Here I thought I was going to get some crazy advantage in board games but I already knew this one. The gaming store I go to has a challenge every Friday night and they play a game and the winner gets a $5 gift certificate. One Friday they brought out a cup of dice and they explained that they were going to roll the dice in the first person to guess what number was rolled correctly was the winner. They recorded everyone's guess in order and someone else counted what the dice rolls was. I literally counted the number of dice and multiplied it by 3.5 and I was spot on. lol
As a professional Dungeon Master, this phenomenon in probability, called the Bell Curve, is really important and useful when fine-tuning dice rolls for weapons, spells, rollable tables etc. etc. For comparison: the classic method to get your ability scores is to roll 4d6 and ignoring the lowest number. This should give you a range of 3-18 in which 10-11 are the highest probabilities. The way I do it in my games is by rolling 1d12+6, which gives a different range (7-18), but with every result being just as likely. This avoids 2 things: characters with a stat below 7 (which is already bad) and characters with stats that are "too flat" (in a full array of 6 abilities, getting 9, 10, 10, 11, 12, 13 is considered very flat). It also shows that the difference between a greatsword (2d6 dmg) and a greataxe (1d12 dmg) is not just that the minimum damage on a sword is 2, but that the sword hits much more consistently, which goes to show that it`s a more maneuverable and precise weapon, while the axe is more likely to get a 12, but also just as likely to get a 1.
a.k.a normal distribution or Gaussian distribution - the general term if PDF (Probability Distribution Function) as there are more depending on the problem
Just Imagine an ongoing series of numbers from 1 to 6 for example. If u Look for the literal middle of that sequence it's 3,5. It's Not what U devide by 2. It's what the middle of the sequence is showing Here V 1-2-3-4-5-6
@@mesmesd I understand. I am talking about my past experience with E(x). When it is solely theoretical, it can be hard to understand. But when it is applied it is easier to understand.
You're the only science teacher I've ever had that makes total and complete sense in such a simple way. Yes I say teacher because you have taught me so much already. I can't thank you enough for posting such spectacular content!! My favorite scientist on RUclips by far! Keep up the awesome work
D&D players know three six sided die make a bell-shaped curve, not a smooth one. You can also plot it by just number of combinations. Only one for 3 and 18, all ones and all sixes. But 4 and 17 can be 112 121 211 or 665 656 566 (3 combinations).. and so on.
A remarkable idea called Central Limit Theorem is at the heart of this interesting experiment. In fact the whole field of thermodynamics works because of the central limit theorem.
Can you elaborate please on how thermodynamics and CLT are so interconnected? Also, I've understood CLT slightly different than what is being shown here. This is showing an example of distributions of a sample. CLT I believe is taking distributions of samples and stating that the true representation of the population is going to be found within the distribution of samples. Please let me know what I'm missing here.
@@scriven-shafts basically, thermodynamics proposes that molecules of gases have different speed, but the most possible speed of the molecules is determined by temperature.
@@scriven-shafts Central limit theorem says that as you roll more and more dice, then no matter what the dice actually look like you will get a bell curve a.k.a. normal distribution. So yes, this experiment is very much a demonstration of CLT.
@@matejlieskovsky9625 thank you. I think I was thinking more an implication of the CLT rather than the actual rule. Your explanation makes sense and Google also says you’re right :)
If only this guy knew just how much he's done to help get my daughter into science. We watch all your videos and try to do as many experiments based off them as possible
When i was a kid, there's a lot dice gambling in my place. Each side of the dice represents an animal/object and you put your money on the animal/object you choose on the gambling paper. The dice is usually shake in a small dedicated gambling bowl and we have to guess the dice inside. I'm able to stimulate the movement of the dice inside by looking at the direction of the host's shakes and also hearing for the number of impact. I guessed 8 out of 10 times correct and the host told me to go away.
Worth mentioning that there are 6 ways to roll a 7 with 2 dice (5+2 and 2+5 are 2 separate outcomes). The video implies that the likelihood of getting a 7 is 3 times that of getting a 12, but its actually 6 times the likelihood.
Also like how he subtly mentions that he dropped those first 10 dice several times to get 35. Something to remember for the next time you see something really extraordinary in a video: you don't know how many takes it took to get it right. Not a knock on the Action Lab, I think it's great that he's demonstrating the principle.
This "knowledge" hited me when I was learning to play "The Game of Ur". You play with 4 "dices" that have an equal chance each on getting a 1 or a 0, then you sum up all of them and then move your piece. When I realized that the "most probable number" to get is a "2" and you make your moves believing you will most probably get a 2 on the next round, ohh boy, that improved my game ALOT!!
