Does a dozen videos on the main channel normally - doesn't win that many Does 1 with actual statistics here - wins by being the luckiest he's ever been
I sometimes watch English ASMR videos to study English with fun, and I'm grateful that I can learn even mathematics with this video! (Please excuse my poor English)
Glad you enjoy them. Thanks for the motivation for this video. It was such an insightful comment as it really proves the maths behind rolling each number but also shows that luck and randomness can still play a key part to the game
33:15 it would be better to put down the 9/3. 9 is the hardest number to put down. If you can ever put it down it will always increase your chance of winning. I looked at the table and it says that 9/3 is the best, but also if you look at the expected value column which shows the current chance to win given the numbers put down, you can look at the chance to win if the numbers put down are 3/9 is 7.9704% and if the only numbers put down are 8/4 the chances to win are 7.0869%. By outrun down 9 and 3 you’d give yourself almost .9% greater chance to win! It’s interesting to note that the chances to win the game are only 7.1432% when starting out first (assuming optimal strategy). A good general rule of thumb is to put down the largest number possible, but there are some exceptions. As you noted, if 7 is gone and you roll a 7, it’s better to put down 5/2 instead of 6/1 or 4/3. I think I know why this is but it’s a complex analysis: Generally, for this game, removing 6 will be more valuable than removing 5, which is more valuable than removing 4. However, removing 3 is more valuable than removing 2, which is more valuable than removing 1. So how do we know which combination is best here? We can rule out 3/4 pretty easily since there’s a relatively decent chance you just roll a 4 and the game is over, or you roll a 3 and have to put down 2/1 which makes it very difficult to win from there. I would guess that 1 is just a very valuable number to have given its versatility to combine with almost anything else. It’s twice as efficient as 2 in terms of being able to be added to create any new number, whereas 2 skips half of all numbers. Keeping the 1 in play will give you more possible combinations. Based on this method, there are other situations where this may be the case as well. For example, if the 1 is already out of play, it will generally be better to remove a 3 instead of 2 because 2 is 50% more efficient than 3 in terms of being able to create new numbers (2 hits every other number whereas 3 hits every third number). I checked this out in the table to see what would be best if 1/7/8 were missing (could also just be 1/7 but that would never be an optimal situation) and sure enough, removing 3/4 is better than 5/2 for these scenarios. The only time in which removing the 2 over the 3 would be better is if you can remove the 8 instead of the 7. The biggest goals here should be to remove the 9 and 8 first, even if you have to use a 1 or 2 to get it done. The overall strategy should be as follows Priority 1: always remove the 9 if possible over anything; same goes for the 8 over anything else besides 9 Priority 2: keep 1 in play. Use the largest number possible, while keeping 1 in play. Priority 1 exceeds this if you can get rid of a 9 over an 8 or an 8 over a 7, even if you have to use the 1 over the 2. Priority 3: if the 1 is removed, keep 2 in play while getting rid of the highest number possible to do this. Basically, use 3 and a number 1 less than what you would need with 2 (better to do 7/3 over 8/2 for a sum of 10 assuming 1 is gone)
I looked and found that if 8 is the only number gone and an 8 is rolled, getting rid of 3/5 is better than 7/1 or 6/2. I think it’s worth noting that 3/5 aren’t next to each other in value, so keeping the 2 is still better even if the 6 is in over the 5. This wasn’t the case where 7 was rolled with 7 already gone because 3/4 are next to each other so that leaves you vulnerable to rolling a 4 and losing whereas getting rid of 5/2 can prevent this. This idea slightly changes my priority 2 where I say get rid of the highest number possible except keep the 1. There are situations where it’s also better to keep the 1 and 2 over the 3, even if it means getting rid of a slightly lower top end number, assuming the really big numbers are already gone (8/9) There’s a ton of nuances but I think the way I’ve laid it out is pretty close to optimal. I hope that my explanation brings some clarification. I also just wanted to say that I really like seeing math applied to games like this. I find things being optimized from an analytical perspective to be very satisfying and relaxing 😅. It’s nice seeing someone with a math background do niche videos like this so thank you for that!
