Roll a D20 an infinite number of times

>Roll a D20 an infinite number of times
>Never roll a 1

Is this theoretically possible?

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en.wikipedia.org/wiki/Repeating_decimal
en.wikipedia.org/wiki/0.999...
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yes

theoretically its possible to only roll 8s

It's just a chance so, yes. But with each roll you're in danger in rolling a 1. I'm probably not the best person to say, I'm sure an user can give a much more detailed explanation whether it's impossible or not.

That doesn't make sense.

Yes, but with each roll the chances of it happening continue to get lower. Someone will know the math; we have several resident mathfags who love to post about the mathematical mechanics of dice and probability.

why

Well, not really. The probability of rolling any number not a 1 is 95% consistently so long as the dice are assumed to be balanced and the rolls are truly random. The probability that trend continues is unlikely, but the probability of each individual roll never changes

>infinite
>never

Pick one.

It is a basic limit problem. As you keep rolling the dice, the chance that you don't roll a 1 gets smaller and smaller. The number infinitely approaches zero, but never actually reaches it. Meaning that it is theoretically possible, just not practical.

Improbable. But not impossible.

you see, OP said infinite. assuming a perfectly fair d20, in an infinite number of rolls, every number happens the same amount (1/20 of the time)

Yes, if you can control your rolls.

As the number of trials approaches infinity, the probability of not rolling a one at least once also approaches 0.

That being said, there is nothing useful you can draw from this, as it is impossible to roll a die an infinite number of times. Any finite number of times, however, has an extremely small chance to not roll a 1.

The presentation of this idea has always bothered me.
The possibility of rolling a 1 on a 20 cited die is always 5%.
The possibility of rolling a 1 twice in a row is less and so on.
No matter how many times you've rolled a one, if you roll the die there will be a 5% chance of getting a 1.
Just making that clear.

Possible but highly improbable.

>Yes, but with each roll the chances of it happening continue to get lower.

To explain the math here, think of it in terms of limits. The base chance of not rolling a 1 on a fair d20 is 0.95. The chance of not getting a 1 when you roll twice is (0.95)^2 or 0.9025.

Let n be the number of times you roll a fair d20. So the limit as n approaches infinity (roll it an infinite number of times) is (0.95)^n which approaches 0. It is a minuscule number that is so close to 0 you can say it is 0.

So possible but highly improbable.

>there is nothing useful you can draw from this

Let's say that physical reality persists in some infinite fashion. Does this mean that every possible animal will exist at some point?

>roll a d20 an infinite number of times
>is this theoretically possible

no

case closed

the part about rolling a 1 doesnt even come into the equation

>The number infinitely approaches zero, but never actually reaches it. Meaning that it is theoretically possible, just not practical.
Wrong, as the trials approach infinity, the limit also approaches 0. It is impossible to not roll a 1 during an infinite number of trials, as the probability is 0. It being "improbable" implies a finite number of trials.

There are many different kinds of infinity, user. First we must define what every possible animal is: is it every possible species that would fall under our definition of animal? Is it any motile form of organic life? Is it any motile form of life at all? Is it every any any individual of any kind of life? Is it every and any possible state of that individual that may or may not exist at any time?

See
and
It like halving the distance between two points. Technically you never reach the second point, no matter how close you get. But that's theory not practical reality.

>Technically you never reach the second point, no matter how close you get. But that's theory not practical reality.
Close; you do arrive at the second point as soon as you reach the time required to arrive at it. You only approach that point while you are approaching that time.

>First we must define what every possible animal is:

>is it every possible species that would fall under our definition of animal?

I had something like this in mind.

No. You will roll exactly an infinite number of 1's.

>It is impossible to not roll a 1 during an infinite number of trials, as the probability is 0.
I agree with the other user. It approaches 0 but infinity never ends so while practically it's impossible, it never actually reaches the end and never actually reaches zero just like those pesky two points.

Surely you must eventually roll a 1.

If we assume a fair dice, the chance of not rolling a 1 is 0.95. Raise 0.95 to increasingly large powers (approaching infinity) and you'll find yourself quickly approaching 0% chance of it happening.

Shut the fuck up.

>It like halving the distance between two points.

Zeno's paradox. If I remember right, the solution is that the sum of all those infinite half-steps is 1. Infinite geometric series.

>Close; you do arrive at the second point as soon as you reach the time required to arrive at it. You only approach that point while you are approaching that time.
What are you talking about? You only halve the distance. No matter how small the distance it is, half the distance still remains.

In theory but not in any practical terms

There is no difference between 0.0 repeating and zero. If the probability is infinitely small then it IS zero.

Only if you halve the steps of time you are taking.

>No. You will roll exactly an infinite number of 1's.

Yes.

>theoretically its possible to only roll 8s

Somehow all of these are correct.
Infinity, ladies and gentlemen!

