How I Used Calculus to Beat My Kids at Mario Kart
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- Опубліковано 29 кві 2024
- Sick of losing to your kids at Mario Kart? In this video we analyze calculus strategies for picking player and kart combinations to improve the odds of winning. Using the integration conception of "area under the curve" helps us understand which characteristics are best for winning.
Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?”
We use unique topics for algebra, trigonometry, calculus, and much more and go beyond context problems and use a technique called mathematical modeling to find solutions to real world questions and real world problems. These videos are great for students who plan to enter technical fields that require real world problem solving, and can be a great resource for teachers looking for ways to bring real world contexts into their classroom.
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Created by Doug Corey
Script: Doug Corey and Jennifer Canizales
Audio: Doug Corey
Animation: Jennifer Canizales
Music: Coma Media
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Next, beat your kids in WII Sports using category theory
Don't get too ambitious. First is Mario Party using Linear Algebra, Pokemon with Probability Theory, and Smash Brothers with Topology
Smash with game theory would be interesting
"But, dad, how did you win again?"
"Well, you see, Mario's cart is contravariant in its wheels which implies that we can do a pushout in the monoidal category of engines which directly means I can teleport to the finish line."
@@m_artoImagine applying simplex game theory onto Mario Party *shudders*
Or Fire Emblem with graph theory
While none of the math in the video is wrong, and it was very entertaining and informative, there is some information about the game which is wrong. The reason acceleration is the most important stat in the new Mario kart game is not because you actually accelerate faster but because it is linked to the mini turbo you get when holding a trigger and doing a turn. They will charge faster, last for longer and go faster if you have high acceleration. Outside of this fact though, and at levels of play where the mini turbo is not being optimized, like the casual environment where the game is probably best enjoyed your observation is correct! Top speed will beat out pure acceleration!
Thank you for this added info! We aren't as well versed with the new updates so this is great to know!
@@MathTheWorld Another way to see the difference is to look at the WR on a track like Moon-View Highway. Because of the amount of boost panels there, the WR uses a high speed kart as drifting doesn't matter as much with boost panels. However for almost any other track the bitty-buggy is used for the WR as it has a higher mini-turbo. Even before the DLC Mini-Turbo was much more important the Speed.
In races however you want to have some speed. This is because items likes mushrooms and stars have a greater effect you if you have higher speed. The online player base started using Walugi + Wiggler exclusively because it had the best combination of speed and acceleration until it got nerfed in the DLC.
In games other then MK8DX, it's a different story.
Mario Kart Wii has high speed bike being better then almost anything because they are inward drifting and because they can wheelie.
MK8 - Fire-hopping is technique that makes high speed vehicles better
MKDS - Snaking causes there to be 5 viable karts.
Hopefully this makes sense.
Correction, the mini turbo stat is a completely different stat that generally goes along with the acceleration stat.
@@smokeyyt8802 That's why the bitty buggy is used I think. It has the highest mini turbo
@@siddanthvenkatesh2744The meta these days is Yoshi (or any character with the same stats),teddy buggy, roller wheels, and cloud glider.
I always picked High Acceleration Low Speed because I originate from the Wii age, where the bots would hit you every 15 seconds with a shell or a banana or something, so going from zero to sixty was pretty important when you're reduced to zero so often
skill issue wii meta was flame runner funky kong, aka high speed low acc
Use a stand still mini turbo. That one tech makes acceleration nearly worthless in mkwii
Not only Is High Speed lo acc Always optimal in mkwii, but you also get hit way less than in mk8 because items are smaller and there are less projectile items.
@@djibytop6724 Also because the redshells are shit at tracking and can be broken by driving somewhat close to a wall
You forgot that the type of circuit is also a factor, more curves means accelaration is better, longer straight segments means speed is better.
We have the same profile picture!
Also more acceleration is equal you will lose less when you do mistakes on your road
@@finnboltz yay!
we did mention this at the end that there are other considerations like the track you are racing on so yes it is an important factor! Top speed isn't always great if you keep falling off the sides because of it
@MathTheWorld Well even beyond that, if we had a more realistic racing game where braking was required, acceleration could still be more important. If we assume both cars brake at approximately the same rate, a car with a high acceleration will have steep peaks and valleys, while a slow acceleration car with high top speed will have higher peaks but also spend significantly longer getting there over the course of a race.
Real racing makes this even more apparent when you look at a series like F1. They intentionally give the cars a slower top speed by introducing wings and spoilers to increase traction. Increased traction allows for tighter cornering with less braking, allowing for more speed to be kept in the corners. So even though top speed matters, acceleration (or in this example, lack of deceleration) often matters more in real life examples.
You’ve convinced me to get good at math. Once I become a physicist I will dedicate a speech to this video.
so true 😂 he has amazing teaching skills
Keep it up!
best graduation speech ever
Go for it, dude. I'd watch it.
