SAM PARKER’S smile was so big, he looked as if he’d just won the lottery. Which he had: to “Hamilton,” the hottest show on Broadway.  Mr. Parker, a young actor who said he wouldn’t be able to afford a regularly priced ticket, lucked out at a recent lottery drawing for 21 front-row seats ($10) and eight standing-room spots ($40) to “Hamilton,” a hip-hop musical about the founding fathers and one of the most elusive tickets. He was among some 350 people who entered the lottery, held under the marquee at the Richard Rodgers Theater.  In snagging a $10 ticket to see the show, he is one of the fortunate audience members who realize that cheap seats remain possible to find — if you have time before a show to pop an entry in a bucket or, increasingly, hit send on your phone.  Broadway lotteries that offer deeply discounted tickets have blossomed since 1996, when “Rent” made some $20 seats at the Nederlander Theater available for every performance. (It started as a first-come, first-served offer but evolved into a lottery.)  The few shows with in-person lotteries host them before every performance with rare exceptions (like President Obama’s scheduled attendance at a performance of “Hamilton” on Monday for a Democratic Party fund-raiser). In this smartphone era, though, in-person ticket derbies are being superseded by digital lotteries, online or through an app.  Lottery economics favor both producers and audiences. People who can’t afford tickets get to see shows on the cheap and on the fly. Producers fill seats — generally in the first two rows, partial-view seats or in the boxes — with enthusiastic theatergoers who tend to be young and savvy about posting their winnings on social media.  Some new shows, like “Hamilton” and “Spring Awakening,” turn their live drawings for tickets — which go for well over $100 apiece — into full-fledged events. Long-running hits like “The Book of Mormon” and “Wicked” continue to be draws.  Even when a show isn’t exceptional, lottery winners supply the kind of engagement that generates buzzy feedback and word of mouth that producers crave.  “As soon as the show ends, who jumps up first? Those first two rows,” said Kevin McCollum, a “Rent” producer who’s currently represented on Broadway with “Something Rotten!” and “Hand to God.”  These days, playing the lottery calls for a mix of old-fashioned luck and golden-touch technique. Here are a few tips to help you navigate the waters.  First some lottery basics. We’re not talking about rush tickets, which are discounted seats that may be available at the box office on the day of the show, sometimes only for students with an ID. Most lotteries take place about two hours before showtime, with a 30-minute window for entering. Handwritten entries go in a bingo cage or other large container, and when the winners are announced they are usually offered one or two tickets. Winners must be present to claim them.  Hit shows always have the busiest lottery lines, as do plays with celebrity power. To better your chances, try Wednesday or weekend matinees, which usually have smaller turnouts.  Over all, the lightest day to try the lottery, according to Kaitlin Fine, the assistant company manager for “Hamilton,” is “whatever day is raining.”  “Some of the lottery start times are scattered so you can try multiple in a day,” said Claudia Stuart, a business manager for a children’s theater company who says she has won lotteries about a dozen times over the past 10 years. “If you’re dead set on seeing a show that day, have a priority list. If you lose one, rush another show, or move on down the list.”  Showing up early doesn’t better your chances. You can show up at 5:50 for a 6 p.m. drawing and win.  A good way to keep track of lotteries is at Broadway for Broke People, a no-frills website run by Ms. Stuart. Playbill.com also keeps lists of lotteries (and rush and standing-room seats) for Broadway and Off Broadway.  Going to a lottery in person can be a show itself. The “Hamilton” lottery features an impromptu mini-concert three times a week called The Ham4Ham Show. Often hosted by Lin-Manuel Miranda, the show’s creator and star, the event has featured live performances by Broadway stars like Kelli O’Hara, Steven Pasquale and Matthew Morrison.  At the lottery for the new Deaf West production of “Spring Awakening,” there are mini sign-language lessons in the half-hour before winners of the $35 seats are announced.  “We’ve taught them signs for lottery, win and lose,” said Alice Rix, who described her job as “lottery master.”  Attending in person also allows you to make friends to better your chances. If you go solo, befriend another person who is alone and make a pact to share your tickets if one of you wins. If nobody wins, you’ve made new friends.  While in-person lotteries are entertaining, not everyone has the time to wait around for the results. Enter TodayTix, a free mobile app for iOS and Android that, in addition to selling last-minute theater tickets, offers lotteries to select Broadway and Off Broadway shows.  Three to six shows are offered every day via lottery. The participating shows are announced at midnight, and audience hopefuls have about four hours before showtime to submit an entry via smartphone.  They can get an extra entry for sharing their submission on Facebook or Twitter. Winners are notified via email or push notification. Some tickets can be paid for through the app, and others at the box office, depending on the theater’s requirements.  Merritt Baer, the company’s chief executive and co-founder, said about 2,500 people apply to the lottery every day for any single performance. Recently the app’s lotteries included “Eclipsed” ($10), a Public Theater production starring Lupita Nyong’o; the Broadway revival of Harold Pinter’s “Old Times” ($19.65), starring Clive Owen; and Stephen Karam’s critically acclaimed play “The Humans” ($19.65) from the Roundabout Theater Company.  Mr. Baer said TodayTix makes Broadway lotteries “more democratic” than their in-person counterparts.  “How many people can get off work in Times Square, or live in New Jersey or downtown and can’t be there?” he said. “It’s a way of expanding access.”  Several Broadway shows have recently started their own online lotteries, including “Matilda,” which offers a limited number of $32 seats each day (MatildaLottery.com) and “Allegiance,” which features $39 seats (allegiancemusical.com/lottery/).  Keep in mind that digital lotteries, conducted via app, Facebook, Twitter and other social media networks, give producers a chance to gather user information, so you may see emails with other offers.  Like Powerball players who pin their hopes on a birth date, lottery hopefuls sometimes call on gimmicks and superstition to win. At a recent “Hamilton” lottery, a woman was spotted kissing her entry slip before she entered. (She didn’t win.) Another waited until the very last 10 seconds to drop hers in. (She didn’t win either.)  Sometimes a little bit of impromptu origami can make a difference.  “I folded the slip in half, unfolded it, and then crumpled it, uncrumpled it and left a little bit of the middle crumpled,” said Jessica Lawrence, 23, a ballet teacher, after winning tickets to “Hamilton.”  Some lottery administrators have caught on to these types of tricks and are specifying how to fold entry slips. Submissions in violation may be discarded.  Another strategy is timing. Ms. Stuart said her family used some delicate choreography to win four “Wicked” tickets.  “I noticed that people drawing the lottery tickets drew from the same depth, so I made sure we got there early and scattered ourselves through the line so our slips would be in different places in the bucket,” she said.  And if your name isn’t called? Applaud for the winners. It’s good karma.  A version of this article appears in print on October 30, 2015, on page C4 of the New York edition with the headline: Cheap Broadway Tickets Can Be a Matter of Luck. Order Reprints| Today's Paper|Subscribe
A $10 front-row ticket to “Hamilton”? It can happen, thanks to lottery drawings. Here’s a guide to trying for deeply discounted tickets to Broadway shows.