How to ruin Battleship

So one day I was trying to entertain my son in the car, and after we exhausted mental tic-tac-toe we tried playing Battleship using only memory.

We started off using really small grids, to make it easier to remember plays, and we also reduced the ships to single cells of the grid, for the same reason.

After we did that, it occurred to me that there wasn't really any difference between imagining the game as a grid with locations like A1 and H10, and imagining it as a single row of cells. And a single row, with cells identified solely by numbers, makes it much easier to remember the plays.

The simplest version of this we tried was with each player having just one ship in a sea of 10 cells.

You can see where I'm going here. Once you do that, the game amounts to taking turns guessing a number from one to ten.