The p-value means "chance of this happening, if the two were equally effective". So 1-p means "change of this NOT happening, if the two were equally effective".
Note that in frequentist statistics, the sentence "Probability this is all luck" doesn't even make sense. Either the universe is so that it was luck, or it is not. In frequentist statistics you do not assign probabilities to models of the universe. You only assign probabilities to observations, given a fixed model of the universe.
Note that in frequentist statistics, the sentence "Probability this is all luck" doesn't even make sense. Either the universe is so that it was luck, or it is not. In frequentist statistics you do not assign probabilities to models of the universe. You only assign probabilities to observations, given a fixed model of the universe.