Sen. Ted Cruz’s hopes for winning the Republican presidential nomination outright have faded, and he has shifted to a strategy of gaming the rules, angling to send enough double-agent delegates to the July convention to snatch victory from front-runner Donald Trump.

It’s a major reversal for Mr. Cruz, who just weeks ago insisted he would win the 1,237 delegates needed to clinch the nomination before the convention. But major wins in Utah, Wisconsin and Colorado have not closed the gap, with a series of East Coast primaries looming.

Now the best option for the senator from Texas is trench warfare at the Republican National Convention in Cleveland.

“I think it’s very simple. The odds are now very high that we go to a contested convention,” he said in a radio interview Tuesday with conservative media honcho Glenn Beck, who has endorsed Mr. Cruz.

“When we get to a contested convention, here’s what’s going to happen: I’m going to have a ton of delegates, Donald’s going to have a ton of delegates, and it’s going be a battle to see who’s going to win a majority,” Mr. Cruz said. “In Cleveland, I believe, we will have an enormous advantage.”

Indeed, Mr. Cruz has proved masterful at working Republican Party rules to pick up extra delegates at state conventions, including in Louisiana, where Mr. Trump won the primary but Mr. Cruz walked away with more delegates.

The Cruz campaign also has excelled at recruiting double-agent delegates, who are bound to Mr. Trump but are loyal to Mr. Cruz. Under party rules, they will be free to switch their votes on the second, third or fourth ballots at the convention.

“Cruz basically has people going there saying, ‘I’m bound to vote for Trump, but Cruz’s machine got me here,’” said Republican political strategist Rob Collins.

He said it puts Mr. Cruz in an enviable position as long as the race ends up at a contested convention.

“More and more pressure is being put on the other candidates to try to win the first ballot or go home,” Mr. Collins said. “The Trump campaign has built everything around winning on the first ballot. That math is still a better possibility for Trump, but it is getting more and more challenging as the days go by.”

After scoring a big win this month in Wisconsin, Mr. Cruz has lost momentum on the campaign trail.

In nearly every remaining contest in April, including those in New York, Connecticut, Maryland and Pennsylvania, Mr. Trump holds commanding leads and Mr. Cruz is battling for second place against Ohio Gov. John Kasich.

“Cruz is not even going to be finishing second for the next couple of weeks. He’s going to be distant thirds in a lot of places,” Trump campaign convention manager Paul Manafort said this week on Fox News’ “Hannity” program.

He predicted that Mr. Trump would reach the 1,237-delegate goal with the final primary contests June 7, which include California, where 172 delegates are up for grabs.

“The whole premise of the Cruz campaign of a second ballot misses the point,” Mr. Manafort said. “There’s not going to be a second ballot.”

Still, the likelihood of a convention fight with multiple ballots has put much of the focus of the race on rules.

Mr. Trump, who has complained that the Republican establishment’s rules are “stacked against me,” announced Wednesday that he hired veteran political strategist Rick Wiley to run the statewide field operations.

“His deep ties to political leaders and activists across the country will be a tremendous asset as we enter the final phase of securing the nomination,” said Mr. Trump.

Mr. Wiley has strong relationships within the Republican Party establishment and ran Wisconsin Gov. Scott Walker’s presidential campaign.

In the radio interview, Mr. Cruz accused Mr. Trump of acting like a gangster because a political operative associated with the Trump campaign threatened to reveal delegates’ hotel room numbers in Cleveland.

“Donald needs to understand he’s not Michael Corleone,” Mr. Cruz said, referring to a character from “The Godfather” films. “I understand Donald has had some very shady business deals with people that are currently in prison — mobsters — but the presidency should not be La Cosa Nostra.”

“Donald needs to stop threatening the voters,” the senator said. “He needs to stop threatening the delegates. He is not a mobster.”

⦁ David Sherfinski contributed to this report.

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