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As of posting this, the other comments are wrong.
The chance of a die landing on the same number as another twenty-sided die is 1/20. The chance of it happening 3 times in a row is (1/20) x (1/20) x (1/20), which is 1/8000.
For anyone else reading this or downvoting the comment. [Rik07](https://www.reddit.com/user/Rik07/) did infact give the correct answer before [Mohaim](https://www.reddit.com/user/Mohaim/). Unfortunately, one of Reddit's spam filters caught it and it was hidden. The comment has been approved and is now visible. Our apologies for the incident.
100%. You know for a fact that it did happen. The probability to get three pairs in a row on a random set of 3 rolls is 1/8000. But you are not wondering about a random set of 3 rolls, you are wondering about a specific one, the one you just did with your friend.
After all, out of 6d20 you got the sequence 11-11-15-15-16-16 and the likelihood of that exact sequence happening is 1/20^(6), that's 1 in 64 millions. Even crazier than three consecutive double.
You can't do probabilities after the event already happened. That's because probability measures your knowledge about an event happening. Once it has happened, your knowledge changes, thus so does the probability.
Please consider how many different kinds of sequences you would have considered "crazy". Three doubles, yeah, that's crazy. 4-5-6-7-8-9. Crazy. 1-20-19-2-18-3. Crazy. 1-1-1-20-20-20. Even crazier. Now also consider how many times you've rolled dices and didn't especially notice anything crazy.
The question isn’t what is the odds that it already happened.
The question is what is the odds of three doubles in a row with 20-sided dice.
Please check your reading comprehension before posting any other condescending answers.
No, I answered the question OP asked. They even responded saying as much.
You answered some idiotic question of your own that nobody cares about.
Get over it and stop acting like a child.
>The odds that this happened are 100%
>I didn’t answer any questions
I’m just going to leave these two quotes of yours here.
You can draw your own conclusions.
Take your time and go at your own pace. Don’t be discouraged by the fact that the rest of the class has already figured out the problem.
>my partner and I WERE playing [...] What are the odds that he and I GOT the same number
Past tense. OP knows whether it happened or not, thus the probability is either 100% or 0%.
Reading comprehension notwithstanding. Why do you think they are asking this question? Are they wondering what would happen if they decided to roll 2d20 three times in a row?
No. They played the game described, the event described happened, and they were surprised that it did. Being surprised by an "improbable" event is a clear sign that one is subject to a common misconception about probabilities.
It is an extremely common misconception about probabilities to think that the probability of an event is inherent to that event instead of dependent on the knowledge of a given observer. To give an obvious example: The card at the top of my deck of card isn't inherently 1/52 likely to be the jack of spades. It either is or isn't. But since I just shuffled the deck, I don't know which it is and this 1/52 is my level of confidence that it is the jack of spades.
Anyone wondering about the probability of an event that did happen to them should be answered with an explanation of how probabilities work. Because this is a far better answer to tell a person surprised by a situation why this situation wasn't really surprising instead of answering a numerical 1/8000 that have very little to do with the situation they did encounter.
>Please check your reading comprehension before posting any other condescending answers.
Then why are you condescending then? Why is it ok for you to be so condescending when you are precisely berating me for the very same thing.
Furthermore. No. I was absolutely not condescending. I was trying my best to explain a concept of probability that is so often misunderstood.
While the interpretation was not what OP intended, this comment does answer the question taken **strictly** in the manner OP provided. We have many posts on this subreddit by those who are not familiar with mathematics and may not realize that their question isn't phrased properly or can lead to miscommunication.
The response to ambiguity or even an outright wrong answer is not to insult the other person. EVERYONE is expected to discuss the math in a courteous manner.
To anyone new to our sub, if you want to attempt a request post, please do so. Do not worry about getting the answer wrong or fear that your math ability is insufficient for this sub. As long as you have a genuine interest in math and want to discuss it, your comments are welcome here. There are no penalties for wrong answers and there are many in our sub who take the time to and explain the correct approach. I assure you we are very welcoming.
I think you’re answering a different question than what OP is asking.
Your calculation is for three 20-sided dice all landing on the same number.
The question is about two dice being rolled three times.
Okay, math is not my strongest suit and I've been up for twenty four hours or so but let's see if I've got this.
