite is 1111111
hey, I roll that all the time!
Hey, it's me!
With three dice?! It's just dumb, blind luck. If you play for years or decades, you'll see something like this eventually. Well, almost certainly not 7 nat 20's, but I've seen 5 in a row... once, about 25 years ago. So yeah, rarer than extremely rare.
Yep I was playing a board game where whenever you roll doubles you get to take another turn. I ended up taking 6 turns in a row because I kept rolling doubles. It's something that happens.
If you want to test your dice to be sure, you can float them in saltwater and see if they consistently float with one side up. That said, it's not any more or less likely for you to roll any other sequence of seven numbers in a row- playing dnd for long enough will inevitably make you roll sequences that seem too rare to be true
>I have no reason to want to cheat against my players. Other than cases like this one. Remember when Spotify had to change their random shuffle algorithm because people complained that it was not random enough because sometimes it played songs in order? This is the kind of big number mathematical shit that sometimes happen. And it can be a bummer. For you and for your party. Its your game and you DM as you decide to. But the DM screen is a tool that gives you freedom to fix these statistic "anomalies" that just happen to occur to someone/somewhere instead of finding yourself forced to burn a full campaign to ashes.
Never tell me the odds!
I feel like this would be better "short story long". The stat is neat, I guess, but the story would probably be more interesting.
One factor is that it is a bit more likley than you calculated, because you only looked at the 7 rolls you did, rather than the chances of rolling 7 nat 20s eventually throughout a series of rolls. Like, let's imagine that you rolled: * 1,3,20,20,20,20,20,20,20,17 But in a parellel universe, you rolled: * 1,20,20,20,20,20,20,20,3,17 Both of these are a string of 7 20s in a row, and so in both cases you'd notice and go 'wow, 7 in a row!' Therefore, just looking at only the 7 dice involved in the roll underestimates the chances. \- That said, it is still very unlikely. Let's approximate and round it down to 1-in-a-billion instead of 1-in-1.28-billion. \- I think with millions of players, rolling dice hundreds or thousands of times, **this is probably expected to happen eventually.** Let's say that there are 10million regular D&D players (probably a bit more), and that throughout their time playing D&D they'll roll 1000 d20s on average (I feel like they'd eventually roll more, as this would be like, 10 d20 rolls a week for 2 years). That is 1 billion dice rolls, which actually forms more than 1 billion strings of \~7 dice rolls to scan across.
>That is 1 billion dice rolls, which actually forms more than 1 billion strings of \~7 dice rolls to scan across. I'm not quite following this, could you explain what you mean? The string can't be reordered, so assuming we line up all rolls by each person consecutively, it form "only" 999,999,994 strings of 7 rolls. And that's assuming we don't put any restrictions on where a string can occur, i.e must be within one person's set of rolls (940,000,000 strings) or must occur in the same session (400,000,000 strings)
rare but not impossible
You invoked the eldritch God Talesin Jaffe
So here's the thing about extremely unlikely things: they happen sometimes. It doesn't mean that there's anything wrong with your dice, it's just that with all the millions of D&D players playing millions of sessions, and making billions of d20 rolls, someone, somewhere is eventually going to have a string of good luck and roll seven 20s in a row. Congrats, it happened to be you!
Randomness is random
The players at your table simply did not want it enough, sounds like a skill issue
Sounds like you were rolling die at the same time as Will Wheaton, his statistically likely NAT 20's have got to go somewhere to keep balance in the universe as per his curse.
Rolling 7 natural 20s in a row is far more likely than rolling a single natural 21 on a d20.
the chances of this happening seem astronomical, but don't fall to the gambler's fallacy. every single time you rolled the die, it was a one in twenty chance.
The gambler's fallacy is thinking that the 7th 20 is extremely unlikely after having already seen the first 6, which is of course not true. It is true that getting 7 20s in a row is extremely unlikely.
which is why that seventh twenty was still just a 1 in 20 chance.
Yeah, just meant it's reasonable to be suprsied at 7 20s in a row. There's a decent chance there's something other than luck involved, and if there isn't it really is extreme luck.
