Mario meets Pareto
mayerowitz.io
mayerowitz.io
I feel like the common trap for designers is to put too much stock in tag lines like "Over 700,000 different builds!"
You're dumping a combinatorial explosion of overhead onto players. If all those choices don't significantly enhance the core game experience, you as a designer as wasting people's time. Doubly so if most of the choice space can be safely eliminated by savvy players. The internet exists after all and someone is going to do the math. Why would you gate the competitive portion of your game behind convex optimization problems? Certainly not to make things more fun.
Some examples of these trends are load-outs in FPS games. Every gun now has tradeoffs for sights, barrel, under-barrel, magazine, ammo, etc. and these choices only come after you've chosen a class/weapon. When the core of an FPS is tactical positioning and aim, these options feel like a cheap gimmick in order to milk slightly more time out of players. Franchises like Halo and Battlefield fell for this trap and have completely ruined their reputations.
You can still give players choices that _add_ to the core gameplay like counterstrike does with the round economy. If the entirety of a choice you're giving a player happens in a menu, that should be a red flag. The game design industry needs to less emphasis on statistics/combinatorics and more on gameplay/narrative.
The most important thing: Don't tell others how to play. Don't tell them "you should pick X because it's the best" unless they explicitly ask for it. Let people play their own way, and don't push how you play games onto others.
> It depends on why you play though; the "combinatorial explosion of overhead" is only a problem if you're trying to min/max, if you play for fun it's more "What character do I like" or "What wings do I find pretty".
Exactly. These choices don't affect players in the same way.
> The most important thing: Don't tell others how to play. Don't tell them "you should pick X because it's the best" unless they explicitly ask for it. Let people play their own way, and don't push how you play games onto others.
I definitely agree with you here.
As a designer, you're defacto telling people how to play by designing choices like this. You're punishing casual, competitively natured players with >700,000 options because they care about performance.
If you don't derive fun from winning the trade-offs are mostly irrelevant and you can simply ignore most of the problem, choose a configuration based on fewer/simpler dimensions (I'm going to pick yoshi and the egg kart because that's awesome), and avoid most of the decision space. This type of player probably wouldn't care if all the configurations performed the same or more likely could be annoyed that their desired configuration performs strictly worse. (If the choices meaningfully affected gameplay, like having an ability to lay eggs or something, that's different).
On the other hand if the dedicated, competitive players are going to solve the optimization problem and coalesce configurations down ~10 choices. The problem space is also irrelevant to this type of player.
But posing this problem negatively affects competitive people who aren't dedicated to the game. Now they have to consider an intractable problem while their friends are waiting on them so they can actually play the game. I know this because I've sat there plenty of times while friends scroll through all the different options wheels/karts/gliders/characters for minutes until they gave up and said something like "Whatever, I just want to race".
So why not just give 10 performance profiles and the same combination of cosmetic choices as before?
Then why don't you make sure all the pretty wings are on the Pareto frontier?
Back when I was playing D&D 4th edition (fairly casually), I started by assuming that all the fighter "feats" were basically equivalent from a damage perspective, and only differed in application or aesthetics. Then I did the math, and determined that there was a 2-3x difference between the weakest and the most powerful feats; so naturally I chose the most powerful ones. But I didn't really enjoy that process -- I felt obligated to do it because... I mean, I'm trying to increase in power? That's the whole point of the game?
Why should choosing an aesthetically pleasing power mean my character is weaker?I would have had much more fun if they'd balanced the feats such that they were all about the same (or at least, all on the Pareto frontier). Then I could really have chosen based on personal taste or roleplaying reasons, rather than trying to avoid having a nerfed character.
ETA: I feel like StarCraft does this very well overall. If nobody's using a unit, they buff in the next balance update; if everyone's using a unit, they nerf it in the next balance update. The result is that there are millions of potentially successful strategies, even at the grandmaster level, as long as you play efficiently. That's a lot more fun to me than 700,000 strategies, of which only 20 are realistically going to win at high levels.
Even something like Counter-strike, where a lot of the differences are pretty subtle, I liked having a good amount of choices just to play a couple rounds with a gun that feels slightly different and see how well I do. I had my preferences but I played with them all.