Love this! I found an old version of this game once, with rules on the back - it said when scoring, to read the remaining numbers across, rather than adding them together. So if you have 1, 3 & 4 still standing, your score is 134! That rule was much more chaotic, and completely changed how you strategise. 😂
Ive always dreaded math in school but ever since ive started watching your math videos its altered my perspective on the subject and you encourage me to want to do math
If you are trying to maximize your odds of winning the game, the most important roll is the final roll. If you try to maximize your odds of that final roll, you either want to be trying to roll 1 die to try and hit the 1 tile, or to be trying to roll 2 die to try and roll a 7. These are the two best odds (1/6) for possible rolls. Depending on how your board state is in the mid game, you would want to try and focus on either going for a 7 roll or a 1 roll for the final roll. This strategy might compromise the midgame slightly, but it will make any game that gets to the endgame much more consistently "likely" to win. This is why I would guess that the 1 tile is technically better to leave.
The version of the game my family owns tells you to score based on the specific numbers up (so for example having 3,5, and 6 up would be a score of 356 while 1,3,5,6 would be a score of 1356). Under those rules, eliminating a 9 is not worth the same as eliminating a 5 and 4 because you are reducing the score by one digit vs 2.
I've never understood using asmr to fall asleep. You miss all the tingles then. That's like taking a nice psycdelic then going to sleep and missing all the goodies.
Okay, so I’m watching the video right now whilst I’m posting this comment, and I’ve got to the point where Dido has apologised for him burning himself, because it may seem disgusting to our viewing eyes. Dido if your reading this comment, 1. Please never ever apologise for you, burning yourself 2. Your videos are amazing anyway, so don’t apologise 3. I hope you have a great rest of the day and keep up the great content!
Me vs Random Dude named Bills table (I think he might be wrong but I’m 13 and his name is Bill so he is at least 40 so I’m probably wrong) My strategy is to make the lowest number I put down as high as possible. For example 6 and 4 is better than 9 and 1 because 4 is higher than 1. Let’s see the results.BTW When I say MAX, that means the maximum/worst score I could’ve had, but couldn’t figure out my final score bc video moved on to next game. Game 1: Bill ends with score of 15 I could keep going, end with a MAX of 9 (9) Game 2: Bill wins I also win Game 3: Bill wins I end with 15 Game 4: Bill ends with 20 I end with 20 So I won once, Bill won once, and we tied twice. Can you make another video JUST using his strategy so me and Bill can have a rematch for the ages?
I'd be very interested to see this table implemented in MATLAB and running, like, a billion Monte Carlo simulations to see how many times it wins and loses. Might be interesting to see the win percentage.
I did Get dissapointed when I realised you had not done any research on what’s actual game theory optimal at this. And also when you judge A system by 1 attempt.. Anyway I do like these videos, just have to Get over my dissapointment, then I’ll relax again.
there is only one video on the internet about this topic, as far as I am concerned, and it just so happens to be freaking ASMR... WHY???? Why not just talk normally *facepalm*??
![[ASMR] Magic Using Mathematics!](http://i.ytimg.com/vi/ekdx0oI5y9E/mqdefault.jpg)
![[ASMR] Magic Using Mathematics!](/img/tr.png)
Leave a like if you enjoyed and subscribe for more ASMR Maths! 💙
can u do a trig calculus vid lol
@@traitor-- s words are best words
@@dlx7844😅
I have literally never realized that you and Dido are the same person until now. I feel very smart (dumb) right now.
hahaha, the more you know!!
Does a dozen videos on the main channel normally - doesn't win that many
Does 1 with actual statistics here - wins by being the luckiest he's ever been
Hmmm is it all luck though or did the maths really pay out!
I sometimes watch English ASMR videos to study English with fun, and I'm grateful that I can learn even mathematics with this video! (Please excuse my poor English)
Unfortunately, there are native speakers who are much worse; you're doing great!
@@colten2524That encourages me a lot, thank you!
you did great but instead of English with fun it should be english for fun
I love both your channels and am actually so happy my comment made it into the video. Shut the box videos are my favorite, keep up the good work
Glad you enjoy them. Thanks for the motivation for this video. It was such an insightful comment as it really proves the maths behind rolling each number but also shows that luck and randomness can still play a key part to the game
2 wins in a row… WHOS THE GOAT?!
