Fun with kinematics!

August 11, 2012 8:05 AM

Racetrack is a game with very simple rules which nonetheless does a surprisingly good job of simulating the acceleration, braking, and handling of a race car. It can teach not only about inertia and kinematics, but also about optimal racing lines. Racetrack can be played with nothing more than a piece of graph paper and a pen, but there is also an online implementation called Vector Racer.
posted by 256 (41 comments total)

"Hey kids! Want to play Racetrack?"
posted by "But who are the Chefs?" at 8:18 AM on August 11, 2012

Neat! The little game widget is dandy.
posted by mwhybark at 8:24 AM on August 11, 2012

Nice! I'm a fan of the racing Euro-boardgame Formula De (aka Formula D), and I would be surprised if there wasn't some common lineage. I'll have to send this to my old gaming buddies, thanks!
posted by Strange Interlude at 8:33 AM on August 11, 2012

I remember seeing this (well the pen and graph paper version) on Why Don't You? as a kid and being briefly fascinated by it.
posted by fearfulsymmetry at 8:44 AM on August 11, 2012 [1 favorite]

For my algorithms peeps: How hard is optimal racing?
posted by erniepan at 8:54 AM on August 11, 2012 [6 favorites]

My friend taught me this game in the 70's, and he liked to play with a crash rule that you would be penalized two turns if you crash. That is, he liked that rule until I played him. At the midpoint of a long straightaway, I chose to accelerate one more time. He paused, and then said, "yeah, you might make it," while clearly he was secretly thinking, "the fool!" The next turn I blew his mind by doing it again. The next turn I crashed spectacularly into the far wall. I then patiently waited my two turns, at which point I was still way ahead of him. He never played me again after that.
One way to prevent assholes like me from ruining the game might be to penalize a number of turns based on the speed (x + y) at the time of the crash.
posted by bitslayer at 9:09 AM on August 11, 2012 [4 favorites]

The game is great for the way you can make a million tiny adjustments to the core rules and end up with different, but still recognizably related, games. Vector Racers is an example of this, with its gravel and other track types.

Crashes are one of the parts of the game just begging for house ruling. The default rules, as I understand them, specify that a single crash eliminates you from the game, but I've seen variations including bitslayer's friend's wait-two-turns rule, Vector Racer's bounceback rule, and complex damage points rules where crashing may or may not affect the performance of your car.

For an example of a very heavily modified version of the game, see Triplanetary.
posted by 256 at 9:17 AM on August 11, 2012 [2 favorites]

30.800
posted by progosk at 9:36 AM on August 11, 2012

If that was your first attempt progosk, that's incredible. I just posted a score of 30.067 after about thirty efforts. I'm trying desperately to beat "Downloader." I was wondering who he was, since I didn't recognize the mefi handle, then I noticed that he has the record on 49 of the 51 tracks on the site. So he's a resident Vector Racers pro and not a mefite at all. For the sake of mefi-pride, I feel that a mefite should hold the record on this track.
posted by 256 at 9:45 AM on August 11, 2012

We used to play this in the office with graph paper back in the early eighties, but a split emerged between most of the other players, who wanted to add extra rules to provide things like special boost points or slippery areas of track, and people like me who preferred the elegant simplicity of the original.
posted by Segundus at 10:12 AM on August 11, 2012

30.067, took me another twenty tries or so. We need to not leave Downloader on top, right?
posted by progosk at 10:22 AM on August 11, 2012 [2 favorites]

To update the algorithms peeps: The difficulty of Racetrack was settled at FUN 2010, by Markus Holzer and Pierre McKenzie. They found that, surprisingly*, it is a game that is fun to play that is in P! The single-player version is NL-complete, and the two player version is P-complete. Much more in their paper.

* - This is surprising because most games that are actually fun to play are in the complexity class PSPACE. The fact that Racetrack is in P (a.k.a. PTIME a.k.a. polynomial time) means that it is computationally tractable for a computer to calculate a winning strategy (unlike, say, Chess, where we can beat humans, but can not figure out for sure what the optimal starting move is without using more computational resources than currently exist on Earth; or Go, where computers can't even beat all the humans). Most games which are efficiently solvable are not very fun, for reasons which would take too long to go into in this footnote.
posted by pmb at 10:36 AM on August 11, 2012 [12 favorites]

Repetita non juvant - the more I try, not only are both my earlier scores proving elusive/unrepeatable, but I find I'm locked in (to 31.067), with every curve looking impossible to optimise any further...
My suspicion is that the trick is in finding a way to just barely jump over the sandboxes; and that maybe there's actually an alternative arrival route via the "i".
posted by progosk at 11:32 AM on August 11, 2012

I have been wondering the same thing, if perhaps the optimal path involves going through the bottom of the E and the lower arm of the F.
posted by 256 at 11:33 AM on August 11, 2012

And a second person (Karl, are you a mefite?) has found the 29.7 path.
posted by 256 at 11:35 AM on August 11, 2012

Bottom of the "e" seems unlikely, given the corner wall under the "F".
posted by progosk at 11:39 AM on August 11, 2012

Oh hey, I used to play this game with my dad all the time when I was little. I forgot all about it.
posted by pemberkins at 11:55 AM on August 11, 2012

Calculating optimal racetrack moves was a third year dynamic programming assignment.
posted by ceribus peribus at 12:24 PM on August 11, 2012

I was thinking dynamic programming, but I don't care enough to actually implement it.
posted by madcaptenor at 12:26 PM on August 11, 2012

I've been re-realizing over the last few years how beautiful games that be played without the aid of a computer can be, and this seems as pure as it can get. I look forward to playing.
posted by ignignokt at 12:44 PM on August 11, 2012

Most games which are efficiently solvable are not very fun, for reasons which would take too long to go into in this footnote.