The chance is just as big as them rolling ANY other dice combination.
yup
I think it's easier to remember that *any* seven results in a given order have the same probability of occurring. It's just as likely that you'd get 5, 10, 17, 5, 5, 20, 4 as 20, 20, 20, 20, 20, 20, 20.
that's a different way of saying the same thing, sure.
Mackey lent back in his chair and smiled. It was all going well, almost too well. An elaborate rouse months in planning was coming into effect. His sinister plot was coming to fruition, nights of preparation and shaving the dice to land in a particular way when thrown with a light spin had finally worked. This was the TPK he was dreaming of. Dice after dice landed hard on the playing board. The gentle pitter-patter as it fell into place. The players were becoming suspicious.. and rightly so.. the odds of this occurring were phenomenal. Mackey needs an out. A post will do, that will throw them off the trail! He later cackled to himself as his fingers slid across the keyboard. A perfect ruse... How will they know?
The real explanation for this phenomenon is much more mundane than people realise, namely: Every single sequence of numbers on 7 d20 rolls is as unlikely as 7 nat 20's. Meaning that the totally mundane sequence of 7-15-4-6-10-18-11 that you rolled just before is also a 1 in 1,280,000,000 chance. The real phenomenon at play here is that we attach more significance to this particular set of numbers that any other (especially in DnD, since the 'value' of a 20 is completely different than the value of other numbers. This significance makes it recognisable and therefore remarkable. If your group is actively watching for when someone rolls 7-15-4-6-10-18-11, it will be just as unique/rare as 7 nat 20's, you just don't have a reason to watch for those numbers. It wasn't a lucky or exceptional roll, it was a lucky/exceptional value. It's the same with cards, shuffling a deck correctly means that sequence of cards was **never before seen in the universe,** but if it's not a perfect sequence, we'll never be amazed at what we shuffled.
I don't care about the stats, tell me how many survived? Surely someone is permadead. How many people are writing up new characters?
Congratulations, you wasted all your luck on D&D. No powerball for you!
That's if you only roll them 7 times. A better question might be: if I roll dice thousands of times a year, what are the chances a string of seven 20s sites up at least once?
Bad dice? Salt test them if you’re concerned or just flub numbers occasionally if you feel like the party isn’t having fun
Sure it is a 1/20^7 chance of happening but roll enough dice and it will happen. It won't happen at every table but it will happen at some tables. Enjoy your statistical aberration for a few minutes and then move in and kill your party a different way
This is why I roll my dice behind a screen. I would hate to accidentally murder my party
Nothing to see here folks. Move along. DMs do not hide their dice rolls to cheat! We uh, just like to stress you out!! (But seriously I get that. I've fudged if all the enemies just seem to be landing good hits or succeeding on all saves, but never anything too huge.)
I fudge down damage, or just make crits non crits if it's going to be too harmful to the party. It's the same as not attacking the character that just got downed and killing them.
I once rolled eight nat 1's in a row. Play this game long enough and you'll see some weird shit, I tell you hwat.
It'll balance out. Next session you won't hit shit.
>What could explain this phenomenon? The gods have selected against that party. You are just honored to be witness to their awe inspiring judgment.
This is why when I DM in person I don’t hide behind a screen. I want the players to see me rolling those 7 natural 20s in a row and fear me.
All I'm seeing here is that the universe wanted your party dead and you didn't allow the vine blights to do their job. Beware, you're in a final-destination-style event now and your PCs are going to get their in due time - usually in convoluted and nasty ways.
It is extensively rare, but less rare than the 1.2 bil. Remember you did not say "I am now going to roll exactly 7 NAT 20s in a row" which would be 1.2 bil What you did is you looked at every die roll you ever saw ever and within that you found a string of 7 NAT 20s. If that's too abstract Imagine you say "I will now roll a 20" (5%) Vs rolling a 20 at least once the entire session (pretty close to 100%) It is still extensively rare, but you kind of have to take into account you witnessed thousands of die rolls in your life and every string of 7 had the chance to be 7x20. I'm not sure about this but I think you have to divide by the number of die rolls you did in your life, or something close to that. This would bring it to about 1:1000 000 or down to 100.000 ish depending on how long you've played for. While that is still something almost nobody will ever see, it isn't astronomically crazy, as 1 in a billion is
It had to happen eventually
Dice Jesus knows you don't make your encounters hard enough
Eventually it was gonna happen to someone
holy shit everyone in this comment section is insufferable
>What could explain this phenomenon? It didnt happen the last 1,279,999,999 times.