>Somehow that's correct.

Is it safe to say that infinity is evil?

No it is not.

Rolling a 1 on a d20 is a 5% chance. If you roll an infinite number of times, then you will roll a 1. Now, whether it will actually be 5% of the time is debatable, but you will definitely roll at least one 1 in an infinite number of rolls.

Almost

Actually, that paradox falls apart when you factor in plank length.

What if the die had 2 sides that read 11 and no side that read 1?

Except that the probably was never 0.0 repeating instead it is 0.000000...01 where the zeros preceeding the 1 are infinite. Therfore, infinitely small, but still not zero.

Where are you deriving "the time required to arrive at it"?

Yeah

No, but it's a dirty word.

Something is not nothing, and there's always 19 other faces for it to land on. There's ALWAYS the chance for the one to not come up with every roll.

Fuck the stats approach. You can never reach infinity - you can always roll again, and you are going to roll until you roll a 1. Therefore, you are going to roll a one before you reach infinity. QED it is not possible to roll an infinite number of times without rolling a 1.

No.

Because you cannot roll a d20 an infinite number of times. You are mortal, and therefore have a finite lifespan, and thus a finite number of times you can roll a d20.

>falls apart when you factor in planck length
Well, what doesn't when you get there?
We're talkin' theory here.

One third is 0.3 repeating. Two thirds is 0.6 repeating. Three thirds is 0.9 repeating. Three thirds is also 1. What is the difference between 0.9 repeating and 1?

Infinity is infinity because there is no end to it. There is no ..01 because there can't be.

This is why we have limits in mathematics, because of stupid people like you.

You just move half a planck length forward

Also, it is recurring, not repeating... How's common core going kido?

From your speed; if you move x distance in t tine, than you will move x/2 distance in t/2 time, and x/4 in t/4, and x/8 in t/8, and so on, assuming no acceleration.

en.wikipedia.org/wiki/Repeating_decimal

The outcome of one roll does not influence the next

You can roll it an unlimited amount of times and only roll (2-20) , yes.
You cannot roll it an infinite amount of times and not roll a single one.
The reason behind this is, if something is done infinite times, every possible result will occur.
It can be done an unlimited amount of times in a row and only have a single result , becuase unlimited does not imply the trial is done infinite amounts, it just means there is no determined inner limit to amount of times you can roll a (2-20) In a row.

...

And you move either 0 plank lengths forward or 1 plank length forward. A plank length is literally a physical limit as to how small a distance you have to move. Anything less and it is not movement. Also, theories like this are utterly dismissed as useless because it's just another "Has no impact on anything physical and is disproven by tapping two pencils together."

>The outcome of one roll does not influence the next

You say that, but what about quantum physics?

I.... have very mixed feelings about this post

>There is no ..01 because there can't be.
It's there.
It's waiting for us at the end of infinity.
3/3 equals 1 and not .9 repeating in the same way that Infinity divided by Infinity equals 1.

No. You cannot roll infinite times.

>You cannot roll infinite times.

but gods can

You assume much and know little.

This guy gets it. There is a difference between "an arbitrarily large number of times" and "an infinite number of times."

It's impossible to roll a d20 an infinite number of times in practice, everything we're discussing is purely theoretical and theoretically speaking it is possible that you will never roll a one. Just improbable to the point of impossibility.

>Infinity divided by Infinity equals 1
>being seriously so wrong
What are infinity cardinals for 200, Alex?

As surely as .5 is half of 1 and .25 is half of .5 there's a half for all things. You'll never move a half planck with that kind of motivation.

>Also, theories like this are utterly dismissed as useless because it's just another "Has no impact on anything physical and is disproven by tapping two pencils together
I like to call this the difference between something being true and something being effectively true. You don't reach the other point but you effectively do.

>at the end of infinity

Just... read that statement back to yourself.

Jesus user, can we not get that far into this?

I like this configuration.

OP is effectively a faggot, even if he hasn't actually sucked a cock yet.

>What are infinity cardinals for 200, Alex?

Actually, the solution is that space and time are not infinitely divisible.

Even though it is true that the infinite half-steps of distance all add up to 1, and the half-steps of time approach zero, that still does not address the fact that the half-steps never actually REACH zero time to accomplish. Thus, you have an infinite number of steps to complete, all of which require a non-zero amount of time. Therefore, you can never reach your goal, as the time required is infinite -- no matter how much time you spend travelling, you still require just a *tiny* bit more to make that last step. And once you do, you find it wasn't actually the last step, and you still need a *tiny* bit more, etc. etc. literally ad infinitum.

The only way to terminate the series is if the remaining distance and/or time cannot be further divided, due to reaching an inherent minimum unit of reality, so you're forced to "round up" and finish. We don't know how big or small these minimum indivisible units of space and time are, but we can know that it must exist. At least assuming we're rejecting Zeno's conclusion that movement is in fact impossible and all that we perceive as such is simply an illusion.

