How I Used Calculus to Beat My Kids at Mario Kart

Next, beat your kids in WII Sports using category 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!

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

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

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

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.

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!

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.

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: https://mk8dxbuilder.com/ - Mario Kart 8 Deluxe stats and translation tables: https://www.mariowiki.com/Mario_Kart_8_Deluxe_in-game_statistics Mario Kart 8 Deluxe Characters Tier List (made by me): https://www.reddit.com/r/mariokart/s/Qf2Yiet4LZ

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

Khan Academy escapee

does watching this count as studying for my ap calc exam in 1 week?

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"

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)

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.

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 !

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!

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.

just discovered your videos , you are one of the small bunch that can make math fun !!!