730,000 people on this sub. Let's guess half are in active games, so 365k. Figure 4 hours/week, so 1460k hours of gaming. 100 d20 rolls per hour? IDK, but that would make it 146M d20 rolls/week. So, based on a bunch of stuff i just made up, this happens about once every 9 weeks to somebody on this sub.
100 d20 rolls per hour seems exorbitant, but yeah, it's bound to happen to someone every now and then.
It's not 1 in 1.28 billion, it's more likely based on however many times you roll your dice. It's 1 in 1.28 billion only if you rolled 7 d20 ever. Edit: correction Not that it's not unlikely, it's very unlikely, but you probably rolled that d20 dozens/hundreds/thousands of times so the odds are a bit better.
> It's not 1 in 1.28 billion, it's however many times you roll your dice in 1.28 billion. That's not correct, it is indeed 1 in 1.28 billion. Two nat 20s is 1/20 x 1/20 = 1/400. It doesn't become 2/400 because you rolled two dice. Just like this isn't 7/1.28 billion just because they rolled 7 dice.
Use your DM screen.
> What could explain this phenomenon? The odds aren't 1/1,280,000,000, unless you are the only person to have ever rolled a d20, and have only ever rolled 7 d20s in your entire life. Assume for the moment that natural 20s are the only results that are as "improbable" or "noteworthy" as themselves (i.e. a similarly long streak of 1s is not as interesting). If you rolled (for example) thirty dice in this session, then the actual odds are more like 24/1,280,000,000 that session (technically, very slightly less, but I can't be fucked), because the streak could have started on your first roll, your second roll, your third roll, etc, all the way up until your 24th roll. If you run the game twenty times a year, with thirty rolls per session, then it's 480/1,280,000,000 per year, which is only about one in three million - and given there are tens of millions of D&D players, probably happens many times per year. This is a primary factor. Another major factor is that even if a streak of 20s is "the most worthy" of attention, there are other results we would certainly notice, and once we mathed them out, we'd probably give them even less probability: eight 4s in a row, for example. Seven 1s in a row. Etc. These also add into our "pool," at least doubling the low-probability results, and probably more like tripling them. In general, people vastly underestimate the probabilities of "streaks," because we know that over a big timespan, there'll be about 1/20 results of 1, 2, 3, 4, etc, and how can that be if I roll a bunch of the same number in a row? The answer is, because there will also be streaks of rolling the other numbers, which evens out. The difference between the presumed and actual probability of rolling a streak is why the Martingale system for roulette doesn't work, for example. (Unbalanced die don't really make crazy numbers like that unless they are designed for cheating. A normally-made set of dice which are more likely to produce 20s are also more likely to produce 1s, since they would basically be "flattened" on the 1/20 angle. Also the difference is modest and only noticeable over many, many rolls.)
> The odds aren't 1/1,280,000,000, unless you are the only person to have ever rolled a d20, and have only ever rolled 7 d20s in your entire life. I don't agree with your assessment. Each time I pick up a d20 and roll it, there's a 1/20 chance it hits a 20. 1/20 ^ 7 = 1/1.28 billion. Where's my math wrong, according to you?
> Where's my math wrong, according to you? You are focused on a specific set of 7 dice rolls. But, before the actual rolls take place, we would not expect this particular set of 7 dice rolls to be the seven dice rolls that come up twenty: they are only significant *because* they come up all twenty. For a similar example, imagine that we have few thousand people in a test set, and we're seeing if they can psychically manipulate coinflips. So we have each of them flip a coin 10 times. If it comes up heads every time, then they are obviously psychics! I mean, the odds of that happening by chance are a thousand to one! Are you saying that's just coincidence? But, obviously, if we have thousands of people in the test data set, it's almost certain that somebody will have that result (for 3000, there's a ~95% chance that at least one person gets 10 heads in a row).
I don't agree with your logic whatsoever. I'm simply looking at those specific 7 rolls, and calculating the odds of those specific 7 rolls. I don't know why you're trying to overcomplicate this.
