A quick pen and paper game: vector racing.

The following is a simple pen and paper game, that I spent countless hours playing at school.
It only requires a couple colored pens (but even a single one would do) and small grid paper.
I mostly played it 1 vs 1, but there is no theoretical limit to the number of players that can join the fun.

The whole game is about racing your way around a drawn track, that can be as simple or complicated as you wish. The game is based on a simple and elegant movement system that simulates acceleration and inertia, and will force you to find the right balance between going fast and still being able to take sharp turns.

It's low supplies count make it a perfect game to waste time at school, or play during boring moments when travelling.

The basics

The paper

So how does this work?
First, you'll need a sheet of small grid paper (the one with 5mm squares).

This is the kind of paper you will need.

The track

Then you draw a racing circuit on it.
This can be as simple or complex, as you want. I usually just scribble a random snaky shape, with a 4 or 5 row of squares marked as a start and/or finish line.

The movement system

Now for the core of the gameplay.
Both players chose a point on the starting line, and take turns making their moves.
Movement always happens from and to intersecting points on the grid.

- For their first move, players are allowed to draw a single one square long line.
- For any further move, the movement is resolved as such.
    - You mark a point on the circuit, that is the symmetrical of your last turn starting point, taken across your last landing point.

This was the last move, and where it will lead you next turn if you don't change course.

    - You can choose to move to any of the 9 adjacent intersections situated directly on or around that landing point.

So you can choose to go to any of the 9 marked points for this turn.

    - Draw a new line from your last position to the newly selected point.

Player has chosen this move among the 9 possible choices.

It's that simple. This small liberty of movement allows you to steer, accelerate or brake your vehicle.

You can either go slow and take sharp turns, or go fast, but risk hitting walls at the next turn.
The whole game revolves around choosing the optimal trajectory, and of course, being better at it than your adversary.
 

The rules 

The basic rules are simple (but allow for lots of variations).
Players take turns drawing their current move, heading for the finish line.
If at one point a player is unable to make a move that does not intersect the track borders, it is considered a crash.
The simplest rule states that when a crash occurs, crashed player skips a turn, and then starts over from the closest in-track point, at a 1 square speed. If you're more experienced, you can make any crash a definitive game over.

First player to make it to the finish line wins.

Variants:

Once you've mastered the basics of the game, you can add or make up many many rules to make the game more fit to your tastes.
Here are some of the variants I practiced, or seen proposed on the Internet.

There are many variations you can make to the track itself:
- Have it looped or not
- Have it as small or big as you wish (We've been known to go especially over the board on that point with my friends. Sometimes playing on both faces of multiple double sheets scotched together in giant marathon circuits)
- Your track can be drawn freehanded or be very precise and made of straight lines (freehand sometimes causes trouble and arguments with identifying ambiguous crashes)
- The simplest track is just a corridor of two mostly parallel lines, but you can draw pretty fancy decor, especially when the game is used as a time waster at school, or for special championship events.

If you've got time to spare, or want to make any given race stand out, you can draw fancy tracks.

The next logical step to make it more interesting is adding various kinds of obstacles:
- Explosive barrels in  the middle of tracks. Touching them causes similar effects to a crash.
- Oil spills/Ice. Represented as puddles on the track.Whenever crossed during a turn, player cannot change course for the next turn.
- Jumps. The track is interrupted at some point, and a start/end line is drawn to materialise the gap.Any movement in this zone must begin on one side of the jump and and on the other.Jumps too short are treated as crashes, and crashed player must restart from the landing line after skipping a turn.
- Gravel/poor conditions. Those zones are materialised as greyed out areas, crossing them during your turn forces you to adopt one of the "slowing down" options for your next move.

Then there are variations to the rules themselves
- Collisions: being on the same spot as your opponent may be allowed or not (it is allowed by default).
- Crashes severity: Crashes could be made a game over condition to make players more careful.This makes the game slightly harder.
- Life points: A given number of "HP" can be attributed to each car (3-5...), to allow for some crashes.Reaching 0 HP resulting in a game over for the incriminated player. You can also scatter optional "life kits" around the track that would help regain 1 HP when crossed.
- On looping circuits, more than one lap can be played.
- Weapons: each car could be allowed to carry an oil bomb, or a mine that would behave as oil spills or explosive barrels.
- Nitro boost or super brakes: can be only used a limited amount of times. Using them allows the player to accelerate or brake by 2 squares instead of one at the chosen turn.
- Customisation: when weapons and HP rules are adopted, all cars could be made equal, or each player could spend a fixed budget on the features he wants to add to his car. For example, each player would have a 100$ fund to build a car, where each HP would cost 15$, brakes or boosts 20$...
Money could also be awarded for each win, and the budget kept across a whole championship.

Try it online right now!

If you have trouble understanding the rules, or wish to play a game right now without having to convince a friend, or just want to practice, fortunately, some awesome dev made a free online version of the game you can try at once.

The game features many different tracks, and the options to play alone against time, or against IAs.
Multiple players can also take turns on the same machine.

 Additional resources

Rightfully so, many persons seem to have enjoyed the game over the years.
Various online resources cover the basic rules and propose custom variations.

- This site does a better job than I do at explaining the rules in more detail: http://www.papg.com/show?1TPE . It's only fair I point you to it as this is where I shamelessly borrowed the illustrations from.
- This site discusses a lot of possible variants to the game : https://www.sjbaker.org/paper_and_pencil_games/graph_racers/
- The wikipedia page for that family of games
- A person that has implemented multiple electronic versions of the game : http://harmmade.com/