Dude physicists and mathematicians are completely different but alr
Your mathmatical reasoning isn't wrong, but if you found yourself capable of holding top speed for long in Mario Kart, then you're either playing 50ccm or your kids just don't know how to use items. In my experience with 200ccm, but also mostly with 150ccm, you don't hold top speed for more than 5s before drifting, getting hit by an item or both. Also in 200ccm especially, high top speed may be detrimental because you can no longer handle the curves. To sum it up, your mathmatical intuition is correct, but your and your children's Mario Kart skills seem to be lacking.
i agree completely. obviously if you are able to stay at top speed for a long time without stopping, top speed is more important. the issue is that this isn’t realistic in mario kart
This is a point I tried to make at the end of the video, but I don't think I was very clear about it. I mentioned the 150 and 200 cc's at the end and how a more competitive race makes acceleration more important because of the reasons you mentioned. But when we were starting out playing Mario kart as a family these were less of an issue.
Speed isn’t a factor in drifts as boosts immediately send you to top speed, and in 200cc it’s different as you want to brake around curves while you drift, so high speed isn’t detrimental, but once again boosts give you top speed, so his concepts absolutely apply very well.
Not sure what 150cc you’re playing but I’m at top speed FAR longer than 5s as well
I play ₂₀₀ often and was able to beat it with speed tho do have to reset sometimes I guess due to an unlucky hit etc
Of course there are plenty of other variables to consider, that's fairly obvious to anyone's who's played any version of Mario Kart, but as someone who's getting back into math after years of (regretfully) avoiding it, I appreciate him laying out calculus ideas in a creative way, making it interesting, accessible, and easy to comprehend for the casual math enthusiast.
In my experience playing the game
Usually you never get top speed
Either because you got hit, there is a curve, a wall, a obstacle, a random lightning
Acceleration is much more important because recovering from getting destroyed is much more important than staying in first place ( a single blue shell and you are done after all)
But as a engineering student, seeing the aplication of what i learned in something i put so much time into is really cool
Very good video!
Mini Turbo is also super important to help bring you to top speed after a turn
I’m not sure if this is too “common knowledge” to make a video about, but in monopoly, understanding statistics concepts is very helpful. For example, knowing the expected value of 2 side sided die is 6 (helpful for predicting where ur opponents might land), and understanding that not every square has an equal chance of being landed on.
Yes! I think about this and use this when I play monopoly. I wonder how many people actually do though?
@@MathTheWorld it would be helpful if u made a video about it
isn’t it 7?
Yes, it's the sum of possible values (1 to 6) times their respective probabilities (all 1/6) which is 21/6 or 3.5. The expected value of the sum of statistically inindependent variables is simply the sum of their respective expected values (3.5 in this case) so the total expected value is 7.
You also need think about the gameboard interactions. Go and Jail have the most cards and triggers to lead to players commonly moving to them, and the spaces directly after them. The short answer is the light blues and orange properties have among the highest probablity of people landing on them. Someone rolling an 8,9 or 6 from Go or Jail lands on them. (7 is chance and community chest on each street.) Between their lower cost to upgrade, they can easily win games. Reds and purples being the next best. Railroads are extremely good for this reason as well, as a bunch of cards force people to go to those space or players will bounce the board rolling doubles hitting railroads repeatedly.
It's wild to me that your kids went for high-acceleration build! When I was a lad playing Mario Kart Wii, I always tried to go for high speed because, in my mind, the whole point of racing was to go as fast as possible. The speed stat absolutely achieves this, but it's certainly not the only important stat
I feel like I mostly went for the high acceleration build because I kept falling off the edge, and I wanted to get back up to speed quickly.
@@jcorey333 you were a more thoughtful child than I
I'm pretty sure he's just better at video games than he thinks, I'm just assuming that his wife hasn't played before and neither have the kids while this guy's already got at least a couple hours of game time
Back in Super Mario Kart I recall I got hit by so much AI BS that acceleration was more important because being able to get back up to your max speed quickly was more important than a higher top speed that you could only maintain for a few seconds before you got hit by some other BS.
in mario kart wii acceleration is a worthless stat because you can charge a mini turbo every time you get hit and go right back to full speed. also if you fall off, you can hit the accelerate button right when you land to get a boost. both of these features were removed in future mario kart games
None of the math in this video is wrong, but there is a main issue here that comes from lack of experience and knowledge of the game itself. Speed (at least Ground and Anti-Gravity speed types) is definitely better than Acceleration (even if Acceleration is not as bad as you could think because in this game you get hit a lot so there isn't just one time where you have to start from a speed of 0), but there is another stat in the game that is better than Speed: Mini-Turbo. This stat is hidden (not shown in the kart select screen) because seems like Nintendo loves trolling (thanks Nintendo). This stat is visible in many Combo Builders you can find online... they will also show you the other hidden stats: all the four types for both Speed and Handling (Ground and Anti-Gravity Speed being particularly important) and Invincibility (this is arguably the worst stat in the game so don't worry about it).