That being said I do think there's something to be said for not just dumping a bunch of options on a player and be like "you figure out how you want to play", even though I've been guilty of that in a couple past games I've designed, thinking more options is better.
Like I remember on of my sequels to a game I tried all sorts of ideas for how to change up options, and instead of pinning down that "okay the hand size is going to be 5 tiles, and if you place next to an ally tile you'll bump them up by X amount, and you can choose what set of numbers the tiles can be (like 1-5, or 1-10, or 1-20)... with my new sequel I've mostly pared it down and I'm taking away game options, because I bet almost no one did anything but use the defaults anyway. At least before I hid them in an options menu you had to choose to open.
I do agree with you, generally, that this is a bit of a cheap trick and far too ubiquitous. However, there is something to be said for giving the player "things to do" like unlocking content. It does add to the experience to have a sense of "this is why I'm still playing".
And even in the case of the OP, concluding that most items are useless is not a substantiated conclusion. As the OP notes, a Pareto frontier is N-dimensional, and the number of points lying on the frontier grows exponentially as we expand to consider all the other variables. Just because a meta exists among "top players" doesn't mean that's the only valid choice; different people can optimize for different things (and even top players are frequently irrational, lazy, and/or cargo-culting).
I don't think my comment was implying any of this.
I was mostly trying to say something along the lines of "solving NP-hard problems isn't good gameplay" rather than discuss micro-transactions, progression systems, or variance/competitive purity.
Consider that Tetris is NP-hard. :) Giving the player optimization problems is one of the fundamental pillars of game design. For many, it's more fun to make a deck of cards in Magic or Hearthstone than to actually play the deck against an opponent.
I'd appreciate a bit of a more charitable interpretation of my responses.
Given the context, a more charitable interpretation would have been something like:
"solving NP-hard problems isn't good gameplay...*in and of itself*"
> Giving the player optimization problems is one of the fundamental pillars of game design.
Yes, but this is not what I'm talking about at all. I don't know how you're interpreting my position as being against optimization problems in games.
> Consider that Tetris is NP-hard. :)
Would you consider that the choices that make Tetris NP-hard significantly enhance the core game experience?
How about MtG or Hearthstone?
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> Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith.
We all know that guy you can’t play games with because he sucks all the fun out of it for anybody else. As a game seller this isn’t just bad, it’s stupid.
That said, the sheer amount of options leads to a class of expert players and build-makers that normal players can rely on. I just wish the game itself provided more tools for navigating it (like an ingame build-guide system).
Even during parties, the properties of choosing different characters do make the game more dynamic which in the end means more fun. What sucks is when one of the players have spent the whole week before plugging all the numbers into Excel and knows how beat everyone else optimally. But where do you draw the line? Is this more unfair than practicing driving one track a whole week?
One have to accept that games can not be always fair. Same thing in sports, try playing tennis vs someone who has competed before, a casual player will not stand a chance to even hit a single ball, even if you give the pro a much worse racket.
Balancing a game to allow casual and pro players to compete on equal terms is extremely difficult and can often backfire into making the game extremely trivial, only depending on roll of dice. Knowing if you are playing an excel-game or a reflex-game should be presented clearly to makes things a bit more fair.
Anything with large bumps will do.
Well obviously, it's probably actually infinite number of things you can do with it. That... should not really be a selling point.
For the most part, once you've got your kart dialed it. It is still "pick your character and go". It's one of my goto games for "I want to do something for a few minutes to unwind" (which usually ends up with me more frustrated and on edge than unwound haha).
Storyline is nice but if I want to watch a movie I'll pop in a DVD and get popcorn. Cutscenes get in the way after the first play through. Timeless games have some storyline but let you enjoy the game even if you skip the cutscenes.
I like Luigi more than Mario. But do I love Mario like a 6 and Luigi like an 8?
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The content's excellent and it was fascinating to see how the differences between characters and karts play out though!
I totally agree; I don't understand the fascination HN has with these types of sites. It all feels like extraneous design just for the sake of it, rather than actually making anything easier or better to understand.
And if you need a 3d graph, you're only a handful of lines away from smoothing out your presentation, so why not?
There's also the more subjective aspect, I think adding the effort to make something look nice and slick, animated well, could be both an interesting challenge and a relaxing pass-time. It's pleasing both to make and digest, in a way, it sits in an intersection of design, art and technique and as an added bonus, could help capture the attention of someone who struggles with short attention spans even better!
