Karl-Anthony Towns has an imaginary friend that sits on his shoulder and offers advice or criticism during games.

Sounds cuckoo, but apparently those two have conversations on the basketball court or when Towns is sitting on the bench and needs a pep talk.

In other words, he’d be a perfect fit for the wacky Timberwolves.

Towns, that is, not his alter ego, whom he named “Karlito.”

Actually, the Wolves probably would create a roster spot for Karlito, too, if they can escape their cursed draft lottery history and secure the No. 1 overall pick Tuesday night.

The misery has to end at some point, right?

A Tank for Towns nosedive left the Wolves with a 25 percent chance at the No. 1 pick and a 64 percent chance that they’ll land one of the top three picks. They can’t fall lower than fourth, which, of course, means they’ll likely finish fourth, knowing their dumb luck.

The Wolves have attractive options that will make them instantly better with a top-3 pick. A lower slot brings some uncertainty. Here is one man’s preference in each case:

First pick: Towns.

Second pick: Jahlil Okafor.

Third pick: D’Angelo Russell.

Fourth pick: Hmmm. Tougher call here.

Assuming the Wolves don’t trade down in that worst-case scenario, they should take Latvian big man Kristaps Porzingis over point guard Emmanuel Mudiay, because they already have invested time and money in Ricky Rubio as their franchise point guard.

No matter your opinion of Rubio, the Wolves need to see how he develops if — and this remains a lingering question — he can stay healthy for a long stretch. Still a big if.

Someone suggested to me recently that the Wolves would be best served landing the second choice so that they can’t screw up the No. 1 overall pick.

Baloney.

Yes, the organization’s history is littered with foolish draft decisions, but Flip Saunders won’t get it wrong with either Towns or Okafor. Both centers look like transformative players. Neither is a consolation prize.

Towns just makes more sense because of his defensive acumen, which is endearing considering the Wolves are abysmal in that department.

Okafor is a more polished offensive player, but Towns has the potential to become a better two-way talent.

The Wolves desperately need a center who can protect the rim and provide some semblance of intimidation in the paint. Nikola Pekovic is not the answer, and his health can’t be trusted at this point anyway.

Towns’ size, length and skill set should have the Wolves salivating with hope he’s available wherever they pick.

He collected 88 blocks while averaging only 21.1 minutes per game in his one season at Kentucky. He averaged 6.7 rebounds playing only half the game.

The Wolves lack a defensive presence in the paint. They finished last in the NBA in scoring defense (106.5 points) and last in field-goal percentage defense (48.7). They were ranked 27th in blocks.

The Wolves often looked overmatched and/or clueless on defense. Opponents could drive to the basket without hesitation.

Towns would help fix that.

A combination of Towns, a healthy Rubio and Andrew Wiggins’ versatility would give the Wolves a solid defensive foundation. That’s why Towns gets a slight nod over Okafor, a ready-made, low-post scorer who looks both fluid and powerful around the basket.

Not getting either of those big men would be a letdown for the Wolves because of their gaping hole, but, let’s be honest, the team needs more overall talent, period.

Russell would give them flexibility in the backcourt and some much-needed outside shooting. He can play either guard position, and he made 41 percent of his three-pointers in one season at Ohio State. A nucleus of Rubio, Russell, Wiggins and Zach LaVine would give Saunders interesting options in the backcourt.

Of course, this is the Wolves we’re talking about, so any hint of optimism usually is accompanied by a bucket of cold water. Long-suffering fans know too well the draft lottery has been a figurative kick in the pants over the years.

Expect the worst Tuesday night but, who knows, maybe the Wolves will get lucky this time. If so, the guy with an imaginary friend would be a sane choice.