I'm not sure to have understood enough well what do you mean, but I think you are making a little mistake. The game is over when the 11th stone is entered on the board. This means one bridge will remain on the board. It's true that the box contains 12 stones but if you read carefully the rules they mention 11 stones instead of 12.
I think that if you play with the right rules you will find the final less mathematic.
ciao
leo