The Major League Baseball amateur draft gets under way at 6 p.m. Monday, but Free State High graduate Cody Kukuk isn’t expected to get selected until Tuesday, when Rounds 2 through 30 take place.

Kukuk, a hard-throwing left-hander who features a 93 mph fastball, an even temperament and a competitive nature, already has signed a national letter of intent to play baseball at Kansas University, but the odds are against him ever throwing a pitch for the Jayhawks.

As a high school prospect, Kukuk has more leverage than a college junior and more still than a college senior. He has an attractive option — playing Big 12 baseball for the hometown university — that will enable him to be bold in contract negotiations with whichever club chooses him.

Scouts who attended Free State’s games to evaluate Kukuk privately estimated he would get chosen anywhere from the third to sixth round. Based on the 2010 draft, that means he very well could get in excess of a $500,000 signing bonus, plus a clause that guarantees his college education will be paid for by the ballclub. About half the players who sign out of high school eventually take advantage of the guaranteed free college education.

Unlike the football and basketball drafts, the most talented players don’t necessarily get picked the highest. Several ballclubs, such as the Pittsburgh Pirates, long have been known to place as high a priority on signability as playing ability. Clubs not interested in investing huge bonuses might draft a 15th-round talent in the sixth round in order to save money. A scout might approach such a prospect, ask him and his family if he were drafted that high would he settle for a signing bonus in line with a much lower-round choice. If the answer is yes, the two parties have a wink-and-nod deal.

Word on the Major League Baseball scouting circuit is that organizations that don’t set aside much money for draft choices aren’t likely to waste a pick on Kukuk because he’ll go to KU before settling for less money than comparable prospects receive. The grapevine has it that Kukuk’s initial bonus request will be in the neighborhood of $1.2 million. That doesn’t mean he won’t negotiate down from there, but it does mean he’s not going to be susceptible to a wink-and-nod deal.

Baseball America makes available to online subscribers the signing bonuses received by draft choices through the years. A study of 2010 draft data revealed that 78 percent of the players selected out of high school in rounds three through six signed rather than continuing their baseball careers in college. Right-hander Ryne Stanek, out of Blue Valley High in Overland Park, turned down an $850,000 bonus offer after being drafted in the third round by the Seattle Mariners. He now pitches for Arkansas.

The average bonus for high school signees by round: Round 3. $562,890.91; Round 4. $515,375; Round 5: $530,428.57; Round 6. $575,000.

Kukuk will become the second 6-foot-4 athlete from Free State High chosen in a professional sports draft in the past five-plus weeks. The Minnesota Vikings selected defensive lineman Christian Ballard with the ninth pick of the fourth round of the NFL Draft.