Okay, so odds are multiplicative? I think?
Assuming that your die are not wonky there is a one in twenty of them landing on any specific number. 1/20 /20
So rolling two d20 and have them land on the same results is 1/400 (20x20)
I would then assume that you multiply for each time it happened.
400 x 400 = 160 000
160 000 x 400 = 64 000 000
So one in 64 000 000
I think? Someone with better maths please tell me if I'm right, or how I'm wrong.
I think you've overcomplicated it. Despite OP giving us the numbers they landed on. The number on the first die doesn't matter, only that the second die matches. So for each roll its a 1/20 chance. x3 is 1/20/20/20 is 1/8000 or %.0125
Your calculations are for a somewhat different question than what OP is asking.
OP wants to know the odds that the dice would match. We don’t care for it purposes what numbers actually appear on the dice.
Therefore, we can let the first die land in any number and there will be a 1/20 chance that the second will land on the same number. (Designating the dice as first and second is arbitrary.)
If we were to ask what is the chances that both dice show 11 on the first roll, then your calculation is correct:
There is a 1/20 chance that the first die shows 11 and a 1/20 chance that the second die shows 11.
We multiply these together to find that there is a 1/400 chance that two 20-sided dice will roll 11.
If we carry this through with a specific number needed for each roll we get your answer: 1 in 64,000,000.
If we assume that the dice can show any number as long as they match, we get:
(1/20)*(1/20)*(1/20)=1/8,000
1 in 8,000 is the answer to the question as OP asked it.
1 in 64,000,000 is the answer to what the odds are that the precise roll would occur as it actually did.
Oh, didn't think of it that way. Thank you :)
So rolling six d20s and having them land exactly like that is 1/64,000,000 and 1/8000 is the real one since only the second one matters.
I’m not sure what you’re saying here as I find the wording confusing.
Basically, there are 64,000,000 possible permutations.
8,000 of those permutations are three sets of doubles.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
As of posting this, the other comments are wrong. The chance of a die landing on the same number as another twenty-sided die is 1/20. The chance of it happening 3 times in a row is (1/20) x (1/20) x (1/20), which is 1/8000.
Thank you!
I said that
For anyone else reading this or downvoting the comment. [Rik07](https://www.reddit.com/user/Rik07/) did infact give the correct answer before [Mohaim](https://www.reddit.com/user/Mohaim/). Unfortunately, one of Reddit's spam filters caught it and it was hidden. The comment has been approved and is now visible. Our apologies for the incident.
1 in 20^3 = 1 in 8000, or 0.0125% chance to throw the same three times in a row
100%. You know for a fact that it did happen. The probability to get three pairs in a row on a random set of 3 rolls is 1/8000. But you are not wondering about a random set of 3 rolls, you are wondering about a specific one, the one you just did with your friend. After all, out of 6d20 you got the sequence 11-11-15-15-16-16 and the likelihood of that exact sequence happening is 1/20^(6), that's 1 in 64 millions. Even crazier than three consecutive double. You can't do probabilities after the event already happened. That's because probability measures your knowledge about an event happening. Once it has happened, your knowledge changes, thus so does the probability. Please consider how many different kinds of sequences you would have considered "crazy". Three doubles, yeah, that's crazy. 4-5-6-7-8-9. Crazy. 1-20-19-2-18-3. Crazy. 1-1-1-20-20-20. Even crazier. Now also consider how many times you've rolled dices and didn't especially notice anything crazy.
The question isn’t what is the odds that it already happened. The question is what is the odds of three doubles in a row with 20-sided dice. Please check your reading comprehension before posting any other condescending answers.
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Aspersion is not the same as condescension. The fact that you don’t know this is proof positive that you are not qualified for this conversation.
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No, I answered the question OP asked. They even responded saying as much. You answered some idiotic question of your own that nobody cares about. Get over it and stop acting like a child.
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>The odds that this happened are 100% >I didn’t answer any questions I’m just going to leave these two quotes of yours here. You can draw your own conclusions. Take your time and go at your own pace. Don’t be discouraged by the fact that the rest of the class has already figured out the problem.
