No way to know what kind of chance you have.
I do know that WDW does not hold back reservations, so there won't be any new ones opening up after you get there unless someone cancels. The odds are not any better just because it's closer to the reservation date or because you are actually at WDW. You should still check if you really want to eat there.
For such a large party, the odds are not good at all. If you're staying at club level you should ask the concierge, not that there's really any better odds for getting 13 in but it couldn't hurt to have them checking...otherwise just keep checking yourself.