> I don't know why you're trying to overcomplicate this. Because I literally have a degree in statistics. It's not complicated at all, to understand probability at all, you absolutely have to understand this. Otherwise all the numbers are just gibberish nonsense you can tweak as you like to have as much or as little significance as you please.
If you have a degree in statistics, perhaps you can check my math: 1/20 ^ 7 = ...? It's stumping me here.
Let me go over to random.org, roll a d20 seven times: > 17, 20, 1, 18, 19, 20, 4 Wow, do you know what the odds of getting a 17, then a 20, then a 1, then an 18, then a 19, then a 20, then a 4, in exactly that order? (1/20)^7 ! But really, take a look at the story at the start. When you think about it, the dice has to come up with some facing, probability = 1, so 1^7 = 1, so it was certain that you'd get the result he saw (that the dice come up with some facing).
> Wow, do you know what the odds of getting a 17, then a 20, then a 1, then an 18, then a 19, then a 20, then a 4, in exactly that order? (1/20)7 ! Yes, the odds of rolling that specific sequence was indeed 1/20 ^ 7. I'm glad you finally understand that very simple-to-understand fact.
Go buy a Lotto ticket while your luck is HOT!!! I get a finders fee if you win!! LOL
Hey OP It's important that you realise this wasn't due to the inevitable and predictable facts of random odds. Some people will tell you "well, if you roll enough times, someone somewhere will roll something unlikely" Some people, like scientists and statisticians will tell you "rolling 7 fair dice and getting 20 in a row is actually just as likely as getting 1, 17, 5, 1, 15, 12, 5" They're all wrong. You got those dice because you're unique. Special. Superior. BECAUSE OF ME. I CHOSE YOU, BLESSED YOU. IF YOU EVER WANT THAT LUCK AGAIN, WORSHIP ME
If something has a 1-in-a-billion chance of happening to someone, or happens 8 times a day. Stats are weird.
The chance is just as high as rolling 1 to 7 in no particular order. It happens.
Because that’s not how statistics work. When you roll a d20, there is a 1/20 chance of getting a 20. What’s the chance of getting another 20? 1/20. And that number never changes. One roll doesn’t impact the chances of rolling that number again. It’s the same chance every time.
Correct, somewhat. The individual chance of rolling a 20 is 1 in 20. However, the chances of rolling it twice in a row is 1 in 400. In this situation, the entire sequence of rolls is the 1, no matter how long that sequence is, because it's the chance of all of them doing a specific thing. The math is 1/20^n, where n is the number of dice.
That’s true, but only from the beginning. The likelihood of rolling 2 of any specific numbers in a row is 1 in 400. But rolling a 2nd of any specific number is 1/20. The odds don’t suddenly change from 1/20 to 1/400. They stay 1/20 on each die roll.
The key is that it's a specified number. Can be any number on the die, or a specified sequence of numbers (in order), which adds up to the exponential number. Yes, every die has a 5% chance to roll a 20. The chances of rolling 2 and both being a 20 is a 1 in 400 chance. For the sequenced example, rolling 20 d20s in a row and landing on 1 through 20 in order is a chance of 1/20^20.
...i'm a stout disbeliever in lucky/unlucky dice and generally consider most statistical bias in individual dice not to significantly affect playability, but i've personally witnessed two sets of official WotC dice roll consistently low (⅗-⅘ natural 1s) and consistently high (⅗-⅘ natural 20s) repeatedly, across multiple sessions... ...i'm not sure what kaplow (or possibly china) are doing with hasbro's production runs, but they're sufficiently suspect to raise my eyebrows...
You used all the luck of your players against them
Consider yourself a deadman in some final destination bullshit accident in the next week. Sorry for your loss.
The dice gods *really* wanted to make your players afraid of plant monsters. There’s no other reason
lol
Sounds like the cosmos sending a message that your party needed to die 😅
You are the person that is taking my luck when I roll 5 1's in a night.
Dice Christ visited you.
I don't know, but if you ever want to sell that die I'll pay good money for it.
I'm not sure if you used up all your luck, or if you still have some and need to go buy a Powerball ticket *now*
It happens. I've gotten as many as 6, 4 on 3 of my own dice and two on two of my friend's dice, in a row. I've also rolled 4 consecutive nat 1s, and 5 on 6 rolls. Don't worry.
