Why do this problem?
Children will be motivated to work systematically as they play this game
because they will want to think ahead.
Would it be a good idea to start with a smaller number of counters. How about four arranged in a square?
How many different ways are there for the first player to begin?
Does the grid have any symmetry that may help you?
Learners could try with a larger number of counters, or the counters arranged differently.
Working with $2$cm squared paper and counters will mean that children can simplify the game easily.