Only the original poster could answer this question exactly because no one else knows the details of the pool of openings he has analyzed.
But here's a sample calculation that is much simpler: if there are 400 openings that have 50 games each, and in actuality P1 wins 57% for every opening (with no ties), the chance that at least one of those 400 openings would have >=60% win rate for P2 is about 95%.
Details: The standard deviation of P1's win rate for each opening is about 7%, so (by the central limit theorem for simplicity) the chance that each of the 400 openings has a <=40% win chance for P1 is about 0.76%. So the chance that at least one of the openings has a <=40% win chance for P1 is 1-(the chance that none of the openings have this). Assume that the results of games with one opening doesn't depend on results from other openings (not quite true, because each game will be counted twice since each player has an opening) and you get to 95%.
It's kind of surprising that with this many games, it's still possible to lack statistical significance, but there are so many possible openings that most of the openings don't have enough data to really be sure. Even so, I took the data and looked at wins/losses using the binomial test for p-value with 0.57 and 0.43 the expected values for wins and losses for P1 (and vice-versa for P2). Here are some things that we have enough data to say with 95% confidence (p < 0.05):
Either player- Opening Mountebank-<nothing> is significantly better than average (winning percentage of 58.0% averaged over P1 and P2)
- Opening Junk Dealer-<nothing> is significantly better than average (winning percentage of 63.2%)
- Opening Potion-Silver is significantly worse than average (winning percentage of 45.9%)
- Opening Potion-Shanty Town is significantly worse than average (winning percentage of 34.9%)
- Opening Smugglers-Silver is significantly worse than average (winning percentage of 40.4%)
- Opening Plaza-Silver is significantly worse than average (winning percentage of 40.9%)
P1 openings- Opening Salvager-Silver is significantly better than average (P1 winning percentage of 68.3%)
- Opening Oracle-Silver is significantly better than average (P1 winning percentage of 72.5%)
- Opening Potion-Storeroom is significantly better than average (P1 winning percentage of 70.3%)
- Opening Sea Hag-Silver is signicantly better than average (P1 winning percentage of 64.1%)
- Opening Swindler-Silver is significantly better than average (P1 winning percentage of 68.4%)
- Opening Hermit-Silver is significantly worse than average (P1 winning percentage of 43.0%)
- Opening Wharf-<nothing> is significantly worse than average (P1 winning percentage of 44.2%)
P2 openings- Opening Upgrade-<nothing> is significantly better than average (P2 winning percentage of 58.8%)
- Opening Potion-Sage is significantly worse than average (P2 winning percentage of 22.2%)
- Opening Fishing Village-Fishing Village is significantly worse than average (P2 winning percentage of 26.9%)
- Opening Lookout-Silver is significantly worse than average (P2 winning percentage 27.0%)
There's not a whole lot here that's surprising, except maybe that Wharf-<nothing> is actually a bad opening for P1 (and not that great for P2 either). One other interesting thing that the lists above don't show is that while Swindler-Silver is a good opening for P1, it just missed the significance cutoff for being listed as
worse than average for P2.
Edit: a note about Rebuild-Silver, which featured prominently in the first post. The tables in the first post used all 90,000 games, while this analysis used only games between two top-100 players (about 17,000 games). In the smaller dataset, Rebuild-Silver was opened less than 50 times, and didn't make it into this analysis.