33:15 it would be better to put down the 9/3. 9 is the hardest number to put down. If you can ever put it down it will always increase your chance of winning. I looked at the table and it says that 9/3 is the best, but also if you look at the expected value column which shows the current chance to win given the numbers put down, you can look at the chance to win if the numbers put down are 3/9 is 7.9704% and if the only numbers put down are 8/4 the chances to win are 7.0869%. By outrun down 9 and 3 you’d give yourself almost .9% greater chance to win! It’s interesting to note that the chances to win the game are only 7.1432% when starting out first (assuming optimal strategy). A good general rule of thumb is to put down the largest number possible, but there are some exceptions. As you noted, if 7 is gone and you roll a 7, it’s better to put down 5/2 instead of 6/1 or 4/3. I think I know why this is but it’s a complex analysis:
Generally, for this game, removing 6 will be more valuable than removing 5, which is more valuable than removing 4. However, removing 3 is more valuable than removing 2, which is more valuable than removing 1. So how do we know which combination is best here? We can rule out 3/4 pretty easily since there’s a relatively decent chance you just roll a 4 and the game is over, or you roll a 3 and have to put down 2/1 which makes it very difficult to win from there. I would guess that 1 is just a very valuable number to have given its versatility to combine with almost anything else. It’s twice as efficient as 2 in terms of being able to be added to create any new number, whereas 2 skips half of all numbers. Keeping the 1 in play will give you more possible combinations.
Based on this method, there are other situations where this may be the case as well. For example, if the 1 is already out of play, it will generally be better to remove a 3 instead of 2 because 2 is 50% more efficient than 3 in terms of being able to create new numbers (2 hits every other number whereas 3 hits every third number). I checked this out in the table to see what would be best if 1/7/8 were missing (could also just be 1/7 but that would never be an optimal situation) and sure enough, removing 3/4 is better than 5/2 for these scenarios. The only time in which removing the 2 over the 3 would be better is if you can remove the 8 instead of the 7. The biggest goals here should be to remove the 9 and 8 first, even if you have to use a 1 or 2 to get it done.
The overall strategy should be as follows
Priority 1: always remove the 9 if possible over anything; same goes for the 8 over anything else besides 9
Priority 2: keep 1 in play. Use the largest number possible, while keeping 1 in play. Priority 1 exceeds this if you can get rid of a 9 over an 8 or an 8 over a 7, even if you have to use the 1 over the 2.
Priority 3: if the 1 is removed, keep 2 in play while getting rid of the highest number possible to do this. Basically, use 3 and a number 1 less than what you would need with 2 (better to do 7/3 over 8/2 for a sum of 10 assuming 1 is gone)
I looked and found that if 8 is the only number gone and an 8 is rolled, getting rid of 3/5 is better than 7/1 or 6/2. I think it’s worth noting that 3/5 aren’t next to each other in value, so keeping the 2 is still better even if the 6 is in over the 5. This wasn’t the case where 7 was rolled with 7 already gone because 3/4 are next to each other so that leaves you vulnerable to rolling a 4 and losing whereas getting rid of 5/2 can prevent this.
This idea slightly changes my priority 2 where I say get rid of the highest number possible except keep the 1. There are situations where it’s also better to keep the 1 and 2 over the 3, even if it means getting rid of a slightly lower top end number, assuming the really big numbers are already gone (8/9)
There’s a ton of nuances but I think the way I’ve laid it out is pretty close to optimal.
I hope that my explanation brings some clarification. I also just wanted to say that I really like seeing math applied to games like this. I find things being optimized from an analytical perspective to be very satisfying and relaxing 😅. It’s nice seeing someone with a math background do niche videos like this so thank you for that!
Bro apologising cause he burnt his hand
Love this! I found an old version of this game once, with rules on the back - it said when scoring, to read the remaining numbers across, rather than adding them together. So if you have 1, 3 & 4 still standing, your score is 134! That rule was much more chaotic, and completely changed how you strategise. 😂
Ive always dreaded math in school but ever since ive started watching your math videos its altered my perspective on the subject and you encourage me to want to do math
I relax to both channels but this is so good 🔥
Rollll the dice. Don't drop them. >
Just an fyi, dice is plural of die. But kudos for actually knowing the word die, it's not well known it seems. Some even say dices for plural, yuck.
loving your Shut the Box videos!