As a game designer, you want to add silly and suboptimal things to your game. Don't fall into the trap of thinking that every decision must be perfectly balanced and equally weighty, because your game will turn out bland and textureless. And beyond the considerations of "optimal" play, putting suboptimal options into your game can serve as both a way of naturally selecting difficulty without having to implement ungainly difficulty sliders, and also accommodate fun/silly challenges for people who just want to mess around.
In a sufficiently complex game every build is on the pareto front as it optimizes some specific cost function.
However, if your one and only goal is winning I suspect that the high dimensional vector space will end up not looking so high dimensional once you account for the correlations between the different features you use. This is already clear from the very strong correlation between speed and accelaration.
[]I myself have played MK64 a lot and sometimes the goal was simply to see the world burn, standing on a corner with a shell waiting for the what would've been the winner of the race. Fond memories.
Even if you're only optimizing for race times, in the case of Mario Kart, the choice of track will have a huge impact on the optimal kart selection. Tool-assisted speedruns pick different karts for different tracks.
Or! In this case, it reduces to a one-dimensional optimisation thanks to the structure of the problem.
What we're optimising in portfolio selection is not the return of a single investment, but of a lifetime of investments. And thanks to compounding, that is a function of both risk and return. So we can find the optimal allocation without making any tradeoff: https://two-wrongs.com/the-misunderstood-kelly-criterion.htm...
The article even hints at this by observing that the discounted sum of future salaries are part of your current wealth. Which is exactly correct and also -- if you're young -- the most significant variable by several orders of magnitude. Curiously, the author understands this but doesn't care.
Acceleration because when (not if) you get hit/crash, you need to be able to catch up quickly.
Svelte has some pretty nice built-in scroll animation support: https://svelte.dev/repl/051cd352ce284d15b55c91c8b30fa32f?ver...
In practice when playing online however, you won't know what track is about to be played, and so the meta right now prioritises mini-turbo stat much higher than speed. Having a high mini-turbo can also overcome the lack of speed by performing additional mini-turbos even on straight sections. Also when playing online you also will be hit by items a lot and need to try dodge other items being thrown at you, and for that having higher acceleration helps too.
Weirdly, this has a huge impact on the game, and it's also not mentioned anywhere. To find it out, you have to go to mariowiki and look up the part statistics. The kart that looks like a boat has great water statistics. That makes sense, but without even documenting that water speed exists, it's mostly just an in-joke by the developers. Why did they do this?
For my part, I got the best rank in single player on all pre-DLC tracks with only toad and the default kart, so it's a part of the game you can entirely ignore if you're not competing against other humans.
Bagging means purposefully being far from first to get good items which allow you to come back hard.
[1] https://www.mariokartcentral.com/ [2] https://www.mk8dx-lounge.com/
How many players are making a living competing mario karts?
Taking part in competitions with prize money doesn't make you a professionnal player. When I was a road racing cyclist in the upper amateur echelon I was making a decent amount of money in finish prizes, was sponsored, was given a high end bike, clothing and enough tires to last a season, and the mechanic wouldn't charge me for his work, all non local travels were paid. Yet I wasn't a professionnal cyclist as I didn't have a salary nor would I have made enough yearly money to support a family and leave a job.
So what are the highest, median and average income of those so called 'Mario Kart pros"?
[1] https://en.wikipedia.org/wiki/Dolly_zoom
My kid (6) crashes all the time, and she is naturally attracted to picking Peach. I'd say because of that, a character with high acceleration is going to be better. Though she also just likes to push the gas.
Though we're playing the one from GBA on Analogue Pocket. Which is probably a lot less advanced as the one in question here (a game for Wii U from 2012), it does resemble Wacky Wheels quite a lot.
Tufte is still alive!
Another thing is the coins. Collecting them gives you a speed boost for each coin you collect.
Your kid has likely better reflexes and motor skills than you have, but on your side you have experience and wisdom accumulated over the years :)
1. Skill absolutely matters, more than the kart, etc. that you pick. Watch some expert players on YouTube playing with weird builds and you'll see that they are still able to do well even when playing with significant disadvantages.
