Talk:Racetrack (game)

Untitled
What is the best way to cross-link the articles called Racetrack and Race track? Should the articles be moved to Race track (facility) and Race track (paper and pencil game), with a disambiguation page and some redirects?--Niels Ø 09:48, Mar 15, 2005 (UTC)
 * I think that Racetrack should redirect to Race track, and the game should be Racetrack (game). If you look at the "What links here" page for this page, you can see that almost all refer to the racing facility, not the graph game. If no one objects I'll take care of these moves in the next day or so. --Fastfission 18:41, 15 May 2005 (UTC)

Martin Gardner?
From :
 * The game was apparently first presented by Martin Gardner in his "Mathematical Games" column in Scientific American.

If anyone can confirm this, it should go in the article.--Niels Ø 22:19, 26 November 2006 (UTC)


 * Nice find, but confirming this will be difficult, since the Scientific American archives in the web are only available from year 1993 onwards and your source says it was read from a book published in 1983. I just read the A quarter-century of recreational mathematics article but in vain. --ZeroOne ( talk | @ ) 01:51, 27 November 2006 (UTC)


 * There is no doubt that Martin Gardner wrote an article about the game - but I certainly played it in the 1970's - so he was reporting something that was widely played throughout Europe at least. I'm the author of . My efforts to track the game to it's ultimate inventor failed - but for absolute certainty, Gardner didn't invent it.


 * Around the time I was playing the game there was also a published space game based on a hexagonal grid that had planets with gravity. The movement rules were the same as the car racing game - except you can accellerate in 6 directions instead of 4 or 8.  You had limited amounts of fuel and used one unit of fuel each time you accellerated.  Gravity was done by red arrows printed onto the board.  If your move starts on one of those arrows, you have to add it's direction to your previous vector.  All six spaces around a planet had arrows pointing inwards to the planet - which permitted you to orbit stably without using fuel - or to use planets to 'slingshot' you around.  You could refuel at any planet by making one complete stable orbit.  The board was laminated and you drew on it with a grease pencil.  As I recall, the objective was to orbit each one of the planets in the solar system at least once and return to Earth.  That was also around in the mid 1970's.


 * Sadly, I don't recall the name of that game. SteveBaker 04:44, 13 December 2006 (UTC)
 * (I remembered and added a section about it - it was called "Triplanetary". My reference proves that was published in 1975 - ergo the idea of "vector-motion" games didn't come from Martin Gardner's 1983 Scientific American column.) SteveBaker (talk) 20:05, 21 February 2008 (UTC)

I translated this nice article into german (http://de.wikipedia.org/wiki/Racetrack) and enhanced it a little. Hopefully you are content :) --82.135.67.23 14:03, 7 June 2007 (UTC)


 * When I learned to play the game (under the name 'Vektorrace') in Denmark in the mid-1970s, it was attributed to Danish inventor and polymath Piet Hein. Whether this attribution was true, I can't say -- but it certainly seems like his kind of thing. Peterravn (talk) 06:19, 13 July 2018 (UTC)

Archive now available
Sci.Am now have archives going much further back and I was able to download the January 1973 article where Gardner mentions RaceTrack. It's finally clear that not only did he NOT invent the game, but he didn't know who invented it either. Thanks to User:108.1.71.20 for fixing the date of that article - I don't know how we wound up with it being said to be in 1983! Anyway, I quoted his article in ours to clarify that. It's interesting that he kinda confirms the European origins of the game. SteveBaker (talk) 13:13, 27 October 2014 (UTC)
 * My IP address has changed since it was 108.1.71.20, as it does almost daily. You're welcome! (N.B. I devoured Gardner's article when it was published!) 70.17.167.176 (talk) 05:52, 30 October 2014 (UTC)
 * Yeah - the other two games he describes in it are also interesting. SteveBaker (talk) 15:22, 30 October 2014 (UTC)

Description of "speeding up"
The description of how to move, specifically how to move AFTER the first move, is written extremely poorly. I can't for the life of me understand it. Would someone please fix it? —Preceding unsigned comment added by RobertBorgersen (talk • contribs) 23:40, 23 January 2008 (UTC)


 * Well, I wrote it (more or less), and I understand it... Perhaps YOU could help. Here's an example (it works in my screen font; I hope it works in yours too):
 * o o  o  o  o  o  o  o  o  o  o  o  o
 * o o  o  o  o  o  o  o  o  c  c  c  o
 * o o  o  o  o  o  o  o  o  c  z  c  o
 * o o  o  o  o  o  o  o  o  c  c  c  o
 * o o  o  o  o  b  b  3  o  o  o  o  o
 * o o  o  o  o  b  y  b  o  o  o  o  o
 * o o  a  a  2  b  b  b  o  o  o  o  o
 * o 0  1  x  a  o  o  o  o  o  o  o  o
 * o o  a  a  a  o  o  o  o  o  o  o  o
 * o o  o  o  o  o  o  o  o  o  o  o  o
 * It shows ONE player's moves; the "o"s (and other letters/digits) are the intersections on the squared paper. She starts at point "0"; first move goes to "1" (one unit to the right). The principal point for the next move is the "x" one unit further to the right, but also has the choise of the eight neighbours (the points marked "a", as well as the points "1" and "2"). The player chooses max acceleration and also turns, going TWO units right and one up to "2". Thus, for the next move, the principal point is the "y" two units FURTHER right and one up, and the player has the choice of either this point or one of the eight neighbours, marked "b" or "3", and happens to choose the point marked "3", again achieving max acceleration. The next principal point is "z", and the eight neighbours are the "c"s.
 * Notice the vector equalities 0-to-1 = 1-to-x, 1-to-2 = 2-to-y, and 2-to-3 = 3-to-z. What this means is that e.g. the horizontal and vertical change in position from point 2 to point 3 is the same as that from point 3 to the next prinicpal point, z.
 * Does this make sense? How can we explain that better?--Niels Ø (noe) (talk) 13:31, 25 January 2008 (UTC)

