Racetrack

On a sheet of "quad pad" (e.g., 8 1/2" x 11" preprinted 1/4" 2-D grid) paper, draw a freehand outline of a racetrack. It can be a loop (oval is fine) and irregularities are good, indeed encouraged. This is the outer boundary of the racetrack. A loop provides a roughly circular track; however other outline shapes are just fine - explore as you gain experience racing. Now draw another freehand loop inside the first. It can be more or less parallel with the first, or have wider and narrower (pinch) spots, with usually at least 1/2" between lines. A straight line is drawn along the grid anywhere across the two lines. This is the starting (and finish) line. Choose a direction for the race to be run (e.g., clockwise).

The players will take turns placing their mark (their "cars") on the track according to the rules below. It can be helpful to use different colors, or different marks (e.g., x and o) to distinguish player's moves. Cars are allowed to land only at grid intersections. The players should go over the track, agreeing in advance about each grid point too near the inside and outside track boundaries as to whether that point is on the track or outside the track (it may help to annotate the track grid points that are not considered to be within the track, to avoid memory conflicts during the race).

Players decide who will move first. The first player places his/her car on a grid point on the starting line; the second player then does the same. A car may not occupy any grid point that is currently occupied. Moves are made in whole number units from one grid point to another, subject to the following restriction: In both the horizontal and vertical direction, the current move must repeat the previous move or be within one (plus or minus) unit of the previous move. This restriction represents momentum from the previous move, and allows accelerating or decelerating one speed unit, in each axis, on each turn.

For the first move, since both players have zero speed in both axes, the cars can move to another grid point (0,1), (1,0), or (1,1) away from their starting point - so long as they don't land on a currently occupied spot or leave the track. Note that the speed built up by acceleration capability (+1 per turn in either or both axis) can only be reduced by the same rate (decelerating at -1 per turn) - as a "wall" is reached or a turn is needed to make a curve in following the track.

Play proceeds with players taking turns and marking the track with their new positions. The winner is the first to complete a lap (cross the finish line). If you go outside the path you have crashed and lose - this time. First player has some advantage (first choice of starting location and move), so Loser goes first for subsequent games.

Notes: It is not a violation for a move to appear to cross the edge of the track so long as the end point of the move is within the track. Speed on the two axes are independent. This is an addictive game. As one might suspect, the use of "quad pad paper" suggests it was invented by engineers - but anyone can play.