You have an endless number of non-footnote comments and even OP-s to elaborate. You're not getting off that easily. Now - explain!
posted by Pyrogenesis at 1:04 PM on August 11, 2012 [3 favorites]

This is neat! And also makes clear that my habit of blowing turns and crashing into walls in racing games is not something I can just blame on twitch, because man.
posted by cortex at 1:07 PM on August 11, 2012 [2 favorites]

Yeah, this is very like Formula De, of the befamed 30 sided dice!
If you would like to play this with friends, I can strongly recommend that board-game.
posted by Iteki at 1:11 PM on August 11, 2012

I love this! I'd never heard of it before, it's amazing how interesting the race line can be with such simple rules.

I just made my brother play a game with me on paper, and I was cracking up imagining our paths being driven in real time. (I'm winning! Yeah, I'm going so fas- BRAKE, BRAKE! ... DAMMIT.) We decided that if you "crash", you have to a come around to a stop at the point where you went off before continuing.
posted by lucidium at 1:24 PM on August 11, 2012

There's also an iOS implementation. It's called Dash Race.

Also on iOS, Vector Rally is good.
posted by hankscorpio83 at 2:01 PM on August 11, 2012

Racetrack and battleship where the two games we played most, graph paper and pencils.
posted by StickyCarpet at 2:17 PM on August 11, 2012

Am I the only one who finds Wikipedia's explanation of the rules to be incomprehensible?
posted by rhizome at 2:47 PM on August 11, 2012 [1 favorite]

Am I the only one who finds Wikipedia's explanation of the rules to be incomprehensible?

I couldn't make any sense of them at first either. Having played the online version it becomes a little clearer.

The idea is that you calculate the point to which your current velocity would take you (ie if you moved up two squares and right one square for your last move - do the same again) then decide whether to move there or to any of the eight adjacent intersections - this will then give you your velocity for the next turn - and so on.
posted by beardless at 3:13 PM on August 11, 2012 [1 favorite]

Figured out the 29.7 route. It's somewhat counterintuitive - you never go faster than 4sq/s rightward.
posted by anthill at 3:16 PM on August 11, 2012

Spoilerpic, please, anthill.
posted by progosk at 3:48 PM on August 11, 2012 [1 favorite]

A non-$70-paywalled version of "The Computational Complexity of RaceTrack" paper can be found here (PDF, page 79).
posted by you at 4:20 PM on August 11, 2012

False alarm, that was just an extended abstract :( Does anyone know if it was published anywhere else?
posted by you at 4:25 PM on August 11, 2012

Love, love, love Racetrack (which we called Graph Racer). It didn't take long before we added machine guns, flamethrowers, caltrops, oil, ramps...
posted by obiwanwasabi at 5:11 PM on August 11, 2012

woot!
posted by midmarch snowman at 5:56 PM on August 11, 2012

29.7! Take the lower branch of the F.
posted by Casimir at 6:20 PM on August 11, 2012

32.4. I think I'm spending too much time in the M-e gravel pit.
posted by ceribus peribus at 6:32 PM on August 11, 2012

Woot! I watched the AI's until I saw one that finished in a time that ended in .7, and adjusted my end route accordingly. spoiler
posted by ceribus peribus at 7:30 PM on August 11, 2012

I first learned of this game from Martin Gardner's Mathematical Games column back around 1973 (I was 12), and we continued to play it through high school, mostly during class. The game board on graph paper is easy to mistake for real work from a distance.
posted by iconjack at 10:23 PM on August 11, 2012

This looks like fun, but it's no Car Wars. Racing/driving is much more compelling with machine guns bolted to your hood.
posted by datter at 5:44 AM on August 12, 2012

I can't believe there are no Mario Kart tracks in the user submitted section.
posted by hot_monster at 9:14 PM on August 12, 2012

Nice! I'm a fan of the racing Euro-boardgame Formula De (aka Formula D), and I would be surprised if there wasn't some common lineage. I'll have to send this to my old gaming buddies, thanks!

Not very much like Formula D/De really: FD has a lot of variability is performance / speed and the "physics" as they exist are coded into the shape of the track and lanes. And FD also has all the tyre / engine consumption as well.

The direct boardgame version of this is called Bolide, a neat little game, available for a reasonable price, that I have failed to convince anyone to play with me.
posted by outlier at 12:31 AM on August 13, 2012