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.

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!

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

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

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’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.

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 !

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.

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.

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"

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.

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.

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.

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)

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.

Gamers, the time has come to learn calculus.

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! :)

I like this. The meta is usually acceleration based. But I’ve noticed switching a little bit of that acceleration to top speed goes a long way. My preferred setup is pipe frame and leaf tires. They’re both 2nd place in acceleration. Compared to scootie/buggy and little wheels. But that top speed boost goes a long way. It’s well worth it.

my brother in christ its a fucking triangle

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 💀

I wish math in school was about problem solving like this rather than numbers and algebra.

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

In Dragon Age Inquisition there are "constellation" puzzles, that pretty much all of them can be solved with the eulerian tour theorem

My preferred combos are shy guy bone rattler, monster wheels and plane glider or sometimes i use dry bowser instead for faster speeds

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

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).

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.

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.

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

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

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.

Nice video, i love the explain. You're a great teacher.

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 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 😌

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

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?”

Thank you for this very cool and enjoyable video :)

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.

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

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

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.

thanks for posting this I got to take calculus next fall and I am a bit nervous

I still remember the Battlefield 3 and Battlefield 4 days, arguing over attachment combinations on the guns and the hitrater results. good times

Yoshi + teddy buggy + azure rollers + paper glider is essentially the default meta so you got basically the exact same stats so i respect it. Mario kart 8 also has hidden stats thats increases your air speed and water speed etc that they dont show so I'm surprised you still got a very good combination without knowing that

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!

Thank you for this video. I wish I had you for calculus.

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

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.

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

Math was great for Neopets. The horse race bet payouts sometimes made it possible to guarantee the worst you could do was break even.

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 😆

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

What an amazing video :) you seem like a great dad !

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.

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.

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

Well well, that may be useful information one day. I never did, and don't cureently take calculus, but, i do sometimes play mario kart. You could even make a graph showing each kart relative to each other with this idea alone.

I've usually gone with higher acceleration cause your gonna get hit by stuff so you don't want to be taking forever to speed up. Also you can recover faster and quick mini turbo's can alleviate speed differences

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

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.

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

For me it was Yugioh for both ideas of optimization, resource management (both for me and the opponent player), statistical probability and believing in the heart of the cards

I reason effectiveness is a product of speed * acceleration, so having mid/mid is optimal. for example 3* acceleration and 1* speed is total of 3, likewise 1* acceleration and 3* speed is also 3, but 2* acceleration and 2* speed is 4. In practice is depends on the track and the circuit, higher acceleration is better on lower 50cc when your opponents are of a lower skill, but at 150cc against better racers that will be at top speed more consistently then Speed>Acceleration

"sir, i just wanted to play mario kart"

Pre-booster, Waluigi/Wiggler/Roller was good in 8 Deluxe due to high mini-turbo. Still worth a try in 8 on the WiiU.

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

Couldn't you just treat the accelerated part as a triangle?

My strategy is to always pick Wario + the silliest looking kart combination and then assert my dominance by mimicking his dancing moves irl. Works every single time. I know f-all about calculus, cause rattling the kids before the race even starts is my best weapon.

Slay the Spire is full of calculations! It would be interesting to compare a mediocre top speed player with an expert top acceleration player…. I remember F-1 Race on Game Boy having some tracks better for the lower top speed.

I use Rosalina with the standard bike, GLA tires, and MKTV parafoil. The concept in the video makes sense, but you don't just accelerate once. You mention getting hit by opponents requiring you to speed up again, but you didn't really discuss how it actually affects the optimal combo. In my experience, it is best to have high acceleration, but not maxed out. That way you get to full speed a little slower, but your top speed is a little higher.

I think Competetive Pokemon would be an very good game to talk about for you. I would recommand talking aboud statistics and probabilities

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.

Definitely picking a character that my friends absolutely hate. That’s my main focus

I didn't even know you could change your stats lol. I just picked the ones that look cool

Lovely! At 50cc and low skill, this is a huge advantage. The inflection point is when the kids look past your apparently silly choices and begin to wonder what is going on: one day you walk by the living room and see them trying your Waluigi on BiddyBuggy or stuff like that. Once they catch up on that though, it's all about git gud, but then you can just retire and keep bragging rights forever, haha

Buckshot roulette is an interesting game that a good knowledge of statistics can help you win. Maybe give that one a look

This was a great video Though I did have to compose myself after I heard you refer to Mario Kart Wii as Mario Kart 7

Elden Ring: doing a ranged build with magic where you can weaken or kill foes before they are close enough to attack you. That feels like math, but not sure how.