The way this game is designed makes high Acceleration combos also have high Mini-Turbo (most characters and vehicles parts increase Mini-Turbo and Acceleration together with very similar scaling), that's why your kids were picking combos with low speed but high acceleration: they actually were aiming to get high Mini-Turbo. Mini-Turbo and Ground Speed are both S Tier stats but Mini-Turbo is better for most tracks, so turns out that the best overall meta combo for frontrunning (the basic strategy of the game that consists on going forward and staying in a top ranking like any conventional race) aims at getting the highest sum of Mini-Turbo and Ground Speed, but since there are many combos that reach the same maximum value the best one among them is the one that has the highest Mini-Turbo. This combo is the one which uses:
- Character: Peach, Daisy, Yoshi, Birdo or Peachette (they all have same stats)
- Vehicle: Teddy Buggy [Read note below]
- Tires: Rollers or Azure Rollers (they have same stats)
- Glider: Cloud Glider, Paper Glider, Flower Glider or Parachute (they have same stats)
[Note] There is also Cat Cruiser that has the same stats with more Invincibility but everyone prefers Teddy Buggy because it has a smaller Hitbox meaning that you're less likely to get hit. There are also other two vehicles (Yoshi Bike and Comet) with smaller Hitbox and more Invincibility than the Teddy Buggy, but they are still sub-optimal because they have a different drifting style: they are Inward Drift bikes. There are two drift types in Mario Kart 8 Deluxe, and you probably remember that from Mario Kart Wii: Outward (Outside) and Inward (Inside). Outward is the "normal" drift style used by most vehicles in this game, and it's very similar to a car drift in real life. Inward is the drift style of a special category of vehicles in this game: Sport Bikes. It isn't really a drift, the vehicle just takes the turn by leaning inside and you cannot take the turn wider once you start the drift. The way Inward Drift is designed in this game makes it generally worse than Outward Drift because it's less versatile and you cannot pull off some techs that make you faster (like Super-Bounces). Maybe you remember that in Mario Kart Wii it was the opposite: Inward Drift bikes like the Flame Runner used to be the best (in that game Inward Drift was way more versatile and had more turning capability, making it better than Outward Drift by miles).
So, we're finally at the end and you're probably asking yourself this question: "Why did my high-speed combos feel better against my kids? How did I manage to beat them?"
There are two answers:
- First of all this game is extremely balanced (unlike Mario Kart Wii that was broken and unbalanced as hell), so your driving skills matter way more than optimising your stats. You probably just have been a better driver than your kids (even if you don't think so). I guess you're all playing casually, so that's not unexpected.
- Your kids are not pros, and you're not a pro either, meaning that none of you are currently able to squeeze the most out of that Mini-Turbo stat. There are many advanced techs that work around charging Mini-Turbos, so the Mini-Turbo stat is really important. Considering the casual environment of the races against your kids, Speed is actually better than Mini-Turbo because you can always squeeze everything from that stat: all you need is pressing "A". Hope this explaination can be useful for you... and maybe your kids will learn something new as well.
To conclude this comment, here are some useful links:
- Mario Kart 8 Deluxe combo builder: mk8dxbuilder.com/
- Mario Kart 8 Deluxe stats and translation tables: www.mariowiki.com/Mario_Kart_8_Deluxe_in-game_statistics
Mario Kart 8 Deluxe Characters Tier List (made by me): www.reddit.com/r/mariokart/s/Qf2Yiet4LZ
Holy yap
sir you need to attend a yappaholics anonymous meeting
@@daales. Shut up and read it's all good
@@daales.exposing yourself as a child with no ability to think
It used to be normal to read more than one paragraph jeeze.
Games and math... that's how we should study this in school. If learning isn't fun or at least interesting, our education system has failed us. This bourgeiose mentality of learning through suffering/frustration must end. Having fun IS learning.
Trigonometry is useful for Minecraft PVP.
-Me Paraphrasing Technoblade (R.I.P.)
Khan Academy escapee
The real reason was because you were playing against kids
Hi, very cool video. Like previously said, the most important stat in mario kart 8 deluxe is the mini turbo which is hidden (thanks Nintendo). However you should also considerate your strategy. You could front run and be at first place all the time but you are more likely to be hit by an item. So you need better acceleration to be back at speed. You could also wait in the back of the field, waiting for good items (rocket, triple mushroom) and make a finishing sprint to win at the last moment. In this case, maximum speed is better. Thanks for the video !
Great suggestions and thank you for sharing!
my brother in christ its a fucking triangle
Well actually its not, its a exponential curve he just drew it as a triangle
@Kaljumees it's not exponential though - distance traveled is quadratic, but at constant acceleration, speed will be linear
Lmfao
It’s almost like you can find any area equation by using calculus.
@@jackinzbox.its almost as if you dont need to take the integral of a triangle since we already know how to find the area of a triangle
6:23 reminds me of the into to the Numb3rs show: "Math is more than formulas and equations. It's logic, it's rationality, it's using your mind to solve the biggest mysteries we know"
does watching this count as studying for my ap calc exam in 1 week?
I've used math for two games: Clash Royale and Clash of Clans.
For Clash Royale I made an excel table and populated it with all 100+ card stats.
The problem with Clash Royale, though, was that every card had some unique function which made it hard to generalize. However, I focused mostly on damage per second, hitpoints and cost. My approach was: find winning/losing 1v1's and find cost-efficient cards that can make up for a card's weaknesses.
For Clash of Clans I went to excel again, fed it with all of the defenses' stats and worked out the most efficient progress order. The idea is to promote defenses with a better ratio of cost per damage per second gained per upgrade. Obviously, there are different approaches but I was focusing more on damage output *gained" per upgrade.
