How I Used Calculus to Beat My Kids at Mario Kart

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.

Created by Doug Corey

Script: Doug Corey and Jennifer Canizales
Audio: Doug Corey
Animation: Jennifer Canizales
Music: Coma Media

© 2023 BYU

[sebastianmanterfield]

Next, beat your kids in WII Sports using category theory

[MaiBeUploading]

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!

[_marshP]

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

[Dewellz]

You forgot that the type of circuit is also a factor, more curves means accelaration is better, longer straight segments means speed is better.

[CosmicLeaf]

You’ve convinced me to get good at math. Once I become a physicist I will dedicate a speech to this video.

[GespenstDesKommunismus]

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.

[iuricunhamurakami]

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!

[charleslevine]

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.

[ItsManu]

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:

[wepmasters]

1:55 Area under the function using a triangle is simpler

[luketurner]

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"

[alexrawlings]

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

[fyxos]

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 !

[flqwd]

The strongest sorcerer of today (8 minutes of calculus) vs the strongest sorcerer of all time (Funky Kong flame runner)

[GameJam]

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).

[tytool]

Another thing is that acceleration helps with drifts & there are a lot of twists & turns which harm the top speed, not to forget items hitting you.

[PhoticsTV]

Nice video! Calculus was the first and only class I failed, mainly because I saw no relevance to it — when was I going to use this stuff?

And since you asked, I made a video about coin farming in Crossy Road. Is it cheating to use math? After doing the math, the results were surprising. I was using the wrong character!

Too bad the math teacher wasn't able to make video game comparisons. There's definitely a lot of math and logic going on in playing and making video games.

[shnobleso]

i nearly always win with a large character, mr scooty, and the littlest wheels

[DavidJohnson-tvey]

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

[Katsunai]

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.