Nice video, though, statistically, you would have 6 options to get 7, 1-6 2-5 3-4 But also 6-1 5-2 4-3 Due to this, the chance of getting 7 as sum is 6x as high as getting 12, since 6-6 can only appear once: each die has a six, so the chance is 1/6×1/6=1/36.
My physical science teacher put on one of you’re videos, and I was like “I watch this guy all the time” and then me and him talked about our favorite video made by you. It was pretty cool
I sort of knew this from D&D crpgs, but didn't know how extreme it was. you think of 10d6 as being 10-60 damage, but yeah, maybe it's better to think of it as "around 35 damage".
To do this for dice with different numbers of sides, the average fo any one die is (highest value + 1) / 2. So 3.5 for six sides, 5.5 for ten, 11.5 for a d20, etc. To find the most common result for 2 or more dice, multiply the 1 die average by the number of dice. If it's a fractional result, the 2 adjacent numbers are tied for most common. So 7 for two d6's, 10 or 11 for three, 14 for four, 17 or 18 for 5, and so on. Doesn't work for a single die since all sides are equally common.
You learn this is middle school are you kidding me Or don't tell me that you are talking about complex possibilities, that can't be compared since this is basic
my friend and i experienced quite a few amazing/awkward statistic anomalies while playing backgammon: the top one would be rolling the dice for determining who starts the game: we got the same dice 4 times, each time we had doubles.
@@fullfungo But the joke was that it's impossible to get a 3.5, and that's not what L C was saying. L C was saying that even if you could get a 3.5, it wouldn't matter because with one die every side has an equal chance.
@@Interestking Robert made a joke, that 3.5 is the best guess, when it is, in fact, the worst guess. L C said, that the average cannot be applied to a single die, which is in fact the premise that the original joke was based on. So to me it seems like they missed the point of the joke (that the method of averages cannot be applied to a single die). I see no contradictions here.
The more dice you have, the closer you'll get to the prediction as a percentage of the value. But also, the more integers there are in that range near the center value. If I only roll 1 die, I'll get it within 3 every time and I'll get it exactly right 1/6 times. Not true for 100 dice.
3:11 to be precise, the possible combinations to get 7 are: 1-6 2-5 3-4 4-3 5-2 6-1 and to get 12 is only 6-6. So the probability of getting 7 is 6 times bigger than getting 12.
It's great that you want to teach Stochastic math as well. You've done a great job teaching it, although I could've wanted to be able to see the reason for this formulas, regarding estimated values as the equivalent for averages in random distributions. Another cool thing would've been to mention the importance of the Central limit theorem, as to the normal distribution that result from it in your last two analysis with 100 and 1000 samples. Big fan of your videos, keep it up with the good science ❤️🙌🏼
There actually is a chance to get a sum of 100 or 600 when you roll 100 dice. It's just incredibly small because all the dice would have to land on 1 or all on 6.
If you play Settlers of Catan, each of the number markers you place on the resource hexes at the beginning has one or more dots on the bottom. The number of dots directly correlates to the probability of that roll occurring. For instance, 6 and 8 have five dots each, which means there is a 5:36 chance of rolling either of those numbers. Likewise, 11 and 3 have two dots, meaning a 2:36 chance.
This is why 7 is the thief in Catan. Evens out your chances of getting anything else, with greatest chances being 6/8, 5/9, 4/10, 3/11, & 2/12 in order of most likely. Always put your pieces on 6/8, for those that play, but struggle with statistics.
You know, I've always sort of half understood this, but this feels like an "explain like I'm 5" video and I actually really appreciate that because now I totally understand why this happens.
I'm pretty sure I have more of a 75% chance of getting the starting side with a coin flip. I can easily get a 12 heads streak just by starting with heads up. I actually ruined a probability experiment back in highschool because of this.
I studied this in game design class because in pen and paper RPGs like Dungeons and Dragons, you can choose for instance a greataxe, which has a 1d12 damage, or a greatsword, which has 2d6. Besides the fact that the minimum damage on the sword is 2 instead of the axe's 1, you should choose the sword if you want to deal more average damage, whereas with the axe you can deal maximum damage (12) more consistently, but also minimum damage. The probability to roll of any number from 1 to 12 is exactly the same
I was about to send this to my roleplaying friends that are subbed to critical failures, until I realised, that it wouldn't work with a single D20 xD Roleplayers would naturally come to know this "rule", since we sum up dice values to get the average quite often (for exemple, when you need to roll 12d10 to find the health of a monster... Either you do it, either you take the average.
The order doesn’t matter for combinations, for example, which is why AB and BA are the same, and therefore would have half as many options than a permutation with pairs.
