According to Old Testament, how long did Saul reign as king?

Using David’s age at at ascension, 30, and the requirement of Moses that 20 years old was minimum age to engage as warrior then only 10 years elapsed from David slaying Goliath unto David becoming king. David was a man (12+ years old, likely 19 years) when he played for a rejected Saul. 1sam13:1 gives Saul time as King as 2 years from then Saul makes war against 1) Amalekites {when rejected and David appointed as court musician}, 2) philistines, 3) kings of Zobah, 4) Edom, 5) children of Ammon, 6) Moab, and as battles were pitched spring each year this is year 6; so 2+6+10=18 years as king?

The variation comes from missing digit(s) in the extant Hebrew manuscripts for 1 Sam 13:1. Dr. Michael Heiser's 2008 blog article about it, 1 Samuel 13:1 – The Matter of Missing Words in the Bible, summarized the problem well:

The Masoretic Text (MT) literally says “Saul was a son of a year in his reigning and two years he reigned over Israel.” Obviously there are two errors in the Hebrew text as we have it today: (1) Saul was not one year old when he became king, and (2) he reigned more than two years.

The first error is obvious, since the book of 1 Samuel tells us plainly how Saul was chosen and anointed king — and he was a full grown man. The second error is plain when viewed against Acts 13:21 (and when reading the account of Saul’s kingship in the OT).

Now, in one regard, this is no different than any other text-critical problem. You detect the error in the present text, then work to find out how it came about, and consult other manuscripts of the Hebrew Bible for the solution. But there’s the rub — in the case of 1 Sam 13:1, there are no other reliable manuscript readings.

Unfortunately, none of the Dead Sea Scroll fragments related to the Book of Samuel has 1 Sam 13:1. See 1984 paper Additions or Omissions in the Books of Samuel: The Significant Pluses and Minuses in the Massoretic, LXX and Qumran Texts by Stephen Pisano, S.J.

The entire verse was also missing from earlier copies of the Septuagint. Some later copies have 30 but deemed as corruption and therefore modern translations of Septuagint omit this verse, such as Chapter 13 of the NETS Septuagint translation. See Dr. Michael Heiser's blog article referred to above for more discussion on this, as well as this article.

To reflect the missing information some translations, such as the NRSV, render 1 Sam 13:1 as follows:

Saul was . . . years old when he began to reign; and he reigned . . . and two years over Israel.

with the footnote:

1 Samuel 13:1 The number is lacking in the Heb text (the verse is lacking in the Septuagint).

Another blog article Rereading 1 Samuel 13:1 by Claude Mariottini, a Professor of Old Testament at Northern Baptist Seminary provides a good explanation why translations differ:

The different readings for the length of Saul’s reign in the translations are only possibilities. Thus, if a translation says that Saul was 30, or 40, or 50 years old when he began to reign and then says that he reigned 42, 32, 22, or 2 years over Israel, that translation is not teaching biblical truth but educated possibilities. The fact is, that since the numbers are contradictory, then one or all of the translations may not be presenting the right information.

In Acts 13:21 we have 40 years, see Acts 13:21, NRSV:

²⁰ ... After that he gave them judges until the time of the prophet Samuel. ²¹ Then they asked for a king; and God gave them Saul son of Kish, a man of the tribe of Benjamin, who reigned for forty years.

Possibly, St. Paul quoted a Septuagint manuscript that is no longer extant. Or he may have relied on Josephus who said in Antiquities of the Jews — Book VI:

To this his end did Saul come, according to the prophecy of Samuel; because he disobeyed the commands of God about the Amalekites; and on the account of his destroying the family of Ahimelech, the High Priest, with Ahimelech himself; and the city of the High Priests. Now Saul, when he had reigned eighteen years,²² while Samuel was alive; and after his death two, [and twenty,] (35) ended his life in this manner.

Finally, yet another article tries to deduce the reign length of Saul from implications it has on other characters's ages: Judges: The reign-length of Saul. The article recommends between 10-20 years and instead suggests one possibility: clause placement corruption in Acts 13:21 and that Paul meant it was David who reigned for 40 years.