That is cool! As it turned out to be a winning strategy!
I did something similar for a shooter game I used to play. You could add mods to your weapon to improve fire rate, damage, magazine size, or reload speed. I made an Excel chart showing "sustained DPS", taking into account damage per shot, shots per second, and time of fire before reloading PLUS time of reloading (that last plus is a big thing that probably almost no one looks at!). Using this, I could maximize my damage output over time.
There's also the opportunity to graph the frontier of optimal possibilities. Perhaps even in multiple dimensions to include the incredibly important boost stat. Any point along the frontier is Pareto efficient. And the expected frequency of spin outs can determine where along the frontier is best for you.
Cool video! Brings me back to playing Mario kart with you. A part of me wants to play you again and see how well I do now.
The strongest sorcerer of today (8 minutes of calculus) vs the strongest sorcerer of all time (Funky Kong flame runner)
Gamers, the time has come to learn calculus.
I've been saying stuff like this for a long time! You use calculus to compare two functions as they go out in time, and that can make you choose the better item in a video game. It can also help you figure out the fastest way to make a turn. You don't need numbers to do this, you just need to compare the area of the two triangles, like you did. I love this!
Pokemon is full of math for winnint strategies.
That was a really nice and intuitive video, I've never played Mario Kart but I understood everything I needed in order to grasp the problem! I really like this style of video, I'm going to check out more of your work!
The one time I remember being proud of the math I used to get an advantage in video games was in modded minecraft. There are processes that produce an given amount of a resource with a chance to consume the input. My question was "How much does one input produce on average before getting consumed?". It's one process for sure, plus one process if the input was not consumed, plus one process if the input was not consumed a second time, etc. I was in high school and didn't know about geometric series, but I ended up finding empirically that 1/(1-p) was the average amount of processes executed with a single input, with p the probability of not consuming the input. I could then setup factories without worrying about buffers overflowing, and I could easily compare the efficiency of various processes with an easy formula for the average! I was blown away a couple of years later once I learned about geometric series and realised why my formula worked.
Not really game related but around the same time, I was wondering about the likelihood of coming across molecules in a single tablet of homeopathy. Much later I showed that it followed the limit of a binomial law and calculated it, but I didn't know about the Poisson law at the time either. When I learned about it in college, I was very proud to see in my classes the proof I had already found.
thank you for your reply! Some others have mentioned minecraft as well so we'll have to look into this more!
I wish math in school was about problem solving like this rather than numbers and algebra.
This is exactly why we made this channel. To show the site of math that really makes it into school. We hope we get teachers that watch this and share with their students.
This is a great video! It really helped me understand what it means to apply the concepts of math! Its also fun to learn about mario kart lol! God bless you and your family!
In Dragon Age Inquisition there are "constellation" puzzles, that pretty much all of them can be solved with the eulerian tour theorem
Well, this sounds cool. I will do some research on that!
I see Eulerian path problems pretty frequently in hidden object and other game types where you occasionally have to solve puzzles. I'm always nostalgic for my school days when I see it. :)
Another thing to consider is the cc level. 200 cc high acceleration is better because the top speed is so high that characters never reach it
Yes, that's exactly the point I try to make at the end of the video.
I remember something like this in Physics just using kinematics. You could use these three equations to get displacement, assuming the perfect scenario, like in the graphs.
t=(v_f-v_i)/a, time until max velocity is reached
d_1=v_it+.5at^2, displacement for time during linear acceleration
d_2=v_ft, displacement for time at a constant velocity
or the ugly combined formula
d=v_ft+(v_i(v_f-v_i))/a+((v_f-v_i)^2)/(2a), extra parenthesis to avoid division confusion
All you need is: starting velocity(v_i, 0 most of the time), max velocity(v_f), acceleration(a), time spent at max velocity(t, used in lower and combined formula).
There is technically a fourth - implemented into the combined formula - adding d_1 and d_2 to get the total displacement, the value you will be comparing to find the optimal build. However, after realizing mini-turbos exist in this game, this math is admittedly kind of pointless.
Edit: Forgot 2a 💀
Yes, we could have used those equations. But I wanted to focus on the calculus ideas that are used to develop those equations. I was also being true to the way I actually thought in this situation. I was not thinking with those equations, but thinking with the calculus ideas and areas. I do wish I would have made a connection with these formulas and the areas at the end of the video. I think that would have added some good connections.
@@MathTheWorld if you factored in friction/resistance (which mario kart does use) then you need calculus.
Thanks for giving a simple, real-world example of calculus! It's been a year since I took an integral, so this was a nice refresher. Hopefully I'll find more uses for calculus in my area of interest, oscilloscope music!
I've played a racing game called GRIP (which is similar to mario kart in many ways) and I can attest that having high top speed is actually detrimental there most of the time. You can go very fast, so fast that you can easily lose control and bump into obstacles or fly off the map, so the better cars tend be more in the middle of the line with good traction. And depending on the map you play, having a car with high acceleration and low top speed is actually better because these maps don't allow you to frequently reach top speed.
