There was an old-fashioned Wild West standoff this week in a onetime frontier outpost.

Two candidates for Town Council in Gila Bend, Ariz., finished with the same number of votes in July’s election, 67 each. A century-old state law mandated breaking the tie with a game of chance.

In this duel, there would be no gunslinging, though there would be a draw — not from a holster, but from a shuffled deck of cards. The hopeful with the higher card would claim the seat.

In an age of increasing distrust in elections and a state that has been a hotbed for voting-related conspiracy theories, Gila Bend’s leaders said they knew the high-stakes tiebreaker, which took place Tuesday, would need to be transparent and carefully choreographed.

“With everything that’s going on, you want it as open as you can possibly get it,” said Patricia Riggs, the town clerk, who oversees elections.

The stalemate in this 1,800-person community, 50 miles southwest of Phoenix, was hardly the first to be decided by chance in a country with tens of thousands of elected local governments and closely divided politics. Races in recent decades have come down to poker games, straw-drawing and, earlier this month in Hawaii, names tucked into plastic eggs and picked from a woven basket.

But Gila Bend’s tie might have been the first involving a candidate who had been in the exact same position years before. Jesus Rubalcava finished neck and neck with an opponent in 2014 and won his first term on the Council with the flip of a $1 coin.

After a court-certified recount earlier this month confirmed his deadlock with the newcomer Athena Guerrero, Ms. Riggs informed Mr. Rubalcava that his election fate would once again come down to chance.

Did that make him lucky or unlucky? Mr. Rubalcava, a high school teacher and former state legislator, wasn’t sure.

“I was in disbelief,” he said. “I couldn’t wrap my head around it.”

It was up to Ms. Riggs and other town officials to choose what form the rubber match would take. Arizona law stipulated only that the tie be broken “by lot.” They ruled out rock-paper-scissors, and they opted against drawing marbles or straws.

“We thought that was kind of boring,” Ms. Riggs said.

High-card draw would be more exciting, they decided, and it would be easy for the public to understand and follow.

Ms. Guerrero was initially wary. “I’m not a gambling type of person,” she said.

But she knew enough to pray for an ace. Ms. Guerrero, who works for a water treatment plant, had long eyed politics, and she imagined the Town Council as a launching pad. Eventually, she said, she would like to be mayor.

Gila Bend, an important stop on a storied 19th-century stagecoach line, is now a manufacturing and farming town where local politics is unavoidably personal. In separate interviews, Ms. Guerrero and Mr. Rubalcava each said they “have nothing but love” for the other.

Neither campaigned aggressively, and the nail-biter was a reminder that every vote counts. Mr. Rubalcava’s mother, brother and niece all failed to cast ballots, he said.

They were not alone. Fewer than 200 of the town’s roughly 600 registered voters participated in the July election.

Ms. Riggs spent three weeks painstakingly planning Tuesday’s showdown, consulting with lawyers and election experts. She devised a list of 19 steps that documented exactly how the draw would go, and she wrote a script to read while she conducted it.

On Tuesday morning, she borrowed a mechanical card shuffler from her sister-in-law and bought two decks at the town’s Dollar General, one for practice. That night, the two candidates sidled up to a table in a school building and exchanged nervous smiles in front of a handful of residents and the sitting Council members.

Ms. Riggs stated the rules, opened and spread a new deck of cards and let Ms. Guerrero and Mr. Rubalcava inspect them. She shuffled and presented the stack to Ms. Guerrero, who cut it. Mr. Rubalcava then cut it again.

The candidates were reminded that, in the event they drew the same number — like that would ever happen — spades would trump other suits.

Ms. Riggs pulled Ms. Guerrero’s card first, a three of clubs. The candidate sighed.

Ms. Riggs flipped Mr. Rubalcava’s card next.

Another three, another tie. The audience gasped. Mr. Rubacalva couldn’t believe it. “Did this really just happen?” he thought.

But his three was a spade, delivering Mr. Rubalcava a chance victory for the second time. The candidates laughed and shook hands.

“Who would have thought?” a stunned Ms. Riggs said to the room.

Ms. Guerrero said on Wednesday that she planned to run for office again, pledging to “come back strong in a couple years.”

Ms. Riggs said she was glad to hear it, then added: “God forbid there’s a tie.”