The note in the problem text let me assume that it is proven that if the game for some grid size n must have a winner there is a sure winning strategy for the first player.
Taking in account that implication only, one cannot, as I did, conclude that there is no sure winning strategy if a game could be drawn.

## I withdraw the conclusion

The note in the problem text let me assume that it is proven that if the game for some grid size n must have a winner there is a sure winning strategy for the first player.

Taking in account that implication only, one cannot, as I did, conclude that there is no sure winning strategy if a game could be drawn.