I don't get it either, and I think I've played the game! You've not described the rules for braking and accelerating at all, only referred to them. What do braking and accelerating do? How much can you brake and accelerate in each turn? Can you brake or accelerate and change your direction at the same time? (In the game I played the answers are: changes the length of the line; only by one square; yes.) 78.148.110.157 (talk) 08:55, 21 February 2008 (UTC)
 * The above was not meant to describe the rules, but to illustrate the description in the article proper.--Noe (talk) 12:18, 21 February 2008 (UTC)
 * Part of the confusion here is that from a mathematical/physics perspective, braking and turning are both forms of accelleration. It would be much simpler to say "On your turn, your car may accelerate by one square" - but sadly, in the language of non-scientists, that's even more confusing that how we have written it.  SteveBaker (talk) 18:52, 21 February 2008 (UTC)

Evidence of the game being played in Argentina in the 1980's.
I just got this email - responding to my web page - not this article - which I thought I'd pass on. I'm guessing that he picked it up from a teacher who'd read the Scientific American article - the dates are about right.


 * gerardo wrote:
 * Hi, my name is Gerardo, I now live in he USA but I'm actually from Argentina, I used to play this game at school for years, on the late 80's and early 90's and we always thought that were the ones that invented it!!! but obviously we are not!!! And although I have to say that I'm really surprised to find your article, it is a pleasant surprise! because it brings me so many good memories!!! we called it "Vector Racing" (in Spanish "Carrera de Vectores") our version wasn't so advanced as yours but it was still really fun to play, we didn't have the turbo boost or any of the other advanced options that you developed, except for the oil slicks. The rest of the rules were pretty similar.
 * We used to play championships that lasted around 10 to 15 races ( one race a day) (2 to 3 weeks at school) including up to 5 competitors, and we used the same scoring system as the "Formula one" does,  and by the end of the Cup the competitor that accumulated the most points was declared the winner, and as a "champion" he would earn the right to create new tracks designs! and of course would get the most desired prize.. the proud to be called "The Vector Racing Champion". We would play up to 4 different championships at the same time like "24 hours of Le Mans" or the "Indy Racing League" and so on.. but we could play only one race of each Cup per day.. that meant 4 hours of school, 4 Cups, one race every hour!!! Lovely!!!! I also remember that we had to write the rules down because we were so passionate about it that we would get into tremendous discussions during the game!!! also sometimes we would get so loud during the discussions or maybe celebrating a great move that we would be sent out of the class!!! and of course that was one of the greatest parts as well!!! we would laugh for hours!!!
 * Ok, well, again, I was really surprised to find your article and I liked so much that I felt like sharing this with you, sorry if I was to extended but I could keep writing about this for hours!!!
 * Best Regards! Gerardo

SteveBaker (talk) 22:41, 8 September 2008 (UTC)

Car and Driver Magazine
John Kirk emailed me today and mentioned that he believes that the game was published in Car and Driver Magazine - probably in 1973, but certainly no later than that. It would be really great to track this reference down since it pre-dates the Martin Gardner/Scientific American publication...and who knows? Maybe it'll tell us who invented the game.

He also mentions another rule variant - where the finish line has a solid wall some short distance behind it so that you have to decelerate to a safe stop in order to win. SteveBaker (talk) 12:18, 30 August 2012 (UTC)


 * It seems that the publication date for Car and Driver is July 1974, page 65. A Google Books search limits you to just a couple of paragraphs of text from that page - but it is clear that this is indeed the correct article.  It would be wonderful to get a scan of that article to see if it offers any new details - especially about who originated the game, and when. SteveBaker (talk) 19:42, 30 August 2012 (UTC)

Modern variations at BoardGameGeek
Thought you might like this link to some modern variations and some board/card games based on it. http://www.boardgamegeek.com/boardgame/18481/racetrack  Stepho  talk 03:35, 31 August 2012 (UTC)


 * Hmmm, yes - it looks like these three games use the RaceTrack mechanic. (And also Triplanetary - as mentioned in our article):
 * The Mississippi Queen
 * Tacara
 * Bolide
 * SteveBaker (talk) 12:48, 31 August 2012 (UTC)

Another Rule Variation
I heard from a guy named Peter Killian that he was playing the game around 1965 in London. His group played a rule that allowed players to pick absolutely any speed/direction they liked on their first move! This is interesting because it requires people to think way ahead to how they're going to get around that first corner. I suspect that this rule only works in variants where the penalty for crashing is draconian because otherwise it would be worth starting with an insane speed and crashing into the first bend on the first turn of the game...on most tracks, you'd be able to accelerate away and still be ahead of the folks who started off slowly enough to get around the bend.