Not sure if you mentioned it in the video, but the mathematical term for the “average roll” is called “Expected Value”. Might be helpful if anyone is curious to research it. I’m sure you know expected value goes much further than just dice rolls as well. It can also be used to calculate expected winnings from casino games and other things as well. It’s a pretty interesting subject!
I designed an amplifier for aircraft with over a dozen resistors proportional to the gain. With 1% resistors there was a wide range of gain possible. The amps were mass produced and tested by a computer that sent me the data. I was shocked by how narrow a gain range was, right around nominal. My take away was the errors cancel more than add.
As far as I know, vantablack only absorbs visible light, and most mice with the exception of the ones with red LEDs use IR light, so they should be able to work.
This is the same reason a coin falling through a pachinko machine will usually land under the starting position. For each peg the coin can fall left or right, so for two peg layers it can fall LL for left, RR for right, and either LR or RL for middle. So there’s a 50% chance it lands in the middle, but only a 25% chance each for the left or right.
Before I see you predict your number, I'm guessing it's going to be thirty-five. That's the most likely of all outcomes. EDIT: Yup. Actually, one thing I wouldn't mind learning is how to figure out the odds of getting the more likely outcome.
You could have fun going down this rabbit hole with your viewers. How many people do you need in a room before the probability of two of them having the same birthday is greater than 50%? And the list of non-intuitive results in probability goes on and on.
How about the Monty Hall Paradox? This problem has even confused Paul Erdos. But there are some visualizations that make it easier to understand. It’s a falsidical paradox.
Respected sir🌟🌟, During interference of EM wave... electric field adds up like vector....if two electric field of EM wave of same amplitude ,frequency,inphase...when added by vector gives,E+E= 2E, but when we add Energy of E field WHICH IS PROPORTIONAL TO E^2...it contradicts (€E^2=2€E^2).... Similarly for distructive interference of two similar PLANE Em wave of PHASE DIFFERENCE of π interfering DESTRUCTIVELY COMPLETELY... IF E field becomes ZERO EVERY WHERE..... WHERE DOES ITS ENERGY GO?what is wrong here? Thank you sir 🌟
Wow man this a the best experiment i have seen in my life, im a psychology student who wrote a experiment called "The dice roll series" in wich the basic idea is to have a prediction of what the dices will do, i find this very scientifical and accurate in terms of deductive and inductive physics, blessings have beautiful week.
This in fact plays an important concept in statistics and mathematic. As long as you add a couple of random numbers (with any or better say random distribution) the results will always show a normal distribution. this is called central limit theorem.
Dice probability is a big part of Settlers of Catan strategy! The robber moves when you roll 7 because it’s the most likely, and therefore the most likely to throw a wrench into the gameplay.
In statistics it is called the regression toward the mean. The sum of the digits of the die is 21... the average, 21/6, is 3.5. A better question to ask is: what is the expected number of unique die faces that will show if I roll an N sided die n times? The answer is N(1-e^(n/N). Meaning that if you roll a die with 6 faces 14 times the expectation is that 5 or (N-1) of the six unique faces will show. This technique can be used to test the fairness of a die, especially those with a large number for faces. The roll rate of unique faces of a die come up the same as the time rate of radioactive atoms decay in a sample of radioactive material. So, for example, if you roll a 20 sided die 20 times then the expectation is that 20(1-e^-(20/20)) or 20(1-e^-1)=12.6 or about 13 unique faces will show (decay) in 20 throws of said die. If you roll that same die 60 times the expectation is that 19 faces (N-1) will show i.e. 20(1-e^-3)=19. Then using Excel for example, x,y plot the expected number of unique faces that show against the actual number of unique faces that show for 60 throws. Do this plot roll by roll. Then do a first order (linear) curve fit of the data. Let the slope of said curve fit be the judge of the die. I would think that a slope of 0.98 to 1.02 would indicate a fair die.
Always enjoy your videos... but this is a great way to explain a Normal Distribution... as well as explaining the mean and variance without using the techy terms. Simply terrif :))
wow, do i have some statistics to discuss with you! I'm currently in the throes of writing a book on the likelihood of (about 85% of the time) guessing the sum total of two fair six-sided dice. I've run the math through chatGPT (which had a quite arduous time even understanding the question but eventually was able to combine the permutations with the statistics related to guessing the outcome). would love to discuss more and show you a bit of what I've seen/learned and about which I've honestly freaked a little. great video, by the way! i learned a lot!
The number is called mathematical expectation, and any tabletop player knows it's the most important number in dice rolls (for example, in Warhammer leadership test is taken on 2d6 and need to roll below the leadership of the squad, so leadership 7 is considered almost the worst you could have, because of only 50% chances of passing the test). In many other games where something is rolled on 2d6, number 7 is also very important.