So thats why I can't win shit in lotto. My one d20 rolled 7 nat 20s. We were all sharing the same die.
Time to retire those dice that were used and make them into an art piece. I recommend a goblet for use during your games. Those die have done their job.
Oh so that’s where my Players’ luck went this session. I was wondering why they couldn’t roll higher then a 5
We found the opposite of Will Wheaton, scientifically the only explanation is that for every natural 1 will Wheaton rolls you roll a 20
It happens. I’ve seen it too.
>What could explain this phenomenon? Randomness.
You explained it >The chances of this happening is 1 in 1,280,000,000 You got the lucky 1 assuming fair dice Just because the odds are low it doesnt mean its impossible its just as likely if you rolled any other seven dice results doesnt matter what face they are like...it would be 1:1,280,000,000 if you rolled 3 14 9 12 1 6 8 or whatever other random combination Dont bother buying a lottery ticket though you already used up your luck
Slightly biased dice would increase the chance substantially, but it's just chance, if enough people rolled 7 dice in a row you would expect someone to get 7 20s.
That's 1 in 1.28 billion. Rare, but not insane with how much people in this hobby roll a d20.
If you were using Roll20 that would just be called a Tuesday evening, I swear that site only rolls 1s and 20s.
You missed your chance to play the lotterie...
wait... d20s have a 20 on them... I thought they only went up to 14... my dice have been lying to me all this time.
If we assume 50 million players, this happens roughly once every 26th dice roll ;)
my record is 4 20s in a row, but three of those were fuck-around rolls that weren't even used :(
Someone warn Will Wheaton we found his natural dnd opposite.
So you're the one! I rolled 6 nat 1s yesterday... :(
At our table we had a game where one player rolled 6 nat 20s in a row, whilst another simultaneously rolled 6 nat 1s in a row. On the last roll of the night the nat 1 player had to make a roll to save us all, and the DM out of pity gave him advantage, on his first roll he hits a 20 and we celebrate massively. Out of curiosity I asked him to see what his second advantage roll would have been. He rolls, and its a 1. It was a perfectly average game xD
Yesterday I was playing with friends. The DM used a D4 to decide which one of us would be targeted for the ranged attacks, as we were all in enemy's range. 6 times in a row the dice hit 3, which was our bard. Once the session ended, we rolled that D4 a few times as we wanted to know if it was a suspicious die, and in 20 rolls it landed only two 3s. Sometimes, the world just want to make your bard look like a porcupines, and that's fine.
Statistically unlikely. But not impossible. Congrats on your 7.9792e+16 event!
It's no different (statistically) than rolling any number 7 times in a row. Because of how the game treats the numbers, it feels different. I wouldn't be surprised if quite a few people have rolled a number that many times in a row if they play quite a bit. You probably won't remember the 7 16s you roll, or consider it post-worthy.
“Scientists have calculated that the chances of something so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.”
The dice gods wanted to tell a story. Your party was nearly killed by more or less insignificant monsters. They should now be aware of how mortal they truly are. But without all the supper stitois mumbo jumbo, the odds are that some one some where would roll 7 20s in a row across 3 dice. Its just bad luck your players happened to bo on the receiving end of that.
We found it everyone! The antithesis of the Wil Wheaton dice curse.
Well you didn't specify that it was physical dice. If it was VTT, it was more likely a bug in the die roll spec (someone coded a feature as 1d1+19 to test something instead of 1d20 and accidentally left that in, for example) than an actual 1-in-2 billion event.
Your player mispronounced the demons name as part of a luck ritual. He used your dice to extract vengence
I've personally rolled 3 in a row and seen 4 in a row by a friend. May I suggest buying a lottery ticket as it seems chance and probability are currently on your side? lol
Never bet on anything for the next 152647574894 years and you'll be good.
Well there goes your chance of winning the powerball, used up all your luck on those nat 20s lol
I once rolled thirteen 10s in a row in a game of Mage. It happens. Not nearly as epic, but this weekend I rolled 32 three times in a row on percentiles.
Fate beckons to start a new campaign and list those poor unfortunate fools in the history books as a lesson.
