Game Theory - How DEADLY Is Mario's Blue Shell? (Mario Kart 8)

Episode Date: April 7, 2023

Mario's bad guys are some of the most iconic in gaming - and I've covered MANY. From how deadly is Bob-Omb and Bullet Bill to whether or not Luigi is Mario's GREATEST enemy. Today, we are revisiting the most DANGEROUS game in the Mario franchise - Mario Kart. There is nothing scarier than being in 1st place and knowing that the Blue Shell is coming for you. How much damage would that REALLY do? Join me today as we find out!

Welcome to Game Theory, where the closest to failing a test I've ever come was my driver's test. It's no joke, by the way. I was one point away from failing my driver's test. In Ohio, we have this stupid thing called the maneuverability test, which tests zero real-life skills. And if the instructor had noticed that I actually did touch the cone rather than being just really close to it, I totally would have failed. But ha ha! But seriously, just give us a parallel parking challenge!

It would have saved me so much embarrassment during my first six years of my first six years out in LA until I finally forced myself to learn how to do it, the old-fashioned way, going to a school parking lot on a weekend and setting up some codes, a fully functioning adult teaching himself essential driving skills that he should have learned when he was 16 year old. But enough about me and my frustrations with parallel parking, let's talk Mario Kart and calculate the lethality of Mario Kart's most feared and most deadly weapon. No Reggie, not the blooper. I'm talking about the Blue Shell, the Victory Slayer, the great equal

Which once used soars to the racer in first place circles around them like a vulture circling its prey and then dives down Stopping them dead in their tracks as the shell explodes into a fiery inferno. So just how deadly is this weapon of mass cart destruction? Let's crack open our physics textbooks to find out. The key to determining the force of the blue shell lies with momentum Now momentum is the measurement of the motion of an object and it's calculated by multiplying the mass of the object by its velocity a light mass moving at slow speeds isn't gonna have that much momentum. A light mass moving at a faster speed is gonna have slightly more momentum. And a heavy mass moving at fast speeds is gonna have the most momentum. It's like me when I'm bowling. Now this may come as a surprise to you, but I'm fairly weak. So I can choose to throw a light eight pound ball quickly, like all the 10 year olds who are bowling next to me, or a heavier 16 pound ball slowly.

Both of those are gonna yield roughly the same amount of momentum and accordingly knock down about the same number of pins, usually around 7. Were I to throw the heavy ball faster, theoretically I'd be able to knock down more pins because I'd have more momentum Except my aim sucks so I just end up in the gutter or in the alley next to me Which has happened more than once and if you're wondering why momentum in this equation is written with variable P I honestly don't know probably just trying to put the P back into AP physics Additionally we need to take a look at one more physics concept here impulse Impulse is a measurement of the total momentum transferred by an action and it's calculus calculus by multiplying force times time.

So say I'm playing home run contest in Super Smash and I have two sandbags. I'm Ganendorf and I punched the first one for two seconds with a force of 100 newtons. Then I switch my character over to Captain Falcon and punch the second one second with a force of 200 newtons. Although I punched the two bags with two different forces for two different amounts of time, both of those actions would have had the same amount of impulse. Therefore it would be expected that the sandbags would fly the same distance. And if you're wondering my impulse here is written with the variable J, I honestly don't know that either.

Probably trying to put the J back into physics is just too complicated for its own good. It's the J in there. It's a very important letter. Now if we can calculate the change in momentum caused by the blue shell, we'll be able to find its destructive forces. Change in momentum is equal to the momentum before the shell hits you minus the momentum after it hits you. The momentum of the shell after it hits you is simply zero. You are no longer moving, so no matter what your mass is, your momentum is gonna be zero. That is how the blue shell works. It is easy. Finding the momentum before the shell slams into you though is gonna be a bit more difficult. Now in my last Mario Kart video, I determined that one of the fastest character cart combinations was Dry Bowser in the B-Dasher with slick wheels and a super glider.