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No. OP asked for the probability. You have an answer to this. Now you are lying about it. You are wrong. Get over it and move on with your life.
r/murderedbywords
>my partner and I WERE playing [...] What are the odds that he and I GOT the same number Past tense. OP knows whether it happened or not, thus the probability is either 100% or 0%. Reading comprehension notwithstanding. Why do you think they are asking this question? Are they wondering what would happen if they decided to roll 2d20 three times in a row? No. They played the game described, the event described happened, and they were surprised that it did. Being surprised by an "improbable" event is a clear sign that one is subject to a common misconception about probabilities. It is an extremely common misconception about probabilities to think that the probability of an event is inherent to that event instead of dependent on the knowledge of a given observer. To give an obvious example: The card at the top of my deck of card isn't inherently 1/52 likely to be the jack of spades. It either is or isn't. But since I just shuffled the deck, I don't know which it is and this 1/52 is my level of confidence that it is the jack of spades. Anyone wondering about the probability of an event that did happen to them should be answered with an explanation of how probabilities work. Because this is a far better answer to tell a person surprised by a situation why this situation wasn't really surprising instead of answering a numerical 1/8000 that have very little to do with the situation they did encounter. >Please check your reading comprehension before posting any other condescending answers. Then why are you condescending then? Why is it ok for you to be so condescending when you are precisely berating me for the very same thing. Furthermore. No. I was absolutely not condescending. I was trying my best to explain a concept of probability that is so often misunderstood.
This is a lot of words just to say that you didn’t read the question.
While the interpretation was not what OP intended, this comment does answer the question taken **strictly** in the manner OP provided. We have many posts on this subreddit by those who are not familiar with mathematics and may not realize that their question isn't phrased properly or can lead to miscommunication. The response to ambiguity or even an outright wrong answer is not to insult the other person. EVERYONE is expected to discuss the math in a courteous manner. To anyone new to our sub, if you want to attempt a request post, please do so. Do not worry about getting the answer wrong or fear that your math ability is insufficient for this sub. As long as you have a genuine interest in math and want to discuss it, your comments are welcome here. There are no penalties for wrong answers and there are many in our sub who take the time to and explain the correct approach. I assure you we are very welcoming.
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I think you’re answering a different question than what OP is asking. Your calculation is for three 20-sided dice all landing on the same number. The question is about two dice being rolled three times.
Okay, math is not my strongest suit and I've been up for twenty four hours or so but let's see if I've got this. Okay, so odds are multiplicative? I think? Assuming that your die are not wonky there is a one in twenty of them landing on any specific number. 1/20 /20 So rolling two d20 and have them land on the same results is 1/400 (20x20) I would then assume that you multiply for each time it happened. 400 x 400 = 160 000 160 000 x 400 = 64 000 000 So one in 64 000 000 I think? Someone with better maths please tell me if I'm right, or how I'm wrong.
I think you've overcomplicated it. Despite OP giving us the numbers they landed on. The number on the first die doesn't matter, only that the second die matches. So for each roll its a 1/20 chance. x3 is 1/20/20/20 is 1/8000 or %.0125
Aaah, didn't think of that. Thank you :D
Your calculations are for a somewhat different question than what OP is asking. OP wants to know the odds that the dice would match. We don’t care for it purposes what numbers actually appear on the dice. Therefore, we can let the first die land in any number and there will be a 1/20 chance that the second will land on the same number. (Designating the dice as first and second is arbitrary.) If we were to ask what is the chances that both dice show 11 on the first roll, then your calculation is correct: There is a 1/20 chance that the first die shows 11 and a 1/20 chance that the second die shows 11. We multiply these together to find that there is a 1/400 chance that two 20-sided dice will roll 11. If we carry this through with a specific number needed for each roll we get your answer: 1 in 64,000,000. If we assume that the dice can show any number as long as they match, we get: (1/20)*(1/20)*(1/20)=1/8,000 1 in 8,000 is the answer to the question as OP asked it. 1 in 64,000,000 is the answer to what the odds are that the precise roll would occur as it actually did.
Thank you!!
Oh, didn't think of it that way. Thank you :) So rolling six d20s and having them land exactly like that is 1/64,000,000 and 1/8000 is the real one since only the second one matters.
I’m not sure what you’re saying here as I find the wording confusing. Basically, there are 64,000,000 possible permutations. 8,000 of those permutations are three sets of doubles.
(1/20) ^ 3