Let me explain it in a Bayesian way. The Bayesian approach would be to consider a whole bunch of hypotheses about how much better Y does than X (and vice-versa), and a prior distribution over how likely you think each is a-priori. Then for each sample S, you update the probability of each hypothesis H by multiplying its probability by P(S|H), then re-normalize.

Well in this case, we're only going to consider two hypotheses. Call them H0 and H1. H0 is the "null hypothesis", and says that X and Y are exactly as fast as each other. H1 is the hypothesis that H0 is wrong and Y is totally faster than X. You'll notice that H0 is oddly specific, and H1 is ill-defined. Don't worry about it.

To start off, pick your prior distribution over H0 and H1. Pick whatever you want, because we're going to ignore it shortly.

Now some evidence comes in. Time to update! We got the ordering XXXYYY. First, let's update H0. P(XXXYYY|H0) = 1 / 6choose3 = 5%. Wow, that's not a very good update for H0. It's probably just false. For expediency, let's just toss it out.

H1 is the remaining hypothesis. H1 wins! Y is faster than X.