Saw one help ( the movie)

ok ive seen all three of the movies and there hella tight but in the first one when the key is in the bath tub why would they give them the key? so he could escape.. that would be stupid and ruin the whole thing cause lawrence was suposeed to kill adam and how was he supposed to do that if hes running around the room unchained. and its obvious that they gave him the chain cause in saw three amanda puts it on his chest. Someone help me out here.