Anyway...yet another person who played it in Europe in the mid-1960's. It's interesting that all of the early reports are from around that time - yet they are scattered throughout Europe. That suggests that the game cannot have spread slowly by word-of-mouth. There must have been some Europe-wide publication of the rules that didn't make it to the USA. The earliest publications we know of is the Car & Driver and Scientific American articles from 1973 - but that's about 10 years too late to account for all of these earliest players.

SteveBaker (talk) 12:40, 5 October 2012 (UTC)

Plain paper rule variation
A friend of mine and I used to play this game a lot at school, years ago. As we were getting better players it got boring, because it was always the player to start first who would always win the game. Thus we reinvented the rules a bit, and played the game on a plain sheet of paper using two pairs of compasses. The concise rules of the plain paper variation follow.


 * 1) First move: each player chooses a starting point and draws a control circle of unit radius around the point, then moves by a straight line from the center to a chosen point inside the circle or on its circumference.
 * 2) Subsequent moves: the player constructs center of a new control circle by adding the last move vector to the endpoint of the last move, then draws a unit control circle around the point and moves by a straight line from the last endpoint to a chosen point in the new control circle.
 * 3) Result: if both players cross the finish line in the same move, the fraction of the last move before the intersection with the finish line is measured and the shorter one wins.

[example moves]

An amateurish implementation of this game was released in 2000 as an entry in the Czech programming contest Becherovka Game.

Bezier variation
Then I reinvented the rules once more, now targeting computers alone, and replaced the straight line moves by smooth Bézier curves. Explaining the rules is out of the scope of this post, but a single player proof of concept prototype is available.

Replies
Nice! As you may very well know, without an independent quotable source, this has no place in the article space of Wikipedia.--Nø (talk) 10:24, 9 November 2014 (UTC)

“Dubious points” along the track
I offer this "discussion of the subject" as I feel it could have some bearing on the content of the article, and it is based on part of the article besides. Regarding this section:


 * "Before starting to play, the players may go over the track, agreeing in advance about each grid point near the boundaries as to whether that point is inside or outside the track.


 * "Alternatively, the track may be drawn with straight lines only, with corners at grid points only. This removes the need to decide dubious points."

Not only must it be determined which grid points one may "land on" at the end of a turn, it needs to be resolved on any "curve-around" whether any given vector would touch the wall anywhere along the vector's midsection. This opens up nearly infinite possibilities for what may or may not constitute "touching the wall", more than could possibly be determined before game play. This effect makes the track-boundaries-as-only-straight-lines-between-grid-points method even more important, as it avoids the problem I've brought up altogether: simple geometry will resolve whether any drawn line touches or crosses the wall. This point could benefit the article greatly, if we but have the courage. 2601:545:8202:4EA5:0:0:0:BCDD (talk) 22:50, 23 April 2018 (UTC)

Wall crash position
The version I found online said something to the effect that on a crash the player was returned to starting velocity and was placed a square back from where they intersected the wall. One ambiguity that creates is whether the wall intersection point is chosen before or after the 1-square adjustment. We went with after, but players would smartly game it to crash as far forward as possible. The return to zero velocity still served to put the player a couple moves behind, but the wreck seemed a lot less consequential than expected. I wonder if you might be able to smash into the first corner at full speed and possibly come out ahead. 2600:8800:7900:1A9:6599:A80C:1D7E:D23F (talk) 02:25, 14 May 2019 (UTC)
 * It may depend on the exact shape and width of the track, but the rule is clearly not a good idea. At a sharp turn, resetting your speed in one direction so that you can start accelerating in the opposite direction is too advantageous.--Nø (talk) 06:43, 14 May 2019 (UTC)

Principal point?
I invented the term "principal point" for this article. I think there might be a better term. Here are some suggestions: What do you think? Whatever we say, it's a neologism - but one that serves the noble purpose of making the article easy to understand.--Nø (talk) 08:46, 30 August 2021 (UTC)
 * Zero acceleration point
 * No-acceleration point
 * Zero force point
 * No-force point
 * No-friction point
 * No-traction point
 * Inertial point
 * Point of Newton's First Law
 * First Law point


 * "Principal point" seems to convey the thought in the simplest and easiest to understand manner.  Stepho  talk 11:13, 30 August 2021 (UTC)

1D version
Is there any known reference to the 1-dimensional version a.k.a. (integer) lunar landing, where starting with some pair (x,v) of integers, one has to find the minimal number of moves to arrive at (0,0)? &mdash; MFH:Talk 23:30, 27 February 2023 (UTC)