Ohio Gov. John Kasich’s presidential campaign has released several ads this week ahead of the April 19 New York primary that go after Sen. Ted Cruz and don’t mention GOP front-runner Donald Trump, who is the overwhelming leader in recent polling on the Empire State and in the overall delegate race.

“Don’t be fooled: Ted Cruz can’t win the nomination outright and he can’t defeat Hillary Clinton, either,” says a narrator in an ad released Friday by the Kasich campaign.

Both Mr. Kasich’s campaign and the pro-Kasich group New Day for America also released ads Thursday hitting Mr. Cruz for the Texas senator’s past comments deriding Mr. Trump for embodying “New York values.”

But even though Mr. Cruz’s line was aimed squarely at Mr. Trump, those ads don’t mention Mr. Trump’s name, either. Mr. Cruz has since said the line was meant to be directed toward New York Democratic politicians.

“Ted Cruz has disrespected the people, has no chance of winning and should get out of John Kasich’s way in New York,” said Connie Wehrkamp, a spokeswoman for New Day for America.

Mr. Kasich cannot win enough delegates to reach the 1,237 needed to clinch the nomination before the GOP convention in July, and he is counting on an open convention as his path to winning the party’s nomination.

But attacks on Mr. Cruz, particularly in New York, could also end up serving to boost Mr. Trump, who has a much more realistic path to the 1,237 delegates than the Texas senator and who has held overwhelming leads in New York in recent polling.

A Monmouth poll on the Empire State released this week had Mr. Trump at 52 percent support, Mr. Kasich at 25 percent and Mr. Cruz at 18 percent.

There are 95 delegates up for grabs in the state, and the 50 percent mark is significant. There are 81 delegates awarded based on the votes in New York’s 27 congressional districts, or three from each district.

If a candidate wins a majority of the vote in a district, he wins all three of the delegates, with a 20 percent vote threshold to win any delegates if no candidate wins a majority.

Similar proportionality rules hold for remaining statewide delegates, meaning Mr. Cruz and Mr. Kasich will likely be hoping to pick off delegates where they can and hold Mr. Trump to under 50 percent of the vote wherever possible to head off the winner-take-all triggers.

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