BOSTON (CBS) — The Celtics can make history on Tuesday night, becoming the first No. 1 seed in the playoffs to also land the No. 1 overall pick in the that year’s NBA Draft.

That is, if the ping-pong balls bounce in their favor, which hasn’t really been the case with Boston and the NBA Draft Lottery. Ever.

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Still, the Celtics are still in an incredible and unique position. They’re off to the Eastern Conference Finals, and though they’re not expected to do much against the defending champs this year, they appear to be just a piece or two away from becoming an actual title contender. They can do that while also likely enjoying a spot atop the draft board for at least one more year.

Boston is still reaping the benefits of Danny Ainge’s 2013 trade with the Nets, when he sent an aging Kevin Garnett and Paul Pierce (and how can we forget, Jason Terry and D.J. White) to Brooklyn for three future first-round picks (2014, 2016 and 2018) and the right to swap picks this season. The Nets went out and won just 20 games, making it an easy decision to swap picks for Ainge.

We’ll see if lottery luck is finally on their side tonight, when at the NBA Draft Lottery get underway at 8 p.m. in New York. The Celtics will be represented on stage by co-owner Wyc Grousbeck, with fellow co-owner Steve Pagliuca behind the scenes to witness the drawing. This is the first time that Grousbeck will represent the club on stage, and he’ll have his 2008 NBA Championship ring with him as his (and Boston’s) lucky charm.

The Odds

The Celtics have never received the No. 1 overall pick since the NBA Draft Lottery began back in 1985. This year, they have a 25 percent chance at landing that first overall selection:

– 25% chance at the top overall pick (the best odds of any team)

– 21.5% chance at landing the second overall pick

– 17.8% chance at the third overall pick

– 35.7% chance at the fourth overall pick

The Suns have the second-best odds at the first overall pick at 19.9 percent followed by the Lakers (15.6 percent) and 76ers (14.7 percent). If L.A.’s pick falls out of the Top 3, they have to send it to Philadelphia.

The Celtics also own three second-round picks this year: No. 37, No. 53 and No. 56.

Possible Picks

Ainge will have options next month, whether he decides to trade the pick and add an established star to a core of Isaiah Thomas and Al Horford or use the pick to add a potential franchise-altering prospect to the mix.

Should he choose to make the selection, here are the main studs he’ll be deciding between:

Markelle Fultz, G, Washington

Washington Huskies guard Markelle Fultz. (Photo by Christian Petersen/Getty Images)

Height: 6-foot-4
Weight: 195 lbs
Age: 19
Stats: 23.2 PPG, 5.7 RPG, 5.9 APG, 48 FG% (in 25 games)

Lonzo Ball, PG, UCLA

Lonzo Ball #2 of the UCLA Bruins sets up a play against the USC Trojans during a quarterfinal game of the Pac-12 Basketball Tournament at T-Mobile Arena on March 9, 2017 in Las Vegas, Nevada. UCLA won 76-74.

UCLA point guard Lonzo Ball (Photo by Ethan Miller/Getty Images)

Height: 6-foot-6
Weight: 190 lbs
Age: 19
Stat line: 14.6 PPG, 6.0 RPG, 7.6 APG, 55% (in 36 games)

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Josh Jackson, SF, Kansas

Kansas forward Josh Jackson. (Photo by Jamie Squire/Getty Images)

Height: 6-foot-8
Weight: 207 lbs
Age: 20
Stats: 16.3 PPG, 7.4 RPG, 3.0 APG, 50% (in 35 games)

Jayson Tatum, SF, Duke

Duke small forward Jayson Tatum. (Photo by Kevin C. Cox/Getty Images)

Height: 6-foot-8
Weight: 205 lbs
Age: 19
Stats: 16.8 PPG, 7.3 RPG, 2.1 APG, 45% (in 29 games)

Jonathan Isaac, F, FSU

Florida State forward Jonathan Isaac. (Photo by Mike Ehrmann/Getty Images)

Height: 6-foot-10
Weight: 210 lbs
Age: 19
Stats: 12 PPG, 7.8 RPG, 1.2 APG, 51% (in 32 games)

Dennis Smith Jr., G, NC State

NC State guard Dennis Smith Jr.. (Photo by Grant Halverson/Getty Images)

Height: 6-foot-3
Weight: 190 lbs
Age: 19
Stats: 18.1 PPG, 4.6 RPG, 6.2 APG, 46% (in 32 games)

Malik Monk, G, Kentucky

Kentucky guard Malik Monk. (Photo by Andy Lyons/Getty Images)

Height: 6-foot-3
Weight: 200 lbs
Age: 19
Stats: 19.8 PPG, 2.5 RPG, 2.3 APG, 45% (in 38 games)

Read: CBS Sports’ Mock Draft

The 2017 NBA Draft will be held on June 22 in New York.

The Bad Luck

We hate to end this on a down note, but it seems the Celtics get burned at the lottery once every decade. In 1997 they were expected to land the No. 2 pick, and actually had the best odds to land the first overall pick (27.51 percent), because Vancouver was an expansion team. That would have landed them a franchise cornerstone in Tim Duncan, but they instead fell to the third pick. Rick Pitino drafted a promising guard in Chauncey Billups, but he traded him to Toronto for Kenny Anderson halfway through his rookie season. Duncan went to San Antonio, and the five-time champ is now patiently awaiting his enshrinement in the basketball Hall of Fame.

Flash back to 10 years ago, when the Celtics finished the 2007 season at 24-58 and entered the lottery with a 20 percent chance to pick Greg Oden or Kevin Durant first overall. Even if they had stayed at No. 2, they still would have landed Durant. Instead, the C’s fell down to No. 5, which was devastating at the time.

Things ended up working out in the end, as Ainge packaged that fifth pick (which became Jeff Green) with Wally Szczerbiak and Delonte West on draft night and sent them all to Seattle for Ray Allen and a second-round pick that became Glen “Big Baby” Davis. A few weeks later Kevin Garnett was holding up a Celtics jersey, and the rest is history.

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So we’ll see if Tuesday night’s lottery ends in similar fashion, and if that luck, good or bad, could be the start to something great for a promising Celtics team.