To the point you made towards the end, the odds of getting a 7 with two d6 is even higher because you can get it not only with the three combinations you mentioned, but also with their opposites (I.e 3+4 & 4+3, 5+2 & 2+5, 6+1 & 1+6) whereas with 12 it can only be achieved one way with a 6+6, so you’re 6 times more likely to roll a 7 than a 12 with 2 d6.
Add up the numbers of one to six on a single die. The total will be 21. 21 / 6 = 3.5. Not that hard to understand why the average will always hover around 3.5 * x where x is the number of dice used.
Could you tie this in with an explanation on quantum mechanics and how individual circumstances can do crazy amazing stuff but on large scale things stay ordinary
When it comes to probabilities, the big one I'd like to see is calculating the probability of 4d6, drop lowest. That's a surprisingly difficult problem.
It would be great if you've added a little extension about how the distribution is called, how it arises and what are its properties like variance and standard deviation - people often struggle a little with these concepts.
The distribution of a large amount of events is approximately gaussian and the standard deviation decreases (i believe by a square root factor) as you increase the number of events. Great to see stats intuition taught in such a short clip!
Here I thought I was going to get some crazy advantage in board games but I already knew this one. The gaming store I go to has a challenge every Friday night and they play a game and the winner gets a $5 gift certificate. One Friday they brought out a cup of dice and they explained that they were going to roll the dice in the first person to guess what number was rolled correctly was the winner. They recorded everyone's guess in order and someone else counted what the dice rolls was. I literally counted the number of dice and multiplied it by 3.5 and I was spot on. lol
wow that’s insane
I've tried with 1 dice, and never got 3.5
@@jamescollier3 bruh 😅
@@jamescollier3 lol
@@jamescollier3 keep trying! Don’t give up now when you’re so close!
Board Game Shop
Me: I want a dice.
Clerk: The correct term is 'die'.
Me: I want 2 die.
Clerk: plural is dice, single is die.
Me: I want 2 die single.
Lmaooo
What are you saying?
Clerk: Sure ☠️
Clerk: Ok, I'll step out for a moment .......
Lol, you made me laugh my lungs off
As a professional Dungeon Master, this phenomenon in probability, called the Bell Curve, is really important and useful when fine-tuning dice rolls for weapons, spells, rollable tables etc. etc.
For comparison: the classic method to get your ability scores is to roll 4d6 and ignoring the lowest number. This should give you a range of 3-18 in which 10-11 are the highest probabilities.
The way I do it in my games is by rolling 1d12+6, which gives a different range (7-18), but with every result being just as likely. This avoids 2 things: characters with a stat below 7 (which is already bad) and characters with stats that are "too flat" (in a full array of 6 abilities, getting 9, 10, 10, 11, 12, 13 is considered very flat).
It also shows that the difference between a greatsword (2d6 dmg) and a greataxe (1d12 dmg) is not just that the minimum damage on a sword is 2, but that the sword hits much more consistently, which goes to show that it`s a more maneuverable and precise weapon, while the axe is more likely to get a 12, but also just as likely to get a 1.
4d6 drop 1 has a mean slightly above 12, and 13 is the most common result. 10.5 is from a straight 3d6.
@@Reashu You are correct. I failed to mention that bit. I had 3d6 in mind, as it's simpler to represent.
I'm onto you DM. My DnD game has just leveled up. Should I cast fire ball or wait until the next encounter... The odds are in my favour.
This is a great idea. Saving this for future reference
a.k.a normal distribution or Gaussian distribution - the general term if PDF (Probability Distribution Function) as there are more depending on the problem
The expectation for a single die is 3.5. It can be hard to understand what this number means. But with more dice, it becomes easier to understand.
Just Imagine an ongoing series of numbers from 1 to 6 for example. If u Look for the literal middle of that sequence it's 3,5. It's Not what U devide by 2. It's what the middle of the sequence is showing
Here
V
1-2-3-4-5-6
Because there is no 0
Thanks for this. So the middle of 0-1-2-3-4-5-6 is 3.5 because there are 7 integers.
@@mesmesd I understand. I am talking about my past experience with E(x). When it is solely theoretical, it can be hard to understand. But when it is applied it is easier to understand.
Of you roll the dice 10 times you will get 35.
You're the only science teacher I've ever had that makes total and complete sense in such a simple way.
Yes I say teacher because you have taught me so much already. I can't thank you enough for posting such spectacular content!! My favorite scientist on RUclips by far! Keep up the awesome work
Veritasium, Mark Rober Smarter Every Day?
@@advaykumar9726 mark rover doesn’t explain the whole thing
He is an amazing educator.
