Randomizing the American's Initial Deployment

     Since I will be running this campaign solo, I want to add a bit of randomness to it.
     My first attempt at this, will be to randomize how the American forces will initially deploy on the battlefield.
     I made up ten setups, and will run a D10 at the start of the game, and then deploy the Americans based on one of the setups pictured below, based on the corresponding die roll.
     I don't know how effective this will be, but I want to give it a go.

The initial American forces will consist of:
5 American Regulars
2 Militia
1 Dragoons
1 Militia Battery