Pre-submission goals, update #3: So, what happens when I fly off the grid?

There is one significant issue I have found (via user testing) that occurs in my Flash version of this game that I do not recall ever occurring when I played this game on paper with my dad.  This would be the possibility of players going so fast that not only do they go out of the track boundaries, but they end up in the position in which all options for their next move are off the playing grid entirely.  I wonder if my discovery of this is a result of my throwing my friends into playing my game without their really having a clue what they had to do, and thus having pretty much no clue (initially) of how to strategize the management of velocity.  But either way, I thought that it would be fairly bad in terms of user experience to force everyone to restart the game if a player went off the grid, so I decided to handle that case.

I consulted with my dad, and he helped me come up with a reasonable solution.  I decided that if a player comes to their turn and all their options are off the grid, that move will be taken for the player as follows:

1. They will move to the "middle" option (i.e. the gridpoint that would maintain both their x- and y-velocities), wherever it may be, off the grid.
2. Then, they will "slide" back onto the edge of the grid.  In other words, if they are off past the top or bottom edge, their y-coordinate will be adjusted, and if they are off past the left or right edge, their x-coordinate will be adjusted.
3. As a "punishment" for going off the grid, their velocity will be reset to (0, 0).

Since the player has no control of this move that's bringing them back onto the grid, they are informed of it, like so:

And on your next turn, you start off at the edge with (0, 0) velocity:

Considerations extracted from first (real-..)game chat

...with additional thoughts spurred from which...

Interface

• show players (names, pics, association to colored piece)
• display whose turn it is (and note "your turn" or "waiting for player __")
• display your current speed (and others' speeds?)
• and re: current speed - show a little compass of -x/+x and -y/+y directions

Instructions

How to interact with the interface:

• click on circle to select move
• gameplay is turn-based so you must wait for other players' moves
• other players' circles are NOT clickable to you when it's not your turn

Gameplay:

• goal is to be first around the track
• how your speed is allowed to change for each turn, and that the game calculates this for you and shows you your available moves
• when you go out of bounds, you lose every other turn for the duration of turns you are out of bounds
• boundaries of track (both inner and outer) are considered in-bounds
• cannot occupy same gridpoint as another player at the same time, but can occupy another player's previous gridpoint

Implementation stuff

• handle out-of-bounds (lose every other turn)
• handle off-the-grid
• detect when a player crosses the start line again (i.e. the winner!)
• don't let players be on the same point at the same time
• display something differently about the optpos when it's out of bounds

Dicussion with Dad, part 1: Handling when a player gets stuck out of bounds

Over lunch with my dad during spring break, I finally remembered to ask him about the one critical point of the game rules that I could not remember: what happens when a player's speed forces them to move out of bounds? -- In other words, all of the 9 possible positions for their current move are located outside the outer edge of the track, or inside the inner edge.  (From playing games with my dad, I definitely remember that this happens sometimes.)

My original idea for handling such a case was to set the player back to their latest prior position (past move) such that subsequent speeds/moves would not force them out of bounds.  As my dad pointed out, this might require backtracking by more than just one previous move, because that might not be enough to allow them to decrease speed within the next move (and stay in bounds).  The process of backtracking and computing at each prior position whether or not the player could stay in bounds from that point would also be a bit of a tedious procedure.  Finally, he maintained that this solution is "unrealistic"; in other words, you don't go backing up your car and slowing down on an actual race track.  Keeping the game realistic isn't especially important to me, but it's kind of a nice feature to attempt to uphold.  (It's kind of like when movies try to stay scientifically accurate.)

My dad's alternative solution is apparently what we always did when we used to play the game (and I just forgot).  It's actually very simple:

1.  When all of a player's options for their current move are out of bounds, the player simply takes the move anyhow.
2.  On their next turn, they lose a turn: their piece/marker stays in place on the grid, but they are considered to hold the same speed in the x and y directions.
3.  On the subsequent turn, they take a move, maintaining the same rules about speed--the x and y speeds may change by 1 unit in either direction.
4.  This alternation between lost turns and normal-movement turns continues for as long as the player is outside of bounds.

Obviously, the point here is to slow the player down while outside bounds, and hence encourage them to get back in bounds as efficiently as possible.

Here's the diagram my dad sketched to show this.  (Ignore the lines on either side of the '2' and the dots they lead to--that was a different idea.)  Suppose a player is forced to move outside the track on the turn indicated by the line next to '1'.  Their next turn, then, is lost; my dad designates this with the circle surrounding the dot.  The circle means they've stayed at that location for a lost turn.  Two more alterations of turn/loss are then depicted, as the player aims to return to the track.

Just to note, I'm not sure yet how I'll indicate visually that the player has stayed in place for the lost turn, since so far in development the game display is not exactly like it would be on paper in some ways.

Long-awaited story boards!

[EDIT: Ah, crap, the images are far too wide for this skinny column.  Click them to see the full image, so that the explanations make sense.]

The aim of these diagrams - which are not necessarily intended to represent proposed visual design - is to show the progression of a sample game at various points.  So here we go:

Initialization
Set up requires choosing a provided closed-loop racetrack (of relatively consistent width) on grid paper, or drawing one yourself.  A start/finish line and direction of travel (see the arrow beside the start line) are decided upon, and each player chooses a symbol and selects a position on the start line.
The possible first moves are shown (for the blue-circle player) as filled blue circles.  Since clearly they have not started moving - a speed of (0,0) - their next move can have a speed of -1, 0, or 1 along each axis.  All possible moves are shown here for completeness, but obviously, you would never move backwards behind the starting line.

Getting going: how to move
At this point, each player has taken 3 moves, and the options for the fourth move are shown for each.  (Dual-color circles indicate that that point is an option for both of those players.)  The basic rule is that for any move, a player can hold constant or change by 1 the number of points to move along each (horizontal and vertical) axis.
For example, if in the prior turn, a player moved (3,2) in (horizontal, vertical) movement, their next move could be any of these options (within bounds): (2,1) (2,2) (2,3) (3,1) (3,2) (3,3) (4,1) (4,2) (4,3)
Note a couple things:

• Players cannot occupy the same grid point at the exact same time.  (BUT, any player can occupy a point that was occupied in a past move by another player.)  Taking a grid point that would be ideal for another player's move could be a strategy.
• Players are not allowed to move to grid points outside the track (obviously).  Clearly, here, the green and blue players have a decreased set of options.  Grid points exactly on the border of the track are considered in-bounds.

Stuck
Now each player has taken 6 moves.  The red player did not think ahead enough and has created a situation in which all possible next moves are located out of bounds.  At this point I have not decided how to handle this situation, but I do not think cutting the player out of the game from then on is ideal.  That's no fun.  I may decide to require some sort of backtracking to a prior position.

The end: finishing/winning
Here, the completion of the game is shown (except the blue-circle player, left out to make the example easier).  Assuming that the red and green players were taking the same turn at the bottom-right of this quadrant of the diagram, notice that 14 moves for each are shown here.  Since the red player reached the start/finish line (and the green player has not yet), the red player wins.
Notice this diagram includes an example of players occupying the same grid point at different times in the game: the green player's 10th move on this diagram is the red player's 8th move.