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Well done to Ci Hui Minh Ngoc from Kelvin Grove State College Brisbane in Australia sent in some comments and strategies for this game:
1st Move Advantage: Yes, it has the advantage as 1st player can choose the centre point. For the two games captured shown, when computer is the first player, the computer started with centre point, though this 1st point did not form the final Rhombus of computer. For the other game, when human is the 1st player started with centre point, human is the winner and the Rhombus is a square which included the centre point as one of the vertices.
Strategy:
I use the properties of Rhombus:
4 sides equal parallelogram. Square is a special Rhombus with angles are 90 degree.
These are additional constraints on parallelogram. That means I must check where the new points are going to place must result “equal length of 4 sides”.
I use the strategy used in creating square, in Square It.
The diagonals of the Rhombus are perpendicular to each other, so strategically, I locate points symmetry around two perpendicular lines (visualise) to maximise the chance to create a Rhombus.
Here are pictures I took after games with computer.
1st player is computer
1st player is human