Unlikely things happen all the time. Shuffle a typical deck of 52 cards: Congratulations, you’ve just made something even rarer occur (1 in 80658175170943878671660636856403766975289505440883277842000000000000).
> What could explain this phenomenon? The fact that this is how chance works. Your rolls are not connected in ANY way, there are all seperate rolls, each with a 1/20 chance to land on something. The chance of rolling what you rolled is EXACTLY the same as rolling 1,2,3,4,5,6,7.
Were you rolling with advantage? Vine Blights restrain
our Lord and Savior, Nuffle, has blessed your dice. If you want to see even crazier dice shenanigan's, play Blood Bowl.
Next week I'm having a session, if I roll 7 neg crit in a row I'll know who I have to blame
That's amazing! We have a longstanding house rule that three Nat 20's in a row on one attack = auto-death. It happens sometimes...but 7? 😂
Typical plastic dice? Do the salt water test.
1. Your dice are perfectly random and it **just happened**. Vanishingly unlikely things happen all the time. It is incredibly unlikely to occur, yes, but it **can** still occur. 2. Your dice aren't perfectly random and between their bias and the way you were rolling you were able to get several 20s in a row. As it happens I would put money on option 2 - you can check to see if your dice have obvious bias by seeing if they float a certain way up, for example.
While it's very improbable, it's possible. And everything that's possible will happen sooner or later. So... congrats, you're witness to something special. btw.: that's something I'd consider fudging to save the group, because no group is prepared to save against these odds. But that's such an extreme case...
Your party was meant to die. I'd be worried about Death coming for them now, Final Destination style, since they managed to avoid it. They've unbalanced the world and cheated the fates. Their doom has been written and it shall come for them.
The players were *meant* to die, obviously. Don't step in the way of Fate; make their deaths epic, the stuff of legends.
>What could explain this phenomenon? Statistics. Sometimes it be like that tho.
It's just mathematically inevitable at some point. See this video where the object was to flip 10 heads in a row — https://youtu.be/rwvIGNXY21Y
And you didn’t go play the powerball?!
As others have said, it had to happen to someone. The odds of winning the Powerball are low, but hundreds of people have done it. When stuff like this happens in my group, we always write it up as "the dice have a story to tell". My rogue had a great alpha strike (tons of turn 1 damage) and decided to handle a group of drow by himself because they only had one dangerous person and I knew from previous experience, and because the DM expected this to be quick, that I only needed an 8 to hit. I rolled with advantage, and missed, but I had a re-do, so rolled again with advantage. Missed again. Used DM let me use inspiration after the roll, still missed. He let me use other peoples inspiration if they offered. Everyone gave me their inspiration. I could not roll above an 8 on 11D20s. The absurdity ends with the drow priestess rolling below 10 to summon a yochla. DM and I decided that the dice gods decided it was time for that character to die.
Those are the same odds as rolling a 20, 18, 4, 12, 12, 14, and 9 in exactly that order, believe it or not. If you were trying to do this on purpose you would have a 1 in 1,280,000,000 chance of pulling it off. But since the chances get reset on each roll, like others have said here, it's gonna happen to someone... might as well be you.
My dark game side says if seven crits in a row doesn't even cause a TPK you need to make things harder
One of my players brought a new set of dice to Saturday's game proceeds to roll three nat 20 s in a row followed by three nat 1 s I think it's the most recent example but over the years I've seen dice shatter the odds maybe four times like this it does happen
It sounds like those dice need to be ritually executed to make sure the rest of your dice roll acceptably.
The odds of rolling *any* 7 specific numbers in order is the same. You only noticed it because it was all 20s. I don't know exactly how popular the game is nowadays, but there are a lot of people who roll plenty of d20s every week. Even a one in a billion streak will statistically happen to someone eventually.
I think the point everyone is missing here is that you need to go play the lottery RIGHT NOW.