I feel like this guy would love a management or strategy game like Crusader Kings 3

While you’re not technically wrong and this explanation can be very helpful in understanding principles of calculus, in reality it’s a slightly trickier problem. One of the major aspects of Mario Kart is that you are constantly slipping on banana peels, getting hit with red shells, etc. This means that you spend a lot more time accelerating from rest to top speed than you would in, say, a drag race. In practice, this means that a car/character selection with high top speed and low acceleration is more beneficial to an experienced player who doesn’t get hit by items very often, while a high acceleration low top speed car/character selection is more beneficial to a less experienced player who gets hit by items frequently. None of this is to say that this video is wrong in any way, I just think it’s interesting to dive a step deeper into this problem. Love the video! Edit: I’m now reading through comments, and I love to see that there are more passionate Mario Kart addicts out here in the STEM world.

You could do Luigi’s gambling game using statistics or the thrill digger game in skyward sword but there are potentially many many many Mario party minigames to choose from - ex air to a fortune using game theory

I have a friend that literally plays the highest acceleration combo with the intent of essentially becoming a time bomb versus your own skill with a normal kart

Nah this video needs to be bigger, deadass

We literally did apply the FTC... velocity is defined as the derivative of position, so integrating velocity to get position is a textbook example of applying the FTC.

4:27 I think the reason for many students getting this wrong is that they heard "When will the blue kart be faster than red kart?" instead of "When will the blue kart PASS the red kart?" because in the first question, the answer they gave would be correct but that was not the question asked.

I never thought calculus could be applied in everyday life like what teachers always say until I saw this video.

This is why I love my KZfaq recommendations 💀💀💀

There is already a full list of Pareto optimal combinations (at least for MK8DX) from which players can choose depending how much they value speed vs mini-turbo (accel.). Also, this video assumes 1) acceleration only matters when accelerating, and 2) top speed can be maintained unless you get hit or drive off the track. Neither of these are true since mini-turbo and cornering exist. Finally, items will change even the simplified calculations made here due to higher top speeds (think Bullet Bill). If we assume the top speed build moves at 10 units/s, while a high acceleration build moves at 8 units/s (top speed) and each gets 1 bullet/race, the high speed combo travels d = 10 units/s * (~8 s) = 80 units, while the smaller combo only travels d = 8 units/s * (~8 s) = 64 units. This extra distance covered while invulnerable can prove significant, particularly since a racer will very likely get many speed-based items in the course of a race.

I figured this out as a 8 year old playing mariokart wii. Although my reasoning was more like "if im faster and dont crash, i win"

If you just play casually just go for heavy characters and the fastest combo. Acceleration is irrellevant because you go full speed the whole race not slowing down thanks to drifting in the corners.

If being challenged is merely frustrating, then making it easier is the way to go. Please use your great capacity for empathy to understand that some of us find a challenge to be stimulating. If the only way through is grinding on the same fights over and over, I get frustrated and quit (Elden Ring). On the other hand, many games encourage you to try new strategies or creative and lateral thinking.

I understand why this wasn't brought up bc it doesn't have an easy calculus explanation and it kinda complicated, but mini turbo is actually way more important than acceleration, both in mk8 and mkwii. when you do a drift and get sparks on the wheels of your vehicle then get a speed boost upon releasing your drift, that is called a mini turbo, and the mini turbo stat affects the quality of this boost. in mkwii it only affects the duration of the mini turbo, but in mk8, not only is mini turbo a hidden stat, but it also affects how much mini turbos increase your speed by and how quickly they are charged. about acceleration in mario kart wii, it really doesn't matter all that much. mkwii has a weird feature not present in other mario kart games know as a stand-still mini turbo, or ssmt. ssmt's can be charged by holding the accelerate button and the drift button at the same time while not moving, and then released to get the same boost achieved from drifting. because of this, acceleration is rarely a factor in mkwii while it comes up a lot in mk8 where you can't use ssmt's to recover from getting hit.

Others have already mentioned the mini-turbo stat, so I'll instead add that getting hit and having to accelerate back up to top speed can be a major factor in how this plays out in reality! A high-acceleration player can deal with getting hit much more frequently than a high-top speed player can. If you're on a particularly hazardous track or playing with some very vindictive opponents, acceleration can ultimately come out on top. Unfortunately, this is a situation where you can't really work out a solution using concepts alone, since which racer pulls ahead depends on the specifics of how often each player gets hit. As a top speed player though, if you can manage to pull out an early lead and get ahead of the chaos of all the other players, it can be very hard for them to break that lead. I used to beat my brother at Mario Kart all the time by building for top speed in this way. I think the main takeaway here is that you're better at Mario Kart than you thought! Acceleration builds are much better at minimizing the impact of mistakes, but a top speed build doesn't have to worry about that if they just never get hit in the first place!

6:18 nah, this is exactly what I’m doing in intro to calc.

Very cool video! I love the combination of video games and math. You should look into the game Minecraft. There's a ton of math that can be done with that game.