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We can always win, if you start first or if your opponent does not know the trick.
If we add the biggest and smallest number (from the list of numbers in which we can add), we subtract this from the target and continue subtracting until we get to the smallest number.
For example, if we can add the numbers 1, 2, 3, 4, 5 and the target is 29. The first step is 1 + 5 = 6, we then subtract 6 from 29 to get 23, and continue until we get to the lowest we possibly can...... 29, 23, 17, 11, 5. We need to get to all of these numbers (which are our milestones), for us to definitely win.
This works for any set of numbers and targets.