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Game Theory: How to BREAK Mario! (Mario Tennis Aces)

Feb 27, 2020
*heartbeat* + *applause* *gasp* *shiver* Peach: Oh, noooo! Hello Internet, Welcome to GAME THEORY! Spend more time analyzing fictional sports than going outside. I know I recently said that Mario is classified as overweight on the BMI scale. But one thing BMI doesn't take into account is muscle mass, which is heavier than fat. And when you look at Mario, sure, he may look like an adorable chubby plumber, but he may actually be the most athletic character to ever appear in video

game

s. I mean, he's appeared in 25 sports spin-off titles. He competed in every Olympic event. Both in summer and winter.
game theory how to break mario mario tennis aces
And he mastered everything from golf and soccer to non-traditional activities like having Waluigi slowly polish him. (Hip hop music) OH YES! Oh, Waluigi, causal lover. You may not make the Smash Bros cut, but you'll always have a spot on Mario's dance card. You will be the challenger who will approach from behind every time. Mario's latest adventure is MARIO TENNIS ACES on Nintendo Switch. What loyal theorist will remember from that,
game theory how to break mario mario tennis aces

More Interesting Facts About,

game theory how to break mario mario tennis aces...

Instead, today I want to take a closer look at the coolest addition to this

game

: zone shots. You see, during matches, players can fill an energy gauge by picking up the ball. Then, with enough energy, you can hit a zone shot, a shot that moves quickly and is almost impossible to return. Almost impossible. You see, that's where this brilliant little strategy is involved. You have the option of taking your zone shot in the corner of the court, where your opponent will have no chance to return it, or shooting directly at him. If you go this route, they certainly have a chance to hit again, but if they miss, their racket may snap in half, forcing them to lose the match entirely.
game theory how to break mario mario tennis aces
Apparently, with Mario hoarding all the gold coins, no one can afford more than one scandal in this universe. ANYWAY, this all got me thinking. Is it really possible to throw a

tennis

ball with so much force that it can

break

the opponent's

tennis

racket? And if it can

break

a tennis racket, what other horrible things could that ball do? I know we've talked about how deadly some things can be in Mario games, but could his deadliest weapon be a simple tennis ball? Let's get out our T1-83s and find out. As with all games, first and foremost we will need to determine a sense of scale.
game theory how to break mario mario tennis aces
But luckily for us, gaming's most trusted ruler, Mario Jumpman Mario, is here for us to use. At 155 cm, Mario allows us to convert game measurements to real-life units. And surprisingly, the courts in Mario Tennis Aces are surprisingly realistic. I found that the game's courts are just a few centimeters away from the dimensions of regulation-size tennis courts, which are typically 78 feet long (23.77 m), and for singles matches, 27 feet wide or 8.23 m. I mean, the French Tennis Federation has already banned skin-tight suits, so I'd expect flying clown cars to be considered illegal in the game as well. But heck, at least the size of the courts is according to the rule books.
Additionally, the game does us a favor by providing a serving speed in miles per hour, which is similar to what is done in real-life televised tennis matches. However, an experienced theorist like me knows that these in-game speedometers should be taken with a grain of salt. So how does the radar gun in Mario Tennis Aces compare? Using frame rates and more pixel measurements than I could reach with a racket, I found that the actual speed of any given server was about 10% slower than the speed shown on the radar. And while it may seem like Team Nintendo is simply crunching the numbers on their characters' behalf to make things faster and more exciting, the same thing happens in real-life tennis matches.
The average speed of the serves is always lower than the speeds that appear on television. And for once, it's not because they intentionally lie to us. Instead, the radar reading is always taken immediately after hitting the ball. At that precise moment, the ball travels at its maximum speed before beginning to steadily slow down due to air resistance and spin. Incredibly, Nintendo is two for two when it comes to precision in this game. And we could also do it three out of three because I also checked gravity based on the speed of the falling tennis ball during serves, and I checked that too. 9.7 m/s squared, which is pretty close to the real-life 9.8.
Overall, this might be the most realistic Mario game ever, as long as you're willing to overlook the giant sanctioned metal ball that allows you to play tennis. Taking a closer look at how tennis rackets break during play, even before doing any calculations, a major concern stands out to me. If you zoom in during a successful zone shot, you can clearly see that the racket is breaking at the handle. The thick part where the player holds the thing. This is a huge red flag, because in real life, when rackets break, it almost always happens in the strings, frame, or neck.
Physically speaking, this makes the most sense because they are the weakest part of the racket. and therefore they are the first to break when any type of force is applied. Either because of the ball or when the player decides that he needs to get angry to leave it and, oddly enough, in the image that ended up going viral for other reasons. Nintendo shows Luigi's racket breaking at the right point, the strings and the neck. But apparently it was too difficult to implement in the actual game, so we're stuck with what's shown in the game, which I guarantee will give us some absurd numbers.
Now, you may remember from the blue shell episode that momentum is a method of determining the force transferred by a projectile. That is the measurement that helps us determine if a ball can break the racket. Momentum equals force times time. It is also defined as the change in momentum, which, for a ball traveling in one direction and then hit in another direction, will be fairly easy to find. Momentum is equal to velocity times mass. Then we need to find the mass of the ball, the velocity toward the racket, the velocity away from the racket, and the amount of time the ball is actually in contact with the strings, giving us a total of four unknown variables that are all pretty easy to find.
We must first assume that the ball has a regulation tennis ball mass of 58.5 grams. But considering how realistic the measurements are in this game and the fact that the ball behaves similarly to a real ball on three different court styles. This is not such a difficult assumption. Ball speed can be calculated using frame rates and pixel measurements. Just like we have been doing in all the episodes. And we get that it is traveling at 96 miles per hour before impact (43 meters per second). And 28 miles per hour (12.7 meters per second) in the other direction after being hit. So with all those numbers in place, we can calculate the change in momentum.
Final moment minus original impulse. Because the mass always has to be in kilograms for this, we shift the decimal point a few pl

