Alice and Bob are playing the neighboring game
which is originally a single person game with the aim of getting the highest points at the end.
You start with an empty 4x4 grid. At each turn, you can choose an empty cell and place a value in it. The placed value is given by the following rules:
- If the chosen cell has no neighboring (horizontal or vertical) cells that are already occupied then the placed value is 1.
- Otherwise the placed value is the number of neighboring cells that are already occupied. So, for instance, if Alice chooses a cell which has 2 neighboring cells (horizontal or vertical) that are already occupied, then her placed value will be 2.
Once all the cells have been filled in then each person's score becomes the sum of the values they have put in. Alice goes first. Who will end up with a higher score at the end, Alice or Bob, if both play optimally?
Here is another version of the game: Alice and Bob version 1