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A day after failing to win any Super Tuesday contest, Ohio Gov. John Kasich predicted victory in his home state's upcoming winner-take-all contest.

"We didn't expect Super Tuesday to go very well, but we almost beat [Donald] Trump in Vermont. We split delegates," Kasich told CNBC's "Squawk Box" on Wednesday. "[We] finished second in Massachusetts. We picked up delegates in Virginia. It was a good night for us."

"Now we're getting into the 'March Madness.' We're moving toward the 'Final Four.' And it goes to home court for me," the governor said, using a college basketball analogy. "We get up to Michigan and then the most important Ohio."

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The winner in Ohio's March 15 GOP primary gets all 66 delegates. The winner of Florida's primary on the same day also gets all GOP delegates — 99.

Calling out rival Marco Rubio, Kasich said if the senator from Florida does not win his home state, he should drop out. "If you don't win your state you leave."

Kasich acknowledged Sen. Ted Cruz, who won his home state of Texas Tuesday, had a good night. But he questioned whether Cruz can compete effectively in the upcoming states to the north. Cruz has positioned himself as the outsider alternative to Trump.

Rubio is seen as an establishment candidate competing with Kasich. However, Kasich rejects that label. "I fought the establishment all my life with great success," he said.

"[If] I win Ohio, which I expect that I'll do, it's a whole new ballgame. It's all back open again," said Kasich, who was joined on CNBC by two of his billionaire supporters, former hedge fund titan Stanley Druckenmiller and Home Depot co-founder Ken Langone.

They both pleaded Kasich's case, based the candidate's resume as a long-time Capitol Hill insider and now a governor of a state.

Kasich said he has the ideas to fix the nation. "You take the common-sense regulations, lower taxes, and fiscal policy that makes sense and you get jobs. It's not that complicated. ... I did it in Washington. It did it in Ohio. And I can go back" and do it again.

Correction: This story was updated to show the Ohio primary is March 15.