The non-math related reason for top speed being better than acceleration:
A lot of items (Mushroom, Golden Mushroom, Star, and Bullet Bill), as well as boost pads will get you close or onto your top speed with no need to worry about acceleration speeds
"sir, i just wanted to play mario kart"
ZZZ
Work your brains out stop sitting on the couch .
just discovered your videos , you are one of the small bunch that can make math fun !!!
Thank you so much!
There are other factors to consider, of course, but this is a decent general rule. Other factors to consider include:
1) The top speed of karts change with your coin count, and the top speed of a minimum speed kart with 10 coins is equal to the top speed of the max speed kart with 0 coins. This means a minimum speed kart player could make it their goal to try and prevent top speed players from getting too many coins, either by trying to remain in front of them and grabbing as many coins as possible, or by trying to hit them in situations they otherwise might not have to.
2) It doesn't account for skill in various areas such as driving optimal lines, knowing how to take shortcuts both with or without mushrooms, getting maximum utilization of mini turbos (And mini turbo is an additional secret stat. A high acceleration kart with high mini turbo can be a LOT better than a high speed kart with low mini turbo if used right), or using/dodging powerups effectively. Powerup usage can be a REALLY big factor in some cases, actually. For example, if you are in a glider section and a blue shell is coming for you, it is more time-efficient to get with WHILE in the air (above ground) because it makes you spin out instead of getting flipped like when you're on the ground, which has a longer recovery time. If you CAN'T get above ground, nose-dive into the void because Lakitu will give you immunity to the blue shell explosion, so instead of waiting for the explosion AND Lakitu, you only have to wait for Lakitu.
I won a race against multiple high speed karts in a high acceleration one by taking near-perfect turns, getting mini turbo boost even on straight sections, maxing my coin counter as fast as possible, and hitting the player who broke away in front of me with a red shell in an optimal time. What was that time? I waited until AFTER their powerup had been revealed to be a coin (since my red shell would have gotten there late if I threw immediately) AND when they were in a glider section above a pit. That caused them to void out and need to get saved by Lakitu, which is MUCH slower than just getting hit and continuing, especially if Lakitu screws you over with respawn point. With those features of my play style, I finished with half a lap on everyone (and keep in mind, these weren't little Timmies or new players online, this was an in-person local tournament with people who were at a comparable skill level and age to me. I just made better use of some of those game-changing techniques in that race).
Wow
Nerd
@@coaled You just watched a video that uses Calculus to optimize the stats of a go-kart in a game primarily made for children and you're saying I'm a nerd because I gave reasons for why there are exceptions to the math 🤣? This video was *made* for nerds, you're not stating anything anybody didn't already know lmao.
@@GameJam230 nerd
@@coaled Okay then lol.
really enjoyed this video! I didn't think of it as calculus in the moment, but had a similar but opposite experience prioritizing acceleration/handling (bc my friends and I love 200cc)
Catan is pure math, knowing about the odds of numbers being drawn from rolling 2 6sided dice. And thinking about dice for exemple, many table top rpg forces you to think about probability to maximize your damage
Hi! I really liked the video, especially the conclusion you made at the end, on how you are able to use the ideas and concepts for your reasoning, on your daily life, without actually sitting down and calculate. I love philosophy, and the same thing happens to me, exactly like you with maths; I notice on my day to day basis how this subject helps me with my thinking so much. I don’t particularly like mathematics, but the conclusion you made at the end made me appreciate it a lot more. Maybe I would love to see some more content regarding this, in the future! :)
Thanks for your comment. You might like these two videos which are ones we made that are a bit more on the philosophy side. They are some of my thoughts about why it is so hard to answer the "when will I ever use this?" question satisfactorily as a teacher.
ua-cam.com/video/cb0VuijlOXw/v-deo.htmlsi=5UtaEjTvzoY2pcX0
ua-cam.com/video/i7qoq3KQiaw/v-deo.htmlsi=QJuV3jic4q-6tEqW
One problem I’ve been puzzling over for a couple days takes place in Guilty Gear: Strive. One character, Bedman, has two attacks where he shoots a projectile at the opponent’s center of mass. A common strategy that players use is jumping into the air and then firing one of these projectiles over and over again. Normally, when playing a large character or a slow character, this is a problem. However, picking the small, fast ninja means that you can just sprint forwards and it’ll go right over your head. After I thought about it for a bit, I realized it’s a related rates problem. You take the running speed of the character, or v’(t). Then, you find the change in Theta of the angle between the two characters. If the change in Theta in the time it takes for the projectile to reach its target is greater than the angle that it can cover, you are able to safely run underneath it. If not, then you can’t. That was when I was thinking, “this is sick! calculus works in video games too?”
I love it! Nice reasoning!
There is definitely a big difference in the top combos of MK Wii and MK8. In MK Wii, all vehicles are more than capable enough of staying on the track, with very little difference in the effectiveness of mini turbos. In MK8, vehicle combos have a hidden mini turbo stat with a huge effect on mini turbo effectiveness, with faster vehicles usually having low mini turbo and also low handling, making them hard to control and bad at building up mini turbos. The coins also complicate things massively. With high acceleration, you can be the first to pick up coins on the track, increasing your top speed. If you collect 10 coins right away, you will have a higher top speed than a high speed combo, so a high acceleration can allow you to snag those first few coins, putting you ahead for a long time.
