One of the odd stories about the origin of the Christian Church that is provided in the Book of Acts is the selection of a replacement for the traitor, Judas. The story found in Acts 1:21-25 narrates the importance of choosing a replacement, and the process to choose the new 12th man. There appears to be only one criteria for selection--the individual must have been a disciple of Jesus who had been with him from the time of his baptism to his ascension.
Two men were brought forward, Matthias and Justus, and Matthias was selected by casting lots. No prayers, no fasting, no spiritual discernment. He was selected rather by a game of chance. And the outcome was deemed the will of God!
In my opinion, the law of probability was at work here, not the will of God.
Post Script: I should point out that there was really a second criteria for apostolic succession in the Acts account--the candidate must be "male." Again, in my opinion, that was a cultural criteria and had nothing to do with God's will. In other words, the Bible neither teaches that "rolling dice" is a method for strategic decision making in the church nor that only men are qualified to hold leadership positions in the church of Christ.