Zigzag is played by two players on a 5×5 square board. At the start of the game, a pawn is placed in the bottom left square as shown in Figure A. Each of the five horizontal lines is oriented: the bottom line goes from left to right, the top line from right to left, and so on, alternating directions.
Each player takes turns taking the pawn and moving it one square. However, the move can only be made in two directions: either upwards or horizontally in the direction of the line. You can see in figure A the possible moves indicated on the two squares marked with a cross.
The winning player is the one who places the pawn on the top right square.
You are offered a game of zigzag, do you prefer to start or let your opponent start? What strategy do you use?
After a few games, the game starts to seem a bit monotonous, you decide to change the rules a bit. The directions do not change, each turn you must move your pawn either up or in the direction of the line. But now you have the choice of moving it one or two squares. Figure B shows the possible moves from the two squares marked with a cross.
With these new rules, do you prefer to start or let start? And what strategy do you put in place?
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