All this talk of gambling feels misplaced to some people. “Calling it a bet makes it sound like the endgame is me possibly not having a baby,” said Ms. Hernandez, the mother in Arizona. “But that’s not the case for people in my position. If one way doesn’t work, you will find another, whether it’s donor eggs or adoption. You don’t want to allow yourself to lose.”

Besides, there are sometimes odds that are so long that they never appear in anyone’s book of bets. Ms. Chambers, the Virginia mother, who is a physician assistant, blew through one employer’s lifetime infertility insurance coverage cap — and then some — in the course of giving birth to three children in 21 months using donor eggs.

She figured she was done once her twins were born. But when they were 9 months old and she was 42, she got pregnant the old-fashioned way, on Christmas no less. And on the way to becoming a mother of four, she had some instructions for the medical professionals who would be attending to her: “I told them that I couldn’t believe that I was going to say this, but please tie my tubes,” she recalled. “I’m all miracled out.”