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Their odds are slim, but the Celtics will watch the draft lottery closely

The NBA draft lottery will be Tuesday night.
The NBA draft lottery will be Tuesday night.charles rex arbogast/AP/Associated Press

In recent years, the NBA draft lottery has provided perhaps the finest example of Danny Ainge’s wizardry.

The lottery is generally reserved for bottom-feeders, for teams hoping to find some luck so they can find their way out of the doldrums. But the maneuvering of the Celtics’ president of basketball operations has often allowed Boston to work on two timelines — fielding a talented playoff roster while also taking a seat on the lottery stage and hoping for even more.

And Tuesday night in Chicago will be no different. The Celtics will once again be represented at the drawing, this time with a keen interest in the draft picks of two other teams. And while the chances of striking gold this time are minuscule, the fact that Boston is in position to add two more high picks is significant.

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The Celtics will receive the Kings’ pick in next month’s draft as long as it is not the No. 1 overall choice, in which case it would go to the 76ers and the Celtics would receive Philadelphia’s 24th overall choice instead.

The Kings occupy the 14th and final lottery slot, so there is just a 1 percent chance that they will vault to the No. 1 position. This year the top four selections, rather than three, will be determined via the lottery, giving the Celtics a bit more hope about moving toward the top of the draft. There is a 3.7 percent chance that the Sacramento pick will land in the 2-4 range.

The Celtics also will be tracking the Grizzlies’ pick. In 2015, Boston sent Jeff Green to Memphis in a multi-team deal, and the biggest prize it received in return was a future first-round choice. It will get that pick from the Grizzlies this year as long as it falls outside the top eight. If the pick remains in the top eight, it will roll over to next season, when it would be top-six protected before becoming unprotected in 2021.

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The Grizzlies currently sit in the No. 8 spot in the lottery. So if form holds, they will keep their pick this year and the Celtics will wait at least one more season to cash in. But there is a 42.6 percent chance that at least one team in the 9-14 lottery spots will leapfrog the Grizzlies and push them back a spot, meaning Boston would get the pick now.

Generally, the chance to grab the ninth overall choice would be enticing. But the Celtics’ strong preference is for the pick to roll over, partly because this is a weak draft, partly because the pick protections lighten moving forward, and partly because the Grizzlies could be entering a rebuild.

But perhaps most of all, the Celtics would like to have this pick as a trade chip to dangle in trade discussions with the Pelicans for superstar big man Anthony Davis. They could still trade New Orleans the ninth overall pick this year, but it would not have the same value as a shiny, unknown future asset.

In addition to adding the No. 4 overall pick to the lottery drawing this year, the NBA also smoothed the odds a bit so the teams with the worst records have less chance of receiving the top choices. This was done to discourage teams from losing intentionally to help their lottery odds, though it’s unclear whether it helped on that front.

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This year, the teams with the three worst records — the Knicks, Cavaliers, and Suns — all have a 14 percent chance of claiming the top pick. Previously, the team with the worst record had a 25 percent chance, followed by 19.9 and 15.6 percent chances of the next two teams.

The team with the worst record has won the lottery four years in a row, but that will be far less likely this time. Because of the alterations, more teams can harbor realistic dreams of landing Duke star Zion Williamson with the first choice.

The Celtics have plenty of possibilities Tuesday, but getting the No. 1 pick is not one of them. And since Williamson is viewed as the one transcendent talent in the draft, Boston will be eyeing where the No. 1 pick lands.

The Celtics would prefer not to see the Knicks or Lakers (2 percent chance) win the No. 1 pick, in large part because they could be best positioned to acquire Davis, and suddenly would have the most valuable asset of all. Or, Williamson’s presence in New York could make Kyrie Irving more intrigued by the possibility of signing with the Knicks.

It also would not be ideal for the Grizzlies to get the No. 1 pick, because it would probably devalue the future first-round choice Boston will receive from Memphis.

Celtics assistant general manager Mike Zarren will be the team’s representative in the lottery drawing room, and team president Rich Gotham will be on the stage during the reveal, sharing a booth with 76ers president Chris Heck, whose team will also be in contention for the Kings pick.

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Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him on Twitter @adamhimmelsbach.