Thank you so much!
If you are trying to maximize your odds of winning the game, the most important roll is the final roll. If you try to maximize your odds of that final roll, you either want to be trying to roll 1 die to try and hit the 1 tile, or to be trying to roll 2 die to try and roll a 7. These are the two best odds (1/6) for possible rolls. Depending on how your board state is in the mid game, you would want to try and focus on either going for a 7 roll or a 1 roll for the final roll. This strategy might compromise the midgame slightly, but it will make any game that gets to the endgame much more consistently "likely" to win. This is why I would guess that the 1 tile is technically better to leave.
The version of the game my family owns tells you to score based on the specific numbers up (so for example having 3,5, and 6 up would be a score of 356 while 1,3,5,6 would be a score of 1356). Under those rules, eliminating a 9 is not worth the same as eliminating a 5 and 4 because you are reducing the score by one digit vs 2.
I've never understood using asmr to fall asleep. You miss all the tingles then. That's like taking a nice psycdelic then going to sleep and missing all the goodies.
Lol tingles don’t last 6-10 hours man 😂
16:27 "this strategy hasn't worked..."
well you didn't follow it on the first turn 😐
LOL I forgot to change the 5 & 3 to an 8 after I was demonstrating how it’s worse than putting down an 8 for that particular strategy 😂
I'd be interested to know what's the probability of winning using the optimal strategy
ASMR Maths > Dido ASMR
No
I won’t take any offence
shut the box videos are the best. thank you for this, and hopefully many more of shut the box. ❤️❤️
Hope you enjoyed 😊
Funny how the simplest way to play the game is the correct one.
Okay, so I’m watching the video right now whilst I’m posting this comment, and I’ve got to the point where Dido has apologised for him burning himself, because it may seem disgusting to our viewing eyes. Dido if your reading this comment,
1. Please never ever apologise for you, burning yourself
2. Your videos are amazing anyway, so don’t apologise
3. I hope you have a great rest of the day and keep up the great content!
Always a classic!
Me vs Random Dude named Bills table
(I think he might be wrong but I’m 13 and his name is Bill so he is at least 40 so I’m probably wrong)
My strategy is to make the lowest number I put down as high as possible. For example 6 and 4 is better than 9 and 1 because 4 is higher than 1. Let’s see the results.BTW When I say MAX, that means the maximum/worst score I could’ve had, but couldn’t figure out my final score bc video moved on to next game.
Game 1:
Bill ends with score of 15
I could keep going, end with a MAX of 9 (9)
Game 2:
Bill wins
I also win
Game 3:
Bill wins
I end with 15
Game 4:
Bill ends with 20
I end with 20
So I won once, Bill won once, and we tied twice. Can you make another video JUST using his strategy so me and Bill can have a rematch for the ages?
I am watching this after new video from main channel !
Bro does now know math (I’m kidding u would think 1+2=3 too if I was awake late😂)
I was supposed to do chores but imma go back to sleep now
W vid idea!
This looks like fun tbh
I ‘m curious but wanr to sleep cause you’re asmr
great video!!!
great vid 👍
The man eat cendy and make video this? Omg so interesting!!
Interesting game :)
Plz dont stop posting in this Chanel
I'd be very interested to see this table implemented in MATLAB and running, like, a billion Monte Carlo simulations to see how many times it wins and loses. Might be interesting to see the win percentage.
I did Get dissapointed when I realised you had not done any research on what’s actual game theory optimal at this. And also when you judge A system by 1 attempt..
Anyway I do like these videos, just have to Get over my dissapointment, then I’ll relax again.
As I wrote it, around 19min.
Now at 20 min you talk about what I was clicking this video for. Awesome!
Loved the last part with the table big time! Awesome. :D. Very great last part of the video!
❤️
💙
Bro, you r literally too serious, but still relaxing though
It’s educational ASMR! It’s meant to be informative 😊
there is only one video on the internet about this topic, as far as I am concerned, and it just so happens to be freaking ASMR... WHY???? Why not just talk normally *facepalm*??
Greetings from Poland - Krakow ;)