1.24% * board area [cm²] / (track spacing [mil])².
I just made that up, ignore it. But seriously -- the probability will depend on so many aspects of your board design and the manufacturing details, I don't think anyone can give you solid numbers.
Some low-cost vendor I ordered from a few years ago would typically send 11 or 12 PCBs when I ordered 10, which suggests to me that they expected one or two failures out of 10. That was for small, double-sided boards. Manufacturing processes may have improved since, but the fact that flying probe tests are still part of the standard offering indicates that the failure rates are not negligible.
Yours is a large 4-layer PCB, if I remember correctly. You will put a lot of time into populating it and bringing it up, and the parts will cost you money as well. There are more than enough things that can go wrong and cost you time to troubleshoot. I would not want to potentially lose days, plus the cost of having to build a second unit, due to some internal short on the board.