aces

, which is always the most unpleasant part of these kinds of physics equations, keeping the units together. I only have to say this to express what I am sure is the sentiment of countless students who take high school physics. I would say that more points and half points are lost on tests that way than ANY other way. And speaking of those really mining things that are always very unpleasant to follow, this is what I always have to remind myself when it comes to momentum.
The ball heads in opposite directions before and after impact. Which means that one speed has to be positive and the other has to be negative. I mean, think about it this way: if they were both positive, that would simply tell us that the momentum had slowed, but was still going in the same direction, which is obviously not the case. The total speed change was the speed entering the racket plus the addition of 12.7 meters per second, going in the opposite direction. In total, the change in speed was 55.7 meters per second. Does all that make sense? Welcome everyone back to school!
Tell your math teacher about this episode, maybe you can watch it in class... Anyway, doing the math gives us 3.26 Newton seconds, which is stupid and means absolutely nothing to any normal human being. So let's put it in terms that actually make sense. To do that, however, we will need to know the impact time, which is as simple as counting the frames that the ball is in contact with the racket. It's only 3 frames, and at 60 frames per second, which translates to 0.05 seconds, which, surprisingly, is about the time a typical tennis ball in real life will be in contact with the strings of the racket.
Mario Tennis Aces, ladies and gentlemen, I now give you the award: Nintendo's most realistic game. Boom! There's the sticker. Slap that one on your box art. Interestingly, this number of 0.05 tells us that Mario and the team are practically professional level tennis players. You see, players can control the impact time between the ball and the racket by adjusting the stiffness of their stringing. Beginners may not be able to hit the ball very hard, so they will typically use a racket with a soft, low-tension net to increase dwell time: the time the ball stays in contact with the ball. chain.
This in turn allows us to fish with momentum to bounce the ball at high speed, but it comes at a price: loss of control. On the contrary, professional players already hit the ball with full force, so they tend to prefer a racket with a tight net to shorten their total impact time, closer to the ones we see present in Mario Tennis Aces. For them, it's all about spin and trick shots. In fact, many will have 2 or more rackets on hand with different string tensions so they can change strategies mid-game ANYWAY with all that information we can determine THANKS FOR WATCHING!!!!! !!!!!!!!!!!!!!!!!!!!!!!!

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