I found that at max speed Dry Bowser can travel 180 kilometers per hour or 50 meters per second. For my fellow Americans that translates to over 110 miles per hour. These races are far from light joy rides through Toad Harbor. They are extreme. So we know his speed, but now we gotta determine his mass. In Mario Card 8, the game uses a system of hidden statistics to define a character's given attributes. Acceleration, on-road traction, off-road traction, and of course, wait. And I was able to track down a chart of these hidden stats.

Dry Bowser is listed as having a mass of 9. That's the good news. The bad news is that that 9 is unitless, so we have no clue what that 9 actually translates to. However, I just so happen to have an end. to have an ace up my sleeve. And that is the ace of Mario Jumpman Mario. It's a very weird deck of cards I'm using. In Mario Card 8 Deluxe, Mario is listed as having a weight of six units. Now, in a past video by my fellow game theorist, Austin, he used Mario Sunshine's water propulsion to calculate Mario's weight at just under 90 kilograms or about a hundred and ninety eight pounds. But uh, in all honesty, I don't trust Austin. He shouts too much.

Hey! I'm offended! So I found another way to verify that number. If Mario is indeed 89.94 kilograms like Austin says he is, and in Mario Kart, Mario is the equivalent of six units of weight, then one weight unit is gonna be about 15 kilograms. Knowing that, let's look at the carts. In Mario Kart, the standard cart is listed as weighing two units. The standard wheels weigh in at two units as well,

and the Super Glider weighs in at one unit. Add these together and you get your basic cart weighing in at five in game units. Five times 15 gives us 75 kilograms. And just how much does a standard Go-Cart weigh in real life? Wouldn't you know it? 75 kilograms! It's almost like Nintendo planned it this weight. Maybe they've known Mario's weight from the beginning, but no, no, there's no way! Anyway, between the scientific evidence in Mario Sunshine and the mathematical evidence in Mario Kart, that's all the proof I need. By the power vested in me, I officially certify Mario's weight to be 90,

Killegrams. 89.94 kilograms to be exact, but 90 kilograms So with Mario's height and weight certified, we have now created a standardized system of weights and measures that can be used across the entirety of the Mario universe It's a lot like the metric system, but a lot. And I mean a lot Nurdier. It also means that we can finally determine Dry Bowser's mass to calculate the impact force of the blue shell So Dry Bowser weighs nine units. The B-Dasher weighs three units, the slick wheels weigh three units, and the Superglider weighs one unit. Add all of that up and Dry Bowser in his fastest cart combination weighs 16 total units. With each unit representing 14.99 kilograms, we can determine that the mass of Dry Bowser in his cart is gonna be 239.8 4 kilograms. Now remember that momentum, the P in AP physics, is equal to speed times mass.

Therefore, the 240 kilogram dry Bowser traveling at a speed of 50 meters per second would have a momentum of 11,992 new. But again, that's just Dry Bowser. We're here to calculate the devastating power of the blue shell Which is able to stop that amount of momentum Instantaneously and that means that we're gonna need to know the blue shells impulse As I mentioned before impulse is a force applied over a period of time So it equals f times t it also equals the change in momentum which we just established The change in momentum the blue shell causes is 11,992 Newton seconds So if we want to know the destructive force that the blue

blue shells delivering in that moment of impact, all we need to do is eliminate time from this equation. Lucky for us, Mario Kart 8 Deluxe runs at a silky smooth 60 frames per second. And it takes 33 frames for a blue shell to bring you to a complete stop. So divide those 33 frames by the 60 frames per second and the time is calculated out to be 0.55 seconds. F times 0.55 equals 11,999, divide both sides by 0.55 and we get that the blue shell would need a force of 205 seconds. 81,803 newtons to stop the speeding dry bowser. But it gets even more forceful than that. Because you see, that 22,000 newtons would only apply if the blue shell is hitting its victims from head on.