Because most of the tracks will have you constantly building up mini turbos in MK8, having a high mini turbo stat leads to much faster times than just fast top speeds on most tracks. Factoring in items and the difficulty of driving high speed combos with low handling, you will also likely get off the track and collide with obstacles much more frequently with high top speed combos, and whenever you fall off the track or get hit by an item, you lose lots of time to anyone with high acceleration.
Of course, there are lots of exceptions with tracks where there are lots of boost panels and few turns, where top speed is way better, since top speed also increases boost panel speed.
In general, I think MK8 is a lot more balanced, with a web of complicated stats and factors such as the track shape and difficulty, coins, boost panels and more having varying effects on the usefulness of each stat. In MKWii, the Flamerunner is just the best no matter what.
You do a great job of explaining calculus concepts, and I do agree with your explanation of why we technically didn't do Calculus in the video, but i feel like the math actually done in the video can be equated to Algebraic levels of physics. As a current physics student, this was taught at the beginning of the curriculum without any Calculus involved, only slope and area. Otherwise, I love your work and am glad that it inspires people to pursue maty and science in their life.
P.S. the Mini turbo stat is the most important stat for experienced players but was hidden in Mario Kart 8. It was around back in the Mario Kart wii days.
Couldn't you just treat the accelerated part as a triangle?
Yes
the graph he drew doesn’t accurately represent the reality of the situation he’s talking about. The graph from 0-5 seconds looks more like a logarithm or square root curve, leveling out at 10 ft/s. It’s not a straight line.
You could certainly estimate it with a triangle, but since the curve had a negative concavity (ie its second derivative is negative) it will be an underestimate. His method looks like it will also yield an underestimate, but it will be slightly more accurate.
If we knew the function of the acceleration curve, we could very accurately estimate the distance traveled with an integral and use the second fundamental theorem of calculus to do so.
Only if the acceleration part of the graph represents a linear curve, e.g. the speed is regularly varying.
Yes, once one is solid on understanding why the area under a speed curve represents the change in distance, then you can use geometry for simple situations like this, where we have represented acceleration as constant and speed as linear. In fact, that's one way to derive many physics equations kids are taught in school.
Fun fact... I actually used trigonometry to solve most of my calc 1 and 2 problems ( only got C's though)... Flunked out of calc 3 with multiple variables... It doesn't work once you leave 3 dimensional space... Lol.
I still remember the Battlefield 3 and Battlefield 4 days, arguing over attachment combinations on the guns and the hitrater results. good times
anyone who has learned calculus and didnt already know this was failed by our school systems. Awesome educational and entertaining content
Thank you!
As others have mentioned, the mini turbo stat tends to be the best, with a high speed stat even being suboptimal in some of the older Mario Kart games. This is mainly because of the frequency of mini turbos and how their activation has changed. In Mario Kart Double Dash and DS specifically, the optimal strategy is to continuously chain mini turbos together in what is known as snaking. In contrast to the newer games where heavier characters with better top speeds are optimal, older Mario karts’ meta were lighter characters with high accelerations and low top speeds, because the mini turbo bonus outweighed the default max speed you could reach. Newer Mario Karts handle drifts much differently, meaning you can’t perform them nearly as much anymore, hence why speed has become more defining
I used to play Double Dash (the GameCube version) and after a while I decided to go for the heavy cars. I realized that my most common delay was falling off the road, and the most common cause was being kicked out by others. And in fact that really improved my game 😌
Hell Let Loose is a game where i've used maths a good bit when using artillery as it is purely number crunching, you can use an online calculator for it but its a lot more fun to do it yourself
Desktop Dungeons for sure. Loads of quick mathematics, it's beautiful.
The thing that also matters greatly is the invisible mini turbo stat, which affects boost distance, a lot of competitive players try and boost this stat and acceleration while leaving top speed behind
In helldivers2, you use worms style arcs to place gernades and stratagems. You can also use angle of impact to determine penetration or ricochet. For example bug with armored legs and face. Create an angle to ricochet the round off the inner leg and into the soft bits.
Interesting video, nice way to show what the intuition tells us (when we think about it). Not perfectly applied to Mariokart because of how complex the game is, but still very interesting.
no wonder why you are a professor! your explanation is so good!
My preferred combos are shy guy bone rattler, monster wheels and plane glider or sometimes i use dry bowser instead for faster speeds
Amazing, I did and redo calculus many times because I love it, and this video gave me lot of insights
I'm so glad! Thank you for sharing!
Most top players in MK usually suggest going for some acceleration that’s at least decent, because getting hit happens very frequently, especially in online matches where all your opponents know what they’re doing (as opposed to bots which usually hold on to their shells for no reason for a really long time, often losing them on defense or to a Boo/shock).
Those are things that I have been thinking about for a while, but I have found that the actual number increase in either max speed of acceleration are large factors.
For most Mario Kart games I have found that higher acceleration is better while learning the tracks, because it helps to recover from mistakes and getting hit by items, and higher max speed is better when I am good enough that I am not going to make mistakes and that I will be able to avoid all items that can be avoided. But there have been exceptions.
