“I HAD made it clear to my family that I would not accept an arranged marriage,” said Tabish Rizvi, who grew up in New Jersey and whose parents come from India. He said he had been too influenced by the romantic relationships of those around him and in American pop culture to go for that.

So early on in his relationship with Dr. Maliha Ahmad, when he suggested that they “take a break,” it was more than a little ironic that he came to see Maliha and himself in the uncomfortable mold of the Rachel and Ross characters from the “Friends” television show.

Dr. Ahmad, 29, and Mr. Rizvi, 33, met at a gambling-themed New Year’s Eve party ushering in 2006. In the New York apartment where the event was held, Mr. Rizvi had temporarily been drafted to run a blackjack table as Dr. Ahmad, then a medical resident, laid down a bet using the fake money provided to partygoers.

Seeing her for the first time, Mr. Rizvi, recalled being dumbstruck by Dr. Ahmad.

“I’m a relatively confident fellow,” he said, adding that he didn’t want to sound foolish. Mr. Rizvi, now a senior manager in New York with FTI Consulting, a bankruptcy and restructuring consulting firm, recalled how he mulled over a clever introduction, but that his hosts relieved him of his table duty. He would have the rest of the night to consider his words.