@@advaykumar9726 They are too dramatic.
Maybe you would be more suited to a spelling teacher!!!
Me after watching this: Goes straight to Casino
I guarantee you that the casinos math game is stronger than yours-
Only reason I watched the video
@@barbarkuni8209 no
@@monk3811 😅
@@klizzyykicks1712 YEPPER!
*D&D players:* "WRITE THAT DOWN, WRITE THAT DOWN"
Farts*
That's why it's got dice with many sides, else there's be this combination advantage
🤣🤣🔥🔥🔥
@@barbarkuni8209 wtf?? 🤨
These bots are a plague even in RUclips. 🤦🏻♂️
D&D players know three six sided die make a bell-shaped curve, not a smooth one. You can also plot it by just number of combinations. Only one for 3 and 18, all ones and all sixes. But 4 and 17 can be 112 121 211 or 665 656 566 (3 combinations).. and so on.
The most impressive part is how fast he can count dice!
🤣
Those are jump cuts
@@AnudeepDONDONDONRlol no shit? I thought he was the flash 🤯
@@AnudeepDONDONDONRlol wooosh
i didn't notice the first cut and was like WTF BRO.
A remarkable idea called Central Limit Theorem is at the heart of this interesting experiment. In fact the whole field of thermodynamics works because of the central limit theorem.
Can you elaborate please on how thermodynamics and CLT are so interconnected? Also, I've understood CLT slightly different than what is being shown here. This is showing an example of distributions of a sample. CLT I believe is taking distributions of samples and stating that the true representation of the population is going to be found within the distribution of samples. Please let me know what I'm missing here.
@@scriven-shafts basically, thermodynamics proposes that molecules of gases have different speed, but the most possible speed of the molecules is determined by temperature.
@@quint3ssent1a Thanks!
@@scriven-shafts Central limit theorem says that as you roll more and more dice, then no matter what the dice actually look like you will get a bell curve a.k.a. normal distribution. So yes, this experiment is very much a demonstration of CLT.
@@matejlieskovsky9625 thank you. I think I was thinking more an implication of the CLT rather than the actual rule. Your explanation makes sense and Google also says you’re right :)
If only this guy knew just how much he's done to help get my daughter into science. We watch all your videos and try to do as many experiments based off them as possible
@BlueScreen nope
@BlueScreen Depends on what you’re studying. Physics is basically math in disguise.
@@mysticdragonex815 well it’s definitely a crucial part of science
@@mysticdragonex815 Math is what then? Cool trick on parties?
When i was a kid, there's a lot dice gambling in my place. Each side of the dice represents an animal/object and you put your money on the animal/object you choose on the gambling paper. The dice is usually shake in a small dedicated gambling bowl and we have to guess the dice inside. I'm able to stimulate the movement of the dice inside by looking at the direction of the host's shakes and also hearing for the number of impact. I guessed 8 out of 10 times correct and the host told me to go away.
I was literally just explaining this to a student in my statistics class yesterday! But you did much better 🤦♂️
It's a good day when The Action Lab uploads
Wtf @Okta Via
@@CreeperLava-cz6mi reported the bot ;D
@@naga_serpentis It will not matter for the bot if you reported it they have many thousand hacked accounts they use to then this shi*
Wait......@Okta Via a bot?
@@Commentify69 the future of RUclips’s gonna be this shiz with bots
Wonder if my dad’s prediction is gonna be right
Worth mentioning that there are 6 ways to roll a 7 with 2 dice (5+2 and 2+5 are 2 separate outcomes). The video implies that the likelihood of getting a 7 is 3 times that of getting a 12, but its actually 6 times the likelihood.
Also like how he subtly mentions that he dropped those first 10 dice several times to get 35. Something to remember for the next time you see something really extraordinary in a video: you don't know how many takes it took to get it right. Not a knock on the Action Lab, I think it's great that he's demonstrating the principle.
Stay mad
@@-Risk- 🤡
I can tell you from years of rolling dice I could legitimately roll under 300 without trying
Fühl ich
relatable :(
This "knowledge" hited me when I was learning to play "The Game of Ur".
You play with 4 "dices" that have an equal chance each on getting a 1 or a 0, then you sum up all of them and then move your piece.
When I realized that the "most probable number" to get is a "2" and you make your moves believing you will most probably get a 2 on the next round, ohh boy, that improved my game ALOT!!
just the most easy to listen to person I hope you keep rolling out videos
This guy is gonna break reality one day
Might happen That's For Sure
He won't. His reality is too statistically accurate.
D&D players: this is gold!
@@oktavia7246 no
I once accurately predicted someone else's dice roll 6 times in a row. As awesome as it should have been, she was freaked out and left.