For some games the max speed difference is so large and the acceleration difference so small that even while learning the tracks going for max speed gave me better results.
There have been games where the CPU are so aggressive with items and the tracks tricky enough that, at least while playing GP, there will always be a track where going for acceleration is worth it, so I just put up with having less of an advantage on other tracks.
This is mostly just going by feel though. I have always wanted to take the time to actually measure it, but I have never been able to sit down and take numbers.
I definitely agree that there are concepts in calculous that most people would benefit from knowing about, even if they don’t have the formal knowledge to do all the calculations.
Rates of change and how rates of change can have rates of change in particular is a concept that I keep seeing people making bad decisions because they don’t even have a general intuitive understanding of.
I have used trigonometry to explain how to approach a specific jump for a shortcut in crash team racing. The jump is only barely possible so making sure the distance is the smallest possible is important.
Math was great for Neopets. The horse race bet payouts sometimes made it possible to guarantee the worst you could do was break even.
And they said we'd never use calculus in our lives.
Jokes on them.
We can now use calculus to beat our kids in a videogame.
I was really into playing as Isabelle with the Tri-Speeder and Azure Roller or Cyber Slick tires in MK8, especially on 200cc; in higher engine classes, your handling becomes incredibly important to remaining on-course, and playing a Light character reduces the amount of time spent correcting your course if you're knocked off the track or into the rough.
Nice video, i love the explain. You're a great teacher.
thanks for posting this I got to take calculus next fall and I am a bit nervous
Great video man :) keep it up!
Thanks!
omg that first photo of y'all on the couch...i could feel that little girl's rage through my monitor lmao
Thank you,I This video helped me with a homework that I didn't understand.
Hey nice video! I have a game suggestion that isn't really like the math here but more directly related to the game but I still think you would enjoy it! Its called Super Algebrawl. Another one that is slightly less directly related to math that has been popular lately is Balatro, and there is a few more games like this like luck be a landlord. Also personally Ive noticed i use the most math when playing Idle games where the only real gameplay other than idling is choosing which upgrades you get and often math helps out there. I think I could think of a lot more if i thought about it more since ive played a lot of different games and I like math so let me know if you need more suggestions :)
I usually use the combination of Yoshi, Sports coupé, azure rollers and MKTV paraglider. It might not be the best mathematically, but I stick to it to get a feel for driving
Love this video! The next step is to then use Data Science/Analytics to tell you how often you're having to restart based on the map and skill level of opponents (thus needing to accelerate more). Combine the two for the perfect combo!
Thanks for the positive feedback! Your suggestion on the follow-up video is right on. Now if only I had the data where I could actually do that analysis.
competitive mmorpgs in general have a lot of excel sheets behind them, looking for what's called 'min-maxing', optimizing everything
I use maths for building magic the gathering decks all the time. Very useful for knowing how likely I am to draw lands vs spells
This is a lesson in how good math can lead to wrong conclusions due to missing variables. There is a hidden stat that influences how fast a mini turbo charges up, and low speed/high acceleration carts usually have a better turbo stat than fast carts. Counterintuitively this means that slow carts in practice are actually faster when nothing is going wrong. It's the low acceleration carts that are better at catching up because their high speed gets multiplied by power ups (mushrooms, stars, etc) that are only available when you're losing.
I'm seeing a lot of critique of your knowledge on Mario Kart, which is fair! It's important to consider all aspects of why one would perform in the game as they do, but I feel like the real takeaway, one I appreciate of this video, is the demonstration of an actual real-world application of calculus in a casual context. It was very interesting to me.
Coins do more for your top speed than your top speed stat btw.
So it's fully viable to use low speed combos just to get more mini turbo.
With soft drifting you can also use drifting to acelerate as if you always had a mushroom.
That makes it so good players in this game only use mushrooms for shortcuts and blueshell dodging.
The thing is that high acceleration recovers better from the huge load of items that can hit you than speed, this and the mini turbo factor explained in another commentary makes acceleration a little bit better
I personally play MK Wii, my combo is Yoshi and Wild Wing. Controversial because of not maxing out speed and running automatic. However: In games where there are any aggressive items I find that my loss in speed using Yoshi rather than Daisy is made up for in using a kart for faster acceleration and speed. Since I use a wiimote and not a GameCube controller it is harder to wheelie (harder doesn’t mean it’s difficult, I just haven’t put in time to practice keeping course while getting into or out of a wheelie). When I played in college I faced off against several sweaty players, the best of whom only ever used Daisy with Mach Bike, never used items, and only played on Circuits for best speed. While he was able to crush me on his courses I could easily beat him anywhere else on any other settings due to my flexibility of build. GG Vinca.
I remember Colin McRae rally - some tracks /time attacks could be went with high speed and hard suspension. But some had to have best acceleration and softer springs. Not only because of tight and slow turns, but rocky surface. And there was a damage component too. Calculus is part of physics and engineering.
