How to Play Racetrack
Racetrack is a two-player-or-more pen and paper game played on squared or graph paper. Players draw a circuit, then race dots around it by adjusting a speed vector on each turn, simulating basic momentum. A car that veers off the track is eliminated, so smooth driving beats reckless speed.
Its appeal is that the rules take two minutes to explain yet the decisions are genuinely interesting. A grid, a couple of pens, and someone willing to draw a track are all you need, making it a reliable choice for long journeys, waiting rooms, or any situation where a board game is out of reach.
A little history
The origins of Racetrack are unclear. The game has been documented in recreational mathematics literature since at least the 1960s and is widely associated with the mathematician Martin Gardner, who described a version of it in his Scientific American column, though he did not claim to have invented it. It has traditionally circulated as an informal pastime under various names including Vector Racer and Graph Racers, and no single inventor or date of origin has been reliably established.
Setting up
- Agree on a sheet of squared paper and a scale. Standard graph paper with 5mm squares works well.
- One player draws the track outline. The track should be several squares wide at all points, have at least one bend, and be clearly closed with a marked start and finish line crossing the full width of the track.
- Mark the start line clearly. All players place their starting dot on or behind the start line, spaced apart so no two dots share the same grid point.
- Agree on the direction of travel around the circuit.
- Decide who goes first, for example by drawing lots or youngest player first.
How to play
- Each player has a current velocity, expressed as two numbers: horizontal speed (x) and vertical speed (y). At the start of the race every player's velocity is (0, 0).
- On your turn you may change your x value by -1, 0, or +1, and independently change your y value by -1, 0, or +1. This gives nine possible adjustments each turn.
- After choosing your adjustment, add the new velocity to your current dot position to find your new dot position, and mark it on the paper.
- Draw a line from your previous dot to your new dot. This line represents your car's path during that turn.
- If that line crosses or touches the track boundary at any point, you have crashed. The standard ruling is that a crashed player is eliminated. Some groups instead apply a penalty (see Variations).
- If your path line crosses another player's dot, the standard ruling is that both players crash. Agree before play begins whether contact eliminates one or both.
- You may not voluntarily remain completely stationary: your velocity cannot be (0,0) unless you are still on your starting move. Once moving you must continue with at least a velocity that differs from zero in at least one axis, unless the only legal moves would all cause a crash, in which case you are eliminated.
- Play proceeds clockwise. Each player takes one turn per round.
- The race continues until one player crosses the finish line or all but one player have been eliminated.
Winning and scoring
The first player whose path line crosses the finish line wins. The finish line must be crossed in the correct direction of travel; crossing it backwards does not count. If two players cross the finish line on the same round, the player whose dot lands furthest past the line wins. If that is still equal, the round is a draw and those players share the win. In elimination formats the last player remaining on the track is the winner.
The fine points
The most common dispute concerns whether a path line that clips the very corner of a boundary square counts as a crash. The standard ruling is yes: if the drawn line passes through any part of the boundary, including a corner point shared with a wall square, the player crashes. Agree on this before the race starts and be consistent. Using a ruler to draw path lines reduces arguments considerably.
A second regular dispute arises when a player claims they have no legal move because every one of the nine possible adjustments results in a crash. In that case the player is eliminated regardless; there is no obligation on the track designer to guarantee an escape route. Players who find themselves in this position have usually accumulated too much speed on a bend and had no realistic way out several turns earlier.
How to win more often
- Brake early into bends. Carrying too much speed onto a tight corner leaves you with no legal move and forces a crash.
- Use the full width of the track on straights and swing wide before a bend so you can take a shallower line through it, exactly as in real circuit racing.
- Count your stopping distance. At velocity (3, 0) you need at least three more turns to reach zero horizontal speed, so plan that far ahead.
- Watch opponents' velocities as well as their positions. A rival carrying high speed into a bend may crash, handing you the lead without any risk to yourself.
- On a multi-player track, avoid drafting directly behind a faster player: if they crash, your path line may run through their dot and eliminate you too.
Variations
Penalty Respawn
Instead of eliminating a crashed player permanently, they return to their previous position with velocity reset to (0, 0) and lose a set number of turns, typically two. This keeps all players in the game and suits younger or more casual groups. Agree the penalty length before the race begins.
Free-Draw Track
Rather than using squared paper, players draw the track on plain paper and simply estimate reasonable moves by measuring or agreeing on distances. This sacrifices mathematical precision but makes the game playable without graph paper and encourages more imaginative circuit designs.
Grand Prix Series
Players race a series of three or more tracks, scoring points for finishing position: typically three points for a win, one for second, zero otherwise. The player with the most points after all tracks wins the series. Tracks are designed alternately by each player, which adds a tactical element to circuit design.
Maximum Speed Cap
A house rule that prevents any single velocity component from exceeding a set number, commonly four or five squares, regardless of accumulated acceleration. This slows the game on long straights, keeps the action on the bends, and makes the race more competitive when players have very different experience levels.
Racetrack: frequently asked questions
How many players can play Racetrack?
Two players is standard, but any number can play on the same track provided there is enough room at the start line to give each player a separate grid point. Tracks for four or more players should be drawn wider than usual to reduce unavoidable collisions in the early laps.
Do you need special graph paper?
No. Any squared paper works. Standard 5mm graph paper is ideal because the grid is fine enough for smooth curves but large enough to draw and read clearly. In a pinch you can rule your own grid on plain paper.
What happens if I forget to move and leave my velocity at (0,0)?
By the rules a velocity of (0,0) after the opening move is not a legal state. If you accidentally produce it, the practical remedy is to replay the turn with a valid adjustment. Agree before the game that accidental zero-velocity turns are replayed rather than enforced as an elimination.
Can I go backwards on purpose?
Yes. There is nothing in the rules that forbids a negative velocity in either axis. However, going backwards rapidly tends to produce crashes just as going forwards too fast does, so it is rarely a useful tactic except to recover from an extreme overshoot.
What is the minimum track width?
There is no official minimum, but a track narrower than three squares at any point is difficult to navigate and tends to produce unavoidable crashes. Five squares wide on straights and four squares at the apex of bends is a reasonable guideline for beginners drawing their first circuit.
What age is Racetrack suitable for?
Most children aged seven or eight can grasp the velocity mechanic with a short explanation and one practice turn. Younger children can play a simplified version where speed is capped at two squares in any direction, which reduces the arithmetic to something manageable.
Does the path line have to be a straight line, or can it curve?
It must be a straight line drawn from the previous dot to the new dot. The vector system is what creates the appearance of curved movement over several turns. Drawing curved path lines is not permitted under standard rules.
What if two players want to occupy the same grid point at the same time?
Standard ruling is that both players crash if their dots land on the same point or if one player's path line passes through another player's dot during the same round. Some groups allow co-occupation without penalty; agree which ruling applies before the race begins.