Nice video, though, statistically, you would have 6 options to get 7,
1-6
2-5
3-4
But also
6-1
5-2
4-3
Due to this, the chance of getting 7 as sum is 6x as high as getting 12, since 6-6 can only appear once: each die has a six, so the chance is 1/6×1/6=1/36.
I thought it was gonna be about how you throw it and then get the number you want..but this is still amazing
My physical science teacher put on one of you’re videos, and I was like “I watch this guy all the time” and then me and him talked about our favorite video made by you. It was pretty cool
Physical Science teacher??? Tf?
@CR3ATiVE_SAURABH in high school or lower they will call chemistry or physics, chemical physics
I sort of knew this from D&D crpgs, but didn't know how extreme it was. you think of 10d6 as being 10-60 damage, but yeah, maybe it's better to think of it as "around 35 damage".
To do this for dice with different numbers of sides, the average fo any one die is (highest value + 1) / 2. So 3.5 for six sides, 5.5 for ten, 11.5 for a d20, etc. To find the most common result for 2 or more dice, multiply the 1 die average by the number of dice. If it's a fractional result, the 2 adjacent numbers are tied for most common. So 7 for two d6's, 10 or 11 for three, 14 for four, 17 or 18 for 5, and so on. Doesn't work for a single die since all sides are equally common.
Omg...my college professor failed to explain probability like you🔥🔥
If that is college material then I’m Newton
You learn this is middle school are you kidding me
Or don't tell me that you are talking about complex possibilities, that can't be compared since this is basic
Time to test this new found knowledge in Las Vegas
my friend and i experienced quite a few amazing/awkward statistic anomalies while playing backgammon:
the top one would be rolling the dice for determining who starts the game: we got the same dice 4 times, each time we had doubles.
So when I roll one six-sided die, I should guess 3.5 for the best chance of getting it correct
you cant average a single value, you need at least 2 values
@@vripscript it was a joke -_-
@@fullfungo If you say so
@@fullfungo But the joke was that it's impossible to get a 3.5, and that's not what L C was saying. L C was saying that even if you could get a 3.5, it wouldn't matter because with one die every side has an equal chance.
@@Interestking Robert made a joke, that 3.5 is the best guess, when it is, in fact, the worst guess.
L C said, that the average cannot be applied to a single die, which is in fact the premise that the original joke was based on.
So to me it seems like they missed the point of the joke (that the method of averages cannot be applied to a single die).
I see no contradictions here.
The more dice you have, the closer you'll get to the prediction as a percentage of the value. But also, the more integers there are in that range near the center value. If I only roll 1 die, I'll get it within 3 every time and I'll get it exactly right 1/6 times. Not true for 100 dice.
3:11 to be precise, the possible combinations to get 7 are:
1-6
2-5
3-4
4-3
5-2
6-1
and to get 12 is only 6-6.
So the probability of getting 7 is 6 times bigger than getting 12.
Those who have played 'Settlers of Catan" know this already 😂
Best Boardgame ever :)
Yeah. There is a reason why 7 is the number for the robber.
It's great that you want to teach Stochastic math as well. You've done a great job teaching it, although I could've wanted to be able to see the reason for this formulas, regarding estimated values as the equivalent for averages in random distributions. Another cool thing would've been to mention the importance of the Central limit theorem, as to the normal distribution that result from it in your last two analysis with 100 and 1000 samples.
Big fan of your videos, keep it up with the good science ❤️🙌🏼
There actually is a chance to get a sum of 100 or 600 when you roll 100 dice. It's just incredibly small because all the dice would have to land on 1 or all on 6.
If you play Settlers of Catan, each of the number markers you place on the resource hexes at the beginning has one or more dots on the bottom. The number of dots directly correlates to the probability of that roll occurring. For instance, 6 and 8 have five dots each, which means there is a 5:36 chance of rolling either of those numbers. Likewise, 11 and 3 have two dots, meaning a 2:36 chance.
This is why 7 is the thief in Catan. Evens out your chances of getting anything else, with greatest chances being 6/8, 5/9, 4/10, 3/11, & 2/12 in order of most likely. Always put your pieces on 6/8, for those that play, but struggle with statistics.
It still did not go well when I played that time.
@@westonding8953 Keep playing the numbers, always aiming for the most probable lands
You know, I've always sort of half understood this, but this feels like an "explain like I'm 5" video and I actually really appreciate that because now I totally understand why this happens.
I'm pretty sure I have more of a 75% chance of getting the starting side with a coin flip. I can easily get a 12 heads streak just by starting with heads up. I actually ruined a probability experiment back in highschool because of this.
