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I would think that Paul is the twelth apostle, which may shed some light on the signifigance of the lot casting in Acts.

Paul is a special case. There is no indication given in the account in Acts, or elsewhere, that Mattias's selection was invalid, or later overturned, or whtnot. I have heard the theory before, that the apostles were presumptuous in doing so, and that God overruled them and selected Paul instead.

But I don't see any actual supporting evidence for this.

As for the 12 foundation stones, we must remember that 12 is a symbol of perfection. As I say, if we have One God in Three Persons, we can surely have Twelve Apostles in thirteen persons.

There is no disputing the rest of the OT evidence that random games of chance were indeed used to "determine" the will of God in various circumstances. Take Jonah, for instance.