Doppel-game

(Title is taken from "doppelganger".)

This game seems to be familiar. And the rules are simple. So, maybe, I might have already posted a game with similar rules. Or a similar game might have been invented by someone else. (Actually, I could include this disclaimer with almost any of my games.)

Here is a game for 2 players played on an n-by-n grid.

First, fill in any one randomly chosen square of the grid.

Players then take turns filling in empty squares of the grid, one square per move, such that any square being filled in is immediately next to -- and in the direction of above, below, right of, or left of -- any square anywhere on the grid that has already been filled in (by either player).

({}'s added for clarity below.)
Say, a player (player A) fills in a square that is immediately next to -- and in the direction of above, below, right of, or left of -- the square that same player (player A) filled in in their last move. Then let the direction from {the previously filled-in square (from the previous move of the same player, player A)} to {the newly filled-in square} be the direction d.
If the direction from {ANY filled-in square immediately next to {the square the other player (player B) last filled in}} to {the square the other player (player B) last filled in} is d, then player A gets a point.

No point is obtained if player A doesn't fill in a square immediately next to the square previously filled in by the same player (player A) or if the direction from {player A's previously filled in square} to {the current filled in square on player A's move} does not equal {a direction from any filled in square (immediately adjacent to the last square filled in by player B)} to {the last square filled in by player B}.

Got that?...
(I said these rules were simple!...Ha! -- Well, the rules ARE simple, once you figure out what they are!)

Play continues until all the squares of the grid are filled in.

The player with the most points wins.

Clarification:
First of all, player A refers to either player, but is the player currently moving.

Call 3 consecutive moves "move m", "move (m+1)", and "move (m+2)".
Player A made moves m and m+2, and player B made move m+1.

The direction from the square filled in on move m to the square filled in on move m+2, if those two square are immediately adjacent (in the direction of up, down, left, or right), is direction d.

Let "square (m+1)" be the square filled in by player B on move (m+1). If the direction from {ANY filled-in square immediately next to square (m+1)} to {square (m+1) itself} is direction d, then player A gets a point on move (m+2).


Any comments?

Thanks,
Leroy Quet