My day gets better when u upload bro
Simply wonderful! Love it.
250,000 views explaining basics. Amazing. Good on you.
Wow this will help with gambling a lot thank you!
I studied this in game design class because in pen and paper RPGs like Dungeons and Dragons, you can choose for instance a greataxe, which has a 1d12 damage, or a greatsword, which has 2d6. Besides the fact that the minimum damage on the sword is 2 instead of the axe's 1, you should choose the sword if you want to deal more average damage, whereas with the axe you can deal maximum damage (12) more consistently, but also minimum damage. The probability to roll of any number from 1 to 12 is exactly the same
I was about to send this to my roleplaying friends that are subbed to critical failures, until I realised, that it wouldn't work with a single D20 xD
Roleplayers would naturally come to know this "rule", since we sum up dice values to get the average quite often (for exemple, when you need to roll 12d10 to find the health of a monster... Either you do it, either you take the average.
This is precisely why I hate d20 systems.
3:03 It's not 'permutations', it's 'combinations'. The order that you count up the dice doesn't matter.
The order doesn’t matter for combinations, for example, which is why AB and BA are the same, and therefore would have half as many options than a permutation with pairs.
Now try that with D20s
Not sure if you mentioned it in the video, but the mathematical term for the “average roll” is called “Expected Value”. Might be helpful if anyone is curious to research it.
I’m sure you know expected value goes much further than just dice rolls as well. It can also be used to calculate expected winnings from casino games and other things as well. It’s a pretty interesting subject!
on my way to the casino rn
I designed an amplifier for aircraft with over a dozen resistors proportional to the gain. With 1% resistors there was a wide range of gain possible. The amps were mass produced and tested by a computer that sent me the data. I was shocked by how narrow a gain range was, right around nominal. My take away was the errors cancel more than add.
Just like sound waves - they can cancel out eachother.
I have a question
Can computer mouse work if it is used on a vantablack sheet.
Ball mouse does
As far as I know, vantablack only absorbs visible light, and most mice with the exception of the ones with red LEDs use IR light, so they should be able to work.
This is the same reason a coin falling through a pachinko machine will usually land under the starting position.
For each peg the coin can fall left or right, so for two peg layers it can fall LL for left, RR for right, and either LR or RL for middle.
So there’s a 50% chance it lands in the middle, but only a 25% chance each for the left or right.
Before I see you predict your number, I'm guessing it's going to be thirty-five. That's the most likely of all outcomes.
EDIT: Yup. Actually, one thing I wouldn't mind learning is how to figure out the odds of getting the more likely outcome.
This is the only time in my life where I feel that playing dnd has given me an advantage.
Plot twist: He did this a million times just to get the right take.
This is a really good way of explaining fundamental statistics!
You could have fun going down this rabbit hole with your viewers. How many people do you need in a room before the probability of two of them having the same birthday is greater than 50%? And the list of non-intuitive results in probability goes on and on.
Oh yeah. The Birthday problem. It’s best visualized by looking at the complement.
How about the Monty Hall Paradox? This problem has even confused Paul Erdos. But there are some visualizations that make it easier to understand. It’s a falsidical paradox.
@@westonding8953 excellent one as well!
I do this with my students sometimes.
This is one of the most useful videos of ever watched.
Thanks 😊
Missing your old outro with yellow and black bands giving more scientific feel ❤️
Me seeing title: "Is this gonna be craps math?"
Me watching video: "Yep it's craps math"
lol
Respected sir🌟🌟, During interference of EM wave... electric field adds up like vector....if two electric field of EM wave of same amplitude ,frequency,inphase...when added by vector gives,E+E= 2E, but when we add Energy of E field WHICH IS PROPORTIONAL TO E^2...it contradicts (€E^2=2€E^2)....
Similarly for distructive interference of two similar PLANE Em wave of PHASE DIFFERENCE of π interfering DESTRUCTIVELY COMPLETELY... IF E field becomes ZERO EVERY WHERE.....
WHERE DOES ITS ENERGY GO?what is wrong here?
Thank you sir 🌟
Convolution is such an amazing operator.
💖 from india
Ok
Same
Me 2
I am also from India.
Hi
You videos are always great and informative.
dream would get 600 10 times in a row
Wow man this a the best experiment i have seen in my life, im a psychology student who wrote a experiment called "The dice roll series" in wich the basic idea is to have a prediction of what the dices will do, i find this very scientifical and accurate in terms of deductive and inductive physics, blessings have beautiful week.
Action lab videos make my day
Your videos are always time well spent!
This in fact plays an important concept in statistics and mathematic. As long as you add a couple of random numbers (with any or better say random distribution) the results will always show a normal distribution. this is called central limit theorem.