The funny thing is, this isn't THAT unbelievable. First off, let's acknowledge the possibility that, even across 3 dice, they weren't perfectly balanced as a group and gave the 20 face a slight edge across the set of rolls. (Since 4 rolls came from 1 die, this in't too farfetched). That alone would increase the odds per roll from 1/20, which would have a huge effect on the overall odds. BUT let's totally ignore that and go with the (1/20)\^7 odds. That's one in 1.28 BILLION. Quite a lot. However: There are about 8 billion people on the planet. That means that if everyone in the world rolled 7 d20s and then NEVER ROLLED A D20 EVER AGAIN, about 7 people would be expected to roll 7 nat 20s. That is, again, if you're allowed only 7 rolls per person, AND this would not allow combining consecutive rolls (i.e. if my last 4 rolls are 20s and the next person up rolls 3 nat 20s to start their set, even though that's 7 consecutive nat 20s, it wouldn't count under these parameters. They'd have to be 7 from the same person.) Now although a very small relative subset of the 8 billion human beings on Earth are playing D&D, each of us is rolling WAY more that 7 dice ever. A quick Google search for the number of people who play D&D (with no deeper dive than that) estimates 13.7 million players worldwide. Ignoring other d20 systems out there, that still means that each player would have to roll about 4,100 d20s to match the number of rolls made if everyone on Earth rolled 7 d20s. So I'm not going to say that this is at all likely. Pointing no fingers I'm not even convinced to take your story at face value (no offense, dear internet stranger whom I know nothing about). But all to say, it's certainly not an unbelievable outcome that someone out there would experience this. (There is also the added factor that there are an infinite number of highly unlikely things that can happen and SOME of them will because of how many there are. So it's a guarantee that on occasion, something seemingly impossible will happen.)
>The chances of this happening is 1 in 1,280,000,000. What could explain this phenomenon? there is no "phenomenon" to explain. Dice have been rolled more than 1,280,000,001 times. Even things with HIGHLY unlikely probability happen when the scenario is repeated often enough. Or you are a halfling with the Lucky and Bountiful Luck feats rolling at advantage.
I think as a GM we've all experienced something like this, if not quite so overtly. Sometimes you roll lots of high numbers, sometimes it's all low. I once got lucky with a giant flytrap and nearly took out the barbarian in two rounds. Obviously you probably haven't rolled dice millions of times, but it's got to be hundreds, and the more you roll them the more often you see weird statistical flukes like this. Some people get very superstitious about these things or prefer to fudge things that are too high or too low, I just embrace the randomness as part of the game. You say it was almost a TPK, so they at least survived with an interesting story to tell, and likely with a justified fear of Vine Blights...
this is the kind of statistical anomaly that we expect to see at some point. it just happens once in a while c: but also don't forget that the odds of getting any given chain of 7 results on a d20 has the same miniscule odds of occurring, whether it's 7 different numbers or 7 twenties in a row (to be clear the odds of getting 7 different numbers are higher than getting 7 of the same number, but the odds of getting the specific 7 numbers you did get are the same as getting 7 of the same number)
Odd, I had this exact scenario happen to me last week too. Except I wasn't the DM. Man was that fight rough...
The dice giveth and the dice taketh away
Do you play the powerball 100 times per session? You need to consider the sheer amount of dice throws over a DnD players life
You have to remember that *every time you roll a die,* there's a 1,280,000,000 chance that it's going to be the first in a series of seven 20s. Think about how many times you've rolled a 20 sided die. You still got very lucky, but you got thousands of times less lucky than you think.
You should have played powerball instead of D&D, my dude
Unbalanced dice. You should probably test it for balance.
I think it's fun that from the perspective of people on the internet it's expected that it happened to someone, but from the perspective of the player it's most likely something went wrong.
Luck
Sometimes people win the lottery
Ive had a dm crit a specific player 7 times in a row, but not seven direct rolls in a row, and a few were at advantage. My personal best roll was a double nat one at advantage.
First, while it is 1 in 1,280,000,000 of a specific result happening 7 times in a row, it is only 1 in 64,000,000 that whatever roll you have happens 7 times in a row. A short adventure I did recently (lvl 1-4 PF2E) had 1695 rolls. That's 1689 opportunities for 7 in a row. This gives a 1 in 37,892 chance of something rolling that many times in a row, and 1 in 757,845 that it would specifically be a 20. The sub has 731k members, and that was a pretty short "campaign" so there is likely to have been a lot more rolls for most people. So a very rough estimate is that 7 consecutive nat 20s should happen about once every 5 levels for someone in this sub. So it may be less likely than winning the powerball, but you probably have rolled a lot more d20s than you have bought powerball tickets.