At this point, Michele Nagamine figures, her Rainbow Wahine are playing with house money.

The Hawaii soccer team was assigned the fourth seed among four teams in this week’s Big West tournament after a 1-1 draw with Long Beach State to conclude the regular season Sunday.

The tournament will be held at Cal State Fullerton, which earned the No. 1 seed by virtue of beating Cal State Northridge in its finale Sunday. After a series of tiebreakers, Northridge, UC Santa Barbara and UH — which all finished at 15 points in the standings in a tie for second — were assigned the No. 2, 3 and 4 seeds, respectively.

UH (6-7-4, 4-1-3 Big West), which is in the BWC tourney for the first time, will face the host Titans at 5:30 p.m. Hawaii time on Thursday. UH went 2-0-2 on the road in Big West play this season, including a 1-1 draw at Fullerton on Oct. 20. It was UH’s first result against CSUF in eight Big West meetings (0-7 previously).

“I think the field at Fullerton is going to play a major factor for all of the teams. It’s massive and the stadium is very cavernous,” Nagamine said in a postgame phone interview. “So it’s going to be a battle, and we’re looking forward to it. Any time you get to play the host team first, with fresh legs — we should be nice and recovered by Thursday.”

Fullerton (12-2-4, 5-0-3 BWC) did not take a loss in a turnaround Big West season. The Titans finished in last place last year, but knocked UH out of tourney consideration on Wahine senior night.

“We’re taking the attitude that we had one goal this entire season, and that was to make it to this tournament,” Nagamine said.

After LBSU scored on a penalty kick in the 42nd minute of Sunday’s match, UH trailed 1-0 at halftime. But sophomore holding midfielder Morgan Meza, a Long Beach native, connected on her first career goal, a rocket from outside the box to knot it up in the 63rd minute.

Goalkeeper Lex Mata had five saves in not allowing a goal from the field of play in 110 minutes.

“I definitely am thrilled for my team. I think they’ve worked hard for this. They’ve defied a lot of the odds,” Nagamine said. “We were picked to finish seventh and ended up tying for second. It was one of those seasons for us where we’re going to enjoy it. It’s a new experience for the kids and the coaches to be in the postseason, and we are going to soak up every minute of it.”

Much was up in the air for the final day of the regular season. There was even a scenario in which UH would be the No. 1 seed and host the four-team tournament. But that required UH to win at LBSU for the first time since 2003. Fullerton and Northridge also needed to draw, and UCSB needed not to win against UC Irvine. Only one came to fruition.