Meanwhile Shakuni: **smirks**
Dice probability is a big part of Settlers of Catan strategy! The robber moves when you roll 7 because it’s the most likely, and therefore the most likely to throw a wrench into the gameplay.
This is just a refresher course for D&D players.
Probability curves, and confidence intervals. Isn't Statistics great when applied correctly? It's how I make a living. Thanks for this, James.
In statistics it is called the regression toward the mean. The sum of the digits of the die is 21... the average, 21/6, is 3.5. A better question to ask is: what is the expected number of unique die faces that will show if I roll an N sided die n times? The answer is N(1-e^(n/N). Meaning that if you roll a die with 6 faces 14 times the expectation is that 5 or (N-1) of the six unique faces will show. This technique can be used to test the fairness of a die, especially those with a large number for faces. The roll rate of unique faces of a die come up the same as the time rate of radioactive atoms decay in a sample of radioactive material. So, for example, if you roll a 20 sided die 20 times then the expectation is that 20(1-e^-(20/20)) or 20(1-e^-1)=12.6 or about 13 unique faces will show (decay) in 20 throws of said die. If you roll that same die 60 times the expectation is that 19 faces (N-1) will show i.e. 20(1-e^-3)=19. Then using Excel for example, x,y plot the expected number of unique faces that show against the actual number of unique faces that show for 60 throws. Do this plot roll by roll. Then do a first order (linear) curve fit of the data. Let the slope of said curve fit be the judge of the die. I would think that a slope of 0.98 to 1.02 would indicate a fair die.
Always enjoy your videos... but this is a great way to explain a Normal Distribution... as well as explaining the mean and variance without using the techy terms. Simply terrif :))
wow, do i have some statistics to discuss with you! I'm currently in the throes of writing a book on the likelihood of (about 85% of the time) guessing the sum total of two fair six-sided dice. I've run the math through chatGPT (which had a quite arduous time even understanding the question but eventually was able to combine the permutations with the statistics related to guessing the outcome). would love to discuss more and show you a bit of what I've seen/learned and about which I've honestly freaked a little. great video, by the way! i learned a lot!
The number is called mathematical expectation, and any tabletop player knows it's the most important number in dice rolls (for example, in Warhammer leadership test is taken on 2d6 and need to roll below the leadership of the squad, so leadership 7 is considered almost the worst you could have, because of only 50% chances of passing the test). In many other games where something is rolled on 2d6, number 7 is also very important.
Me rolling another two from two 6-sided dies to decide who goes first in MTG: "Dammit Action Lab!"
To the point you made towards the end, the odds of getting a 7 with two d6 is even higher because you can get it not only with the three combinations you mentioned, but also with their opposites (I.e 3+4 & 4+3, 5+2 & 2+5, 6+1 & 1+6) whereas with 12 it can only be achieved one way with a 6+6, so you’re 6 times more likely to roll a 7 than a 12 with 2 d6.
Just saw this (going to erase my response saying the same thing).
All right! Las Vegas here I come!!!
The data collection is very appreciated
Simply amazing!
genious explanation, thank you man!
I love how applicable this video is. A good deal of what I do deals with statistical probabilities.
This is why "maximized spells" feat is a good one.
I like how he gives us a solid technique to "cheat" but not the actual cheat itself. We have the tools just gotta out them to use now.
Add up the numbers of one to six on a single die. The total will be 21. 21 / 6 = 3.5. Not that hard to understand why the average will always hover around 3.5 * x where x is the number of dice used.
This would be a great introduction/ framework for the concept of entropy
Could you tie this in with an explanation on quantum mechanics and how individual circumstances can do crazy amazing stuff but on large scale things stay ordinary
As a dnd Fan, I was hoping for the d20 but there isn't, still a great vid for taking advantage of D6
When it comes to probabilities, the big one I'd like to see is calculating the probability of 4d6, drop lowest. That's a surprisingly difficult problem.
I think we learned this as Regression To The Mean in Statistics.
It would be great if you've added a little extension about how the distribution is called, how it arises and what are its properties like variance and standard deviation - people often struggle a little with these concepts.
The distribution of a large amount of events is approximately gaussian and the standard deviation decreases (i believe by a square root factor) as you increase the number of events. Great to see stats intuition taught in such a short clip!
very good PLEASE MORE MORE MORE OF this type of videos
1:29 I bet the RUclips Gamer "Dream" could get a 99 and a 601 on a roll.
Hahahaha
Game of Probability!
I learnt something new when he proceeded to call a coin a dice with two side 😂😂
Greatly explained!
The more dice you roll, the more accurate the prediction is.
This guy is one of the best science teachers ever