Fortune telling is a misnomer. I use it in the title simply because it is the only concept outside of Mormondom that comes close to describing patriarchal blessings. Personal revelation is a better descriptor but I don't think that will mean much to non-Mormons.

In a blog posting Mark Paredes explains patriarchal blessings to a Jewish audience. See "This Week’s Torah Portion: Patriarchs, Blessings, Tribes—and Mormons." It made me realize that those outside Mormondom may be uninformed so I'll explain it a little further.
Patriarchal blessings are given to worthy members of the Church by ordained patriarchs. Patriarchal blessings include a declaration of a person's lineage in the house of Israel and contain personal counsel from the Lord. As a person studies his or her patriarchal blessing and follows the counsel it contains, it will provide guidance, comfort, and protection. See Patriarchal Blessings.
Ordained Patriarchs are generally elderly men with long histories of church service. Being a patriarch is a church job or calling as it is normally referred to.

The blessing has two purposes. The first is to declare a person's lineage. The second is to give personal counsel.

This is direct revelation to a person about his or her life. The patriarch is merely the conduit the Lord uses to convey this information. The patriarch verbalizes what he is inspired to say to the individual. The blessings' content is transcribed and given to the person. Also, a copy is retained by the Church for its records.

A person's lineage is the tribe of Jacob the person belongs to either by bloodline or adoption. Paredes' blog makes clear that the tribe of "Ephraim" is responsible for the spiritual gathering of Israel. Paredes is from Ephraim as am I. Ephraim and Manasseh were Joseph's sons. Obviously, Paredes' Jewish readers would be interested in this aspect of patriarchal blessings.

Most people I know are of Ephraim. However, I have known of people from other tribes such as Manasseh, Benjamin, Dan and Levi. I'm only mentioning instances where I know for certain where someone is in one of these unusual tribes.There is a lot of hearsay and folk tales circulating.

Because each of us has many bloodlines running in us, two members of the same family may be declared as being of different tribes in Israel.
It does not matter if a person's lineage in the house of Israel is through bloodlines or by adoption. Church members are counted as a descendant of Abraham and an heir to all the promises and blessings contained in the Abrahamic covenant. See Patriarchal Blessings.
Personal counsel in a blessing takes on many forms. Sometimes a person is told specific things about their future spouse or children for example. Sometimes the information is very general. Sometimes a person is told to guard against certain behavior like selfishness. Sometimes a person is told very specific things about his or her future life. Again, sometimes it is very general.

In mine, I'm told about specific talents that I have. I think this is relatively common overall.

The blessing is intended to be a guide for us. Everything in a patriarchal blessing is conditional on personal worthiness. If you become wicked, you may not get some of the things you have been promised. 

Example 1:
Elder LeGrand Richards told the following story to illustrate this point.
“I was visiting a patriarch a while ago. He told about a blessing he gave to a woman who came to him from one of the missions. Among other things he told her that her progenitors had made a great contribution to the bringing forth of the gospel in these latter days. And after the blessing was given she said, ‘I’m afraid you made a mistake this time. I am a convert to the Church; I am the first one of my family to join the Church.’
“‘Well,’ the patriarch said, ‘I don’t know anything about it. All I know is that I felt prompted to say that to you.’ And when he told me the story, she had just been in the genealogical library and had found that some of her relatives—her grandparents or her great-grandparents—had made great sacrifices in the early days of the Church. … She found that she was descended from some of the early pioneers. The patriarch did not know of it himself. He had spoken by the inspiration of the Holy Ghost” (“Patriarchal Blessings,” p. 6).
I hurried to my parents’ house and saw that my dad could hardly breathe; he had a tingling in his arm and a horrible pain in his chest. It was a heart attack! I urged my brother to take my father to the emergency room. . . . My father was dying on his way to the hospital, and I implored our Father in Heaven not to let him die that Christmas. In desperation I implored the Lord for forgiveness, and a voice whispered in my ear, “Read your patriarchal blessing!” How could I think about my patriarchal blessing at a time like this? But the prompting continued, strongly urging me to read the blessing.
I stood up, found a copy of my patriarchal blessing, and began to read it. And then something amazing happened. I realized that several times the blessing mentioned that I am a beloved daughter of Heavenly Father and of my earthly parents and that if I honor my parents on earth, He will prolong their lives, they will have the opportunity to see my children grow, and they will rejoice with me in our posterity. 
As I read, an understanding came to me. My father hadn’t yet seen my unborn child, neither had he seen this child grow. He wouldn’t die at that moment, I realized. My blessing was my answer that day.
Example 3:

My patriarch gave a fine blessing, but I just did not feel that the experience was as great as everyone made it out to be. I admit that in a way I was even disappointed. I had expected so much, and it seemed that I did not receive what I had wanted. I questioned my own worthiness. Could it be my fault that I was not feeling anything spectacular?
After days of pondering, I knew I was at fault. I realized I needed to do some preparation in my own life to receive the personal witness that my patriarchal blessing was from God. 
For the next few weeks, I fasted, prayed, and sought forgiveness of any sins I had. I was changing slowly. I could not tell a great difference, but by the time my patriarchal blessing came to me in the mail, I was ready. 
I waited until Sunday evening to read it when all was quiet. Even as I opened the envelope, I could sense a different feeling come over me. I began to read. I had not read more than a few lines when amazing statements appeared. I could not believe this was my blessing! It seemed my whole blessing was full of material I had never heard before, and the things which I did remember began to have new meanings. A full-time mission, celestial marriage, eternal life—I now saw these expressions, that I had thought were trite, as the great promises they were. I had missed so much when I first received my patriarchal blessing. My “nice prayer” had turned into a personal revelation from God to me. 

Since the Church retains copies of blessings, you can get a copy of your own blessing as well as those you are directly descended from.

See Gospel Study: Study by Topic: Patriarchal Blessings for complete information and links to other quality resources on patriarchal blessings.

Note: Fortune telling falls under the "occult":

Church members should not engage in any form of Satan worship or affiliate in any way with the occult. “Such activities are among the works of darkness spoken of in the scriptures. They are designed to destroy one’s faith in Christ, and will jeopardize the salvation of those who knowingly promote this wickedness. These things should not be pursued as games, be topics in Church meetings, or be delved into in private, personal conversations” (First Presidency letter, Sept. 18, 1991).



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