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College basketball in December is a matter of trust, like used cars and blind dates. Going in, you believe things will work out better than they invariably do.

In the case of the Great Eight, there is at least accuracy in the number, half of it on display Tuesday night at the United Center, the remainder scheduled for Wednesday at the same times. As for the immodest modifier, Great is, in the main, at least premature.

“I’ll bet you at least two of the Final Four teams come out of here,” Utah coach Rick Majerus said. “Kansas, Arizona, Purdue perhaps. Who else? Kentucky. I’ll take odds against the field that at least two of those are there at the end.”

Ah, but the presumption of the Great Eight is not of what may be, rather it is of what was. The event is based on an illusion. The last eight teams when it matters reassemble when it does not. And sponsored by frozen pizza, an affront to Chicago, if not to Chicago’s climate.

“In the Big Eight, everybody but us is a Top 25 team,” Providence coach Pete Gillen observed, getting the name wrong but reinforcing the point that almost any college basketball this time of year is invariably more calisthenics than breath-robbing drama.

Believing that it is anything else is like trying to load a bag from the top. Paper, plastic or two nights in Chicago?

“We don’t pretend to be the team we were,” Majerus said, “but Arizona is the team that was.”

And that, dear Brutus, is the burden of being the incumbent national champion.

“Oh, we’re not going to get anybody’s second best shot,” said Arizona coach Lute Olsen. “There’s nobody we will play who won’t be excited to play us. And we should be just as excited.”

Arizona let Kansas wander off to a 20-point lead, scratched back to within two late, and lost by three at the end in what could be the greatest Great Eight game ever, a spare number, only 14 so far.

Revenge is a valuable inspiration, and not a bad way to schedule.

“It was a matter of pride,” said Kansas guard Ryan Robertson. “This was not exactly as big a game as last year but we don’t want to be second to anybody.”

Last year would have been the NCAA regionals, won by Arizona, depriving Kansas of its supposed championship. At the end of this one, Kansas players hugged one another as if this was something a bit less portable than a one-night gimmick, more like a tournament game in March, like the one lost by the Jayhawks to the eventual champions.

Kansas coach Roy Williams looked at the tape of that defeat for the first time the day before the game.

“I spent the summer full of hurt and sorrow,” Williams said. “Looking at that tape, I got ticked off. I was mad about it. I told the team.”

Maybe Williams might have saved such valuable pique for when it mattered more, somewhere on the other side of the vernal equinox. If Majerus is to be believed, these two shall meet again.

Arizona has kept all its most important parts, reassembled in anticipation of chasing the title once again. This is a familiar incentive for the building, though the regular residents are having trouble reconciling noble purpose with galloping ego.

In fact, Scottie Pippen received boos when he appeared merely in a video commercial on the Jumbotron, in case Pippen is wondering what kind of reception he will receive should he ever again dress for work here.

Kansas came to the Great Eight with a higher rank (No. 2 to No. 4), a preseason trophy (the NIT championship compared with Arizona’s loss in the Maui final) and the poster team for the obvious: Nothing that happens before March means anything.

Providence, losers to Utah in the first game, no longer are blessed by God Shammgod, who is now on the injured list of the Washington Wizards, his number worn by freshman John Linehan. If Providence could not retire God’s number, at least it should retire his name.

Utah, undefeated with victories over a nation (Hungary) and a state (the California All Stars,) and now a city, should improve its ranking from No. 16 so that all that is needed to designate its national status would still require all of Majerus’ fingers but now he would have to remove only one of his shoes.