Mario Kart 8's 585 Builds, One Pareto Frontier
Mario Meets Pareto
In Mario Kart 8, choosing a driver, kart body, tires, and glider involves trade-offs between speed, acceleration, and mini-turbo. With 585 unique builds, finding the best is a multi-objective optimization problem. Applying Vilfredo Pareto's concept of efficiency narrows the options to 14 Pareto-optimal builds, but the final choice depends on personal preferences. This article demonstrates how Pareto frontiers help filter out dominated choices, with applications beyond gaming, from meals to investments.
The Pareto front helps you eliminate objectively all the sub-optimal options.
- jerf
This is a really important concept for developers.
One aspect for developers that I see quite often is the assertion that "We can't have X without giving up more Y", most commonly "we can't have more security without giving up on user experience". With the Pareto idea in mind, we can see that that statement is true, if and only if you are in fact on the Pareto frontier of security and user experience already.
However, many times these confident pronouncements are being made when the system under question is quite evidently not on the Pareto frontier in the first place and indeed you can get more of one without giving up the other.
Making it more tricky is that in business, you can never discard "money" as a dimension, so unless you're taking "money" as one of the dimensions in the original comparison you want to do, it sneaks its way in. Or, a composite time/money, or "cost to business", or some other similar concept, time & money aren't orthogonal and don't need to be treated as two separate dimensions in general, though you can if you want. Which puts you into the 3D case, and as the page says, that grows the frontier quite a lot, which is good in some ways and bad in others. Nevertheless, in my opinion it is still often the case that even in that space we are often making "tradeoffs" without checking that we're on the Pareto frontier in the first place.
- uzerfcwn
I did similar analysis a couple years ago for optimizing item builds in WoW classic. The tricky part in WoW is that there are 15ish item slots with hundreds of item choices for each slot, so the total number of builds is well over 100^15.
I ended up using a divide-and-conquer style approach, where I 1) pruned items that weren't on the Pareto frontier individually for each slot, 2) took the two slots X and Y that had the least items after pruning and grouped them by calculating Z:={x+y|x∈X,y∈Y}, 3) pruned items that weren't on the Pareto frontier in Z, and 4) repeated steps 2-3 until there was only one group remaining, comprised of the full Pareto-optimal item builds.
This ran in a couple of seconds, as opposed to the other solutions I tried that took somewhere between minutes and years. The downside was that including set bonuses into the model took extra work.
- __s
> You probably won't pick a driver sitting on the edge of the frontier because you want some balance between speed and acceleration
for super mario kart speedruns go with bowser/dk: https://www.speedrun.com/smk/runs/zp68nr8m
That seemed to hold up for Mario Kart 8 too going with Bowser at the edge of their pareto frontier, https://www.speedrun.com/mk8
needing acceleration is a skill issue
- moomin
Of course I, and most of the dads I know, optimise for something else: what’s the car that will keep me competitive, but probably losing, to the kids?
- a3w
I did not understand https://news.ycombinator.com/item?id=49096439, but I understood this.
- tgtweak
2020: https://www.civisanalytics.com/resources/the-best-mario-kart...
OG credit to: Henry Hinnefeld
2015: https://hinnefe2.github.io/python/tools/2015/09/21/mario-kar...
- CobrastanJorji
I love when people do an amazing job carefully explaining something complicated in a way that makes it seem very intuitive. Excellent job. Way to show off those technical communication chops!
- cortesoft
There are a few things that are assumed to be true when talking about the Pareto frontier here, but aren’t always true.
One, that more of something is always better, e.g. it is always better to have more speed.
Maybe, but what if having too much speed causes you to run off the track and perform worse? It could be that there is actually a peak in the utility of speed that declines as it increases.
There could also be important relations between attributes that make determining a Pareto frontier impossible or at least more difficult. For example, some pairs of attributes work best when they are a specific ratio, and increasing one or the other will actually decrease utility unless the other is increased at the same time.