If your victory condition is to take the last piece of the board you will always want to follow the strategy of having your move leave the board with a Nim sum of 0. Therefor 1-1-2 --> 1-1 would be the winning move, which is in accordance of the winning strategy.

If however your victory condition is for your opponent to have to make the last possible move, then you have to break the winning strategy in the very end. You will want to stay in control of the board by using the winning strategy up to a point, where you can set up a board in which your opponent's only possible moves leave the board with Nim sum 0 (basically whichever move he could possibly take has to leave the board with a Nim sum of 0). Therefor 1-1-2 --> 1-1-1 is the winning move, as your opponent is forced into a position, where he can not help himself but leave the board with Nim sum 0, which in the end means that he has to pick up the last piece.