Actually you will have more 'luck' if you keep the same order and no it doesn't matter which order you pick just pick one and stick to it. You see if you change order continually or otherwise then instead of looking at the probability that the random order is never 1124 (or whatever order you pick) then you are looking at the probability that it happens to be the whatever random sequence you choose which would be .5*.333*.25*.2
I'm afraid you are mistaken. It feels like sticking with the same pattern is more likely to yield a win sooner, but it isn't.