The blue shell takes it one step further by flying over you and then diving into your face at an alarmingly steep 60 degree angle. So using trigonometry, I found that blue shells would require double the amount of force we just calculated. 43,670 newtons flying right at a racer's cranium in order to stop them in their cart dead in their tracks Compare that number to the bullet bill episode where I found that bullet bills have a force of 2,570 newt This is 20 times that amount of force making the blue shell the deadliest quote-unquote bullet in the mushroom kingdom In last year's Mario card episode, I found that in a worst-case scenario some impacts reach 2,000 Gs While the blue shell doubles that to a force of

of nearly 4,000 G's. In other words, why try competing to be the lead in this race when you can just kill off the player who's in first with your blue shell? Because that is exactly what's happening here. It's like sending the most family-friendly hit man to bump off someone who sorry was simply better at you in a stupid party racing video game. And I'm still not done because as any player who's in second place knows it's not the impact that gets ya, it's the explosion around the impact. Using more pixel measurements, I was able to calculate that the maximum blast radius of the blue shell explosion is 3.1 meters Now, there's a handy-dandy formula called Broads method that we can use to determine the energy of this explosion I've mentioned it before during the How Deadly is the Babam episode, but since it's a lot more math I'm just gonna speed speed up here.

The first variable in this equation of death is pressure. Pressure is equal to force divided by area. As calculated earlier, the head-on force required to stop Dry Bowser at max speed is 21,830 newton. Unlike with the Blue Shell, the explosion force is going to be head-on and not at an angle. Using pixel measurements and Mario as our newly certified ruler, I found that Dry Bowser has a cross-section of 1.87 square meters when he's racing. Therefore, the pressure of the blast would have to be 21,803 Newtons divided by 1.87 meters squared or 11,616 pascal. The pressure of the outside environment would simply be one atmosphere, which can be translated to 1001,325 pascal.

The volume is to find because all you need to do is determine the volume of a hemisphere with a radius of 3.1 meters. The formula there is 2 thirds times pi times R cubed, which calculates out a volume of 62.39 cubic meters. The final variable that's needed is the heat capacity ratio of air, which is a constant equal to 1.4. And just like that, we found all the variables needed to calculate out the energy of the blue shell explosion. After solving the equation, I found that the blue shell explosion has an energy of 17,000. 617 kilojoules. For comparison, that is the same amount of energy found in 4 kilograms of TNT. Loyal theorists might remember the United Nations Explosion Consequence Analysis website from the Bobom episode. With an equivalent of 4 kilograms of TNT, anyone within 15 meters of that detonation is going to expect a ruptured eardrum.

Anyone within 5.9 meters is going to be suffering from severe lung damage. And most dangerously of all, anyone within 30.5. meters of that explosion are just gonna be flat out dead. D.E.D. Dead. Thanks to Blue Shell's Mount Wario would be covered in police tape. Huge craters would start appearing in Toad Harbor. The TSA won't let me bring hand cream onto flights, but Mario and friends were able to bring the equivalent of 4 kilograms of TNT into Sunshine Airport without raising any red flags.

You better hope that you're racing with insurance, friends, and I'm not talking car insurance. I am talking life insurance, because these games are deadly. So there you have it. Blue shells are practically heat-seeking missiles designed as a turtle shell. The shells will absolutely kill the first place driver upon impact, as well as anyone within a 3.5 radius around them. They're all dead!

The Mushroom Kingdom is slowly killing off all of its best-most skilled drivers! Leave it up to Nintendo to violate the Geneva Conventions with a game that's rated E for everyone. So the next time that you pick up a blue shell in a mystery box, Take a moment to comprehend the sheer amount of power that you're holding. If you're in first place and receive the indication that the blue shells approaching, take those final seconds and make peace with your maker. I hope those two and a half laps in first were worth it, because the true winners of Mario Kart are the survivors,

the ones who stay smack dab in the middle. Basically, the Mushroom Kingdom is self-selecting for the most mediocre drivers of the bunch. Like me and my driver's test. The brakes, hit the brakes! But hey, that's just. Just a theory. A game theory. Thanks for watching.