2. In practice, you don't really need to know the value of the hidden mini-turbo stat because higher acceleration == higher mini turbo. For 99% of players, acceleration can just be used as a proxy for mini-turbo.
With that in mind, is this style of presentation (i.e. different elements jumping out or moving into focus as you scroll down the page) easily doable OOTB with any JS libs? Or is this pretty much a custom job?
https://hinnefe2.github.io/python/tools/2015/09/21/mario-kar...
In all other games, character choice doesn't affect item distribution.
But I also didn't realize this was the case on SNES. I only ever played the SNES version as a young kid, and it was a Japanese NTSC version on a PAL television through a cartridge adapter and it was pretty janky.
Very cool and I see the vision
Unfortunately on firefox for Android 13 on my nothing phone (2a) almost all on-screen assets flicker non-stop. I thought I was a style decision at first but now that I'm further down it's very clearly a bug.
Still very cool, learned about pareto efficiency from a video about this exact topic a few years ago that only computed the pareto front for accel and speed because they couldn't represent higher dimensions well. Maybe same author?
Worth noting that the tires and gliders are independent, so one can first find their pareto frontiers, then combine that with those of the drivers for all dimensions
=> https://en.wikipedia.org/wiki/Efficient_frontier
While reading this article, I saw those graphs and thought, "Where have I seen this before?"
Having spent the past year building a journey planner algorithm, which heavily builds on pareto optimality/sets, from scratch, I was waiting for the full set of pareto optimal solutions. I.e. all kart combinstions that are best in at least one way.
Should be doable by iterating through all possible stats and merging[1] into a set for each one. We might get a lot of solutions, but it should be somewhat managable.
Has anyone tried this?
1: Merging is to take the new entry and 1) removing any existing entry that is dominated by it, and 2) adding the entry if it is not dominated by any existing entry.
It immediately has me looking for other places to apply this. This'll be top of mind for a while!
But this isn't _really_ about Mario Kart I suppose...
But they seem to have ignored kart physics and made it more like a car, where bigger cars might accelerate slower but can accommodate a more powerful engine.
I hadn’t actually thought about it before but as an incredibly skinny person what you said lines up with my experience in a kart. I could seemingly go slightly faster than others but more easily span off and lost control.
When I wrote that comment I was thinking one might tune the kart for the driver to make up for lack of acceleration which would reduce top speed.
I wonder, in practice, does defining my preferences and weights and then using a genetic algorithm find the optional solution? That would take me less thought, because I already know exactly how to define a score function and use a random API.
Look up NSGA and NSGA-II for a good starting point. Then Kagi your way deeper into the rabbit hole.
"all elements on the frontier are not equally good."
Peach is just as good as Daisy, for example, so I'd say: "Not all elements of the frontier are equally good."
If this was more than a tool for teaching multi-objective optimization, I'd like to see how the Pareto front changes over Mario Kart releases!
https://www.mariowiki.com/Mario_Kart_8_Deluxe_update_history
No, A Pareto, the excellent economist.
OK I might be an old bitter cynic, but the beginning got my hopes up for something clever. The only value I see here is explaining the Pareto frontier, but it doesn't take a genius to independently figure out, if you have 2 attributes, and someone else has one of the attributes at least equal, and another higher, that someone else is a better pick…
Of course, what the article doesn't even touch, is that some attributes could get worse results as they get higher: imagine having an acceleration and speed so high that you effectively can't steer your car.
Also a pedantic argument could be made on the cosmetics possibly actually affecting performance…
If you don't want to use the "artificial, unintuitive interface" (bit rude IMO) you could just google "best mario kart setup".
The selection of attributes is not exactly arbitrary. AFAIK speed has always been by far the dominant stat in mario kart, then acceleration. Choosing e.g. better handling at the expense of speed is an immediate disadvantage. If your problem is that this doesn't help you to choose atteibutes in the general case, take it up with the chaos of the natural world...
This article solves a problem people have (not knowing what setup to pick) in a very stylish way (subjective) and teaches the reader something along the way (what a Pareto frontier is).
Not a particularly constructive comment if you ask me.
The article starts with the premise and fails to deliver. The visual layer of the article is nice. But ultimately the example of using the Pareto's frontier is a FAIL because it doesn't deliver on its promise of finding the best kart setup.