I read that historically, Romans fought in checker board formation, composed of 3 lines. But I play Rome Total War and in the game, that deployment means a nice recipe for high casualties. In the game, I deploy a single line, with my cavalry (or a couple of units) protecting the flanks, and as soon as the center of the line engages, rush my troops at the flanks to the rear of the enemy and order them to charge at these engaged troops from their rear, killing them and their morale in a very short amount of time and winning the battle. Now I know that RTW is just a game but it is a realistically made game indeed. And thinking about this tactic, it makes a lot of sense to me. So I wonder, why didn't the Romans employ a similar tactic in their battles? My main concerns for the multiple line formation are:

1) Wouldn't this deployment have shortened their width and made them more prone to encirclement?

2) If it didn't, then it must be the case that Romans had always fought with a numerical advantage. In that case, the battle is already not a very balanced battle.

Having these in mind, I can't see how 3 lines provides an advantage over a single line.