>Is this theoretically possible?
Yes.


Probability (P, expressed as a decimal between 0 and 1) of getting at least one nat 1 on a fair d20, over the course of N rolls:

P = 1-(0.95^N).

As N approaches infinity, P approaches 1.

Take a relatively small arbitrary number, like 200, and put it in there, and you get about P= 0.99996.


So, it is theoretically possible, but I'm not putting any money on it.

No, because you can't roll a D20 an infinite number of times. Bad question. Ask a bad question, get a bunch of bad answers. Also you're making inherent assumptions about the nature of the die. It it had no 1 on any of its faces, then the answer is "yes, of course, you moron."

If you mean "what is the probability an event A with p=0.05 never happening over N trials as N approaches infinity?" then the answer is 0, so, no, you cannot never roll a 1. Mathematically this reduces to lim(0.95^N) as N->infinity which evaluates to 0.

Also Zeno's paradox holds water only if space and time are both infinitely divisible. This is not an assumption that can be reasonably tested, but Max Planck's theories claim that space is NOT infinitely divisible, undermining the assumptions behind Zeno's paradox and making it invalid.

How so? That is the definition of speed. Acceleration would not change the problem, so long as we knew the initial acceleration (and its rate of change, if any) as well as the initial velocity.

Just... ask yourself what you hoped to accomplish with that post.

>Jesus user, can we not get that far into this?
>Wheredoyouthinkyouare.jpg

It's only theoretically possible as long as you have a finite N. As soon as your N stops being finite, it is not theoretically possible.

Only if you can control enough factors to deterministically throw the die. In a similar vein, there is a robot that appears to be able to do it with a coin, but without testing it an infinite number of times its accuracy being 100% cannot be experimentally shown.

What if, in the process of repeatedly halving the distance between theoretical points, I pause for a cigarette?

Physically, you can't halve a Planck length.

>Is this theoretically possible?

No.

Also,
0.9... = 1
Achilles reaches the tortoise
Zeno's arrow is moving, he just didn't know about special relativity and frames of reference
The other twin is older due to multiple different inertial frames during his journey
Cooperate with the other prisoner if you don't know when the game ends, backstab him if you do
The cat is a macroscopic object so quantum effects aren't noticeable at that size, but it's true of small particles
There are no hidden variables, Einstein was wrong
Switch the goddamn door when Monty gives you the option

Also next time you should go to Veeky Forums if you need help with high school math and physics problems

No. If you roll a fair D20 infinite times, you will get a 1. The odds of not getting a 1 start at 19/20 at n=1, and becomes zero as n approaches infinity. It's possible to get no 1s in any given number (even if you were to roll it multiple googolplexes of times or whatever arbitrarily large number you prefer), but you will always get an even number of each outcome if you roll infinite times.

Yes, that's been brought up.
The post you are responding to was in response to an user who was bringing in time to arrive for some reason.

He's got you there user

memes

Fuck your metal dice. You're not infinitely rolling that on MY table.

>0.9... = 1
No.
3 times 0.3... = 1

>Switch the goddamn door when Monty gives you the option
This is not always right either.

>The cat is a macroscopic object so quantum effects aren't noticeable at that size
Excuse you.

Is that somehow an established meme?
Or are you just broken?

en.wikipedia.org/wiki/0.999...

>not knowing that memes are the base unit of all reality
Get back to me when you finish memetics 101, slugger.

Looks like the answer to this question is no. But what about rolling an infinite number of dice an infinite number of times? Would any of those infinite dice never roll a one?

>There is a difference between "an arbitrarily large number of times" and "an infinite number of times."
This. Infinity does not just mean "really really large." It means forever. You cannot have a positive probability that never occurs in infinity because it NEVER stops checking. With a finite chance, you can get to the end and find yourself lucky. The whole POINT of infinity is that it doesn't HAVE an end.

This is also why limits taken to infinity have coherent answers. The limit of the summation of 1/(2^N), where N=1 and goes to infinity is equal to 2. Not alllllllllmost 2, or 1.99999....999998, but literally 2. That's because when it goes to infinity, it goes *all the way* to infinity.

See

no you fucking ape

You are right, it is easier than that. That is Aristotle's solution with the assumption of infinitely divisible space and time being wrong as you said. Apparently the infinite geometric series is an exhaustive solution by Archimedes made with the assumption being right.

But how is the word "memes" a fair answer to the question?
>inb4 because memes

The way I explain this to people is the infinite hotel metaphor.

If a hotel has infinite rooms, and infinite guests in all those rooms, but someone show's up asking for a room how does the manager accommodate him?

This; people always say "the limit as x approaches n", rather than "the limit of x at n"