I don't know if it's because I was taught well or if it simply was natural to me, but it felt very intuitive that the calculus was used without anti derivatives or functions(though I did expect them to appear eventually to get a more precise calculation to get a better idea of when it's worth it and when not; but seeing as it's pretty casual it makes sense to not go that far)
the rough location of the "equal distance" point/the y representing speed also felt obvious, but maybe it's because I was taught the subject not that long ago...
that aside, I certainly enjoyed the video. thank you very much!
Not necessarily as directly correlative as Mario kart, but the Wii sports resort archery accuracy can be intuitively understood as the path integral for distance between moment the arrow is released from the bow and when it hits the target. Minimizing this integral means less energy is expended during the flight of the arrow, which (I think) means ALWAYS prioritizing using the highest releasing velocity as possible, as wind resistance and wind speed influences the path of the arrow
As someone with a deeper knowledge of why acceleration is actually better, this hurts not just by brain but also my heart
Regarding other games, I’d say that any RPG that shows the player’s health bar is helped by conceptual math. In competitive Pokemon, you can get a visual of how much damage you’ve done, which reveals certain information about nature and defensive EV spreads of the opponent’s pokemon. This comes with experience of course, by memorizing how much damage x attack should do to y pokemon if they’re investing completely in bulk, none at all, or somewhere in the middle.
This is very much the case for irl racing as well. One must choose if they're going to accelerate out of a corner first, or are they going to bank on high speed and pull ahead on sections of straight roads. The choice very much delends on yhe type of track and how many corners exist.
Fortune Street on Wii gives you a hige advantage if you understand math well. Some basic probability and algebra can definitely help mitigate the luck portion of the gameplay.
You have made a video about something I learned in Mario Kart about 30 years ago.
My go to is a heavy character like DK or waluigi, on the flame rider with Azure roller wheels and the default glider. It has higher speed, higher acceleration, and inside drifting allowing me to cut corners better as well.
flame rider doesn't have inside drift
@@aluigiFromKart Frick. I may have mixed up the flame rider and comet in my head. I use both of them depending on the track.
pretty cool choices i must say
Gold metal mario on the city tripper with azure rollers and the standard kite. Good acceleration but still some weight, plays nicely in 200 CC
this was a really enjoyable and interesting watch even if it’s a surface level look at the game
the actual best stat is hidden, and it’s called mini-turbo. It’s how quickly you can charge sparks while drifting as well as how long the boosts last
despite this and what other comments mentioned this basic concept is good to know for outside mario kart, and using mario kart to deliver it kept it intuitive and fun
I wouldn't call it surface, just at a novice level of playing, which is where my kids were at. And in mk Wii they wouldn't drive with manual so mini-turbo wasn't a factor.
@@MathTheWorld that’s true it’s definitely not surface level, and in mk wii im not sure if mini turbo is the best stat (i forgot you were exclusively talking about mk wii) so my comment may be completely wrong then
Thank you for this video. I wish I had you for calculus.
Thanks! I wish I had you in my class as well!
You need to know how much time will you spend at top speed vs how much time you will spend accelerating. Also in mario kart you need to take into account all the stops and slows that you are getting applied constantly, the rubberband effect and the object pool wich will make you target of blue shells for being first
I use math in Pokemon all the time. I calculate damage for pokemon survival vs attacks a lot. One thing I generally found is regardless of base stats investing in both defense stat in question and HP results in lower %damage take. Sometimes it’s a lot in one stat over the other but often enough slight tweaks can change a lot in surviving a lot vs never or little of the time.
I only played Mario Kart until MK Wii but my favorite combos were Bowser with Flame Runner and Dry Bones with Dry Bomber. I mainly use Bowser and switch to Dry Bones on some tracks with shortcuts. I felt so smart using him to skip parts of the track without having to use mushrooms since he had high enough accel to make off-road jumps for the shortcuts 😆
One of my kids loved Dry Bones!
I actually play Dry Bones
High acceleration, high mini-turbo, medium speed.
I enjoy the small frame with high invincibility and great handling.
Only weakness I see is the minimal weight
Mini turbos off of drifting are a wrinkle though. You can boost your speed off of turns to level out the advantage on curvy tracks.
The way I look at it is, you can look at one of these cart scenarios in terms of position, or velocity, or acceleration. Calculus is what lets you switch between the three.
Mom: "Don't play video games all day long"
Me: "I am working on calculus, mom"
Early Street Fighter 4 was dominated by frame data knowledge. Basic Integer Addition was the name of the game. And once players understood the input method of "plinking", the game's hardest combos were not just accessible to everyone, but were easier to perform.
And then there was the geometrt of hitboxes and hurt boxes.
As a math teacher, myself. I would like to see this video.
What an amazing video :) you seem like a great dad !
I know this is supposed to be simple calc. video, but the most important variable is your mini-turbo (the speed boost in which you gain from doing a drift). *EXTRA CHALLENGE*, try to calculate the best possible cart combo and strategy to theoretically beat the world record 150cc time on a course of your choice (plz do sunshine airport). I just thought this would be a cool, head-aching video idea!
This is something we understood without calculus all the way back when I played fzero and we used that red car.
Now this is the type of content that youtube is meant for!
Pre-booster, Waluigi/Wiggler/Roller was good in 8 Deluxe due to high mini-turbo. Still worth a try in 8 on the WiiU.