Late one night in 2002, Sam Yagan got a call from a former Harvard buddy with an idea for their next big company. What if they made a website with a button you could press to set up a blind date?

Yagan told him to call back when he was sober, but continued to think about it. To set up people on random dates successfully, you would need an enormous database of users and their preferences. You also would need a system that could pick a place to meet that was close to both people.

Yagan and that friend, Chris Coyne, didn’t develop the idea. Later that year, they joined with others to create OKCupid, a free dating site that matches users through mathematical algorithms based on answers to questions about their tastes. As OKCupid expanded its active user base to 3.8 million, becoming one of the most popular dating sites for young singles, Coyne’s original idea continued to percolate.

On Tuesday he’s finally getting his wish, with the debut of OKCupid’s Crazy Blind Date application. The free app for iPhones and Android phones is intended to eliminate the effort it takes to set up a date. If you’re free for an hour at 7 p.m. on a Wednesday, you can fill the slot with a date. You select a local bar or coffee shop to meet from the app’s recommendations, then choose among four people the company’s algorithm has suggested who are also free at that time.

The dates are not totally blind — you can see names, ages and faces — but the photos have been scrambled. You meet, and afterward the app asks how it went. The better it was, the more you pay, from nothing up to $3.

“If it were a perfect world, I would charge by success,” said Yagan, 36, who has been married for nine years. “If you could start a dating site where you just got paid for marriage or sex, that’d be pretty cool. This is the closest we can come.”

OKCupid was acquired in 2011 by New York-based IAC/InterActiveCorp, media mogul Barry Diller’s holding company. Last October, Yagan took over its portfolio of dating sites, which had $518 million in revenue in 2011, up 29 percent from the prior year. The company’s other sites include Match.com, for people looking for serious relationships, and OurTime, for daters over age 50. Most of the sites either ask for a monthly subscription fee, like Match, or charge users to send messages. OKCupid, aimed at users ages 18 to 34, makes money mainly through advertising.

OKCupid attempted a Web-based version of Crazy Blind Date in 2007, but not enough users had smartphones at the time, the company said. Now the industry is shifting to mobile, with more people using apps than websites for dating in 2011 for the first time, according to an IBISWorld report. The OKCupid mobile app and website receive 20 times as much activity as in January 2012, according to the company.

Yagan has tracked all kinds of data on users to determine what they want from OKCupid — his company’s blog, OKTrends, displays line graphs detailing things like a country’s per capita GDP versus the percentage of people who are looking for casual sex on the site. Ultimately, he said, users are just looking for fun and convenience. But the average visit to the site lasts 20 minutes, since users must sift through messages or work on developing enough of a rapport with someone to attempt a first date.

Using the Crazy Blind Date app, the time spent on a smartphone can be less than two minutes. Your co-worker says you look good today? Go on a date tonight, and the app will pull options based on OKCupid’s algorithm. Less forethought could be a good thing, said Sarah Wexler, author of “Awful First Dates: Hysterical, True, and Heartbreakingly Bad.”

“It helps build anticipation that the date is going to go well, because they’re from Boston, and I’m also from Boston,” Wexler said. “If all you know about somebody is they’re single, you’re probably go into it with more realistic expectations.”

The concept — spending less time online to meet new people offline — has already propelled other dating sites. HowAboutWe lets users post an idea for an activity to do on a date, then find another person who is interested in joining them. Grouper sends groups of three men and three women to meet at the same bar.

Yagan knows Crazy Blind Date will draw criticism. Without a chance to talk to the person before the date, there’s no natural filter for dangerous people, except reviews people give to OKCupid after the fact. And anyone can use the app, not just OKCupid users, so the company won’t have much information on some daters. As a safeguard, the app uses Foursquare Labs’s options for local bars and coffee shops nearby, “so you can’t meet in someone’s house, or an alleyway, or a car,” Yagan said.

Yagan’s dreams for Crazy Blind Date to generate profits depend on people grading their dates honestly. People who go on a good date may be tempted to say it was bad, just for free use of the service. That would cause problems for the matching algorithm.

If people are honest, Yagan says, the ratings should mostly be positive — even if their dates don’t end in romance. “I know the first day somebody’s going to be like, ‘You set me up with my sister! You set me up with my boss!’ ” he said. “But even bad dates can make for good stories.”