If the lead of a play or musical is sick and an understudy performs instead, can you ask for your money back? I'm especially interested in knowing about cases where the lead performer is a big star.
It all depends on how that star is billed in the show, so check your Playbill or the theater's marquee for clues. For example, both Matthew Broderick and Nathan Lane are listed above the title in the current revival of The Odd Couple. If one of them should miss a performance you could ask the box office to either reschedule your tickets (good luck, since the show's run is completely sold out) or give you a refund. After all, it is those two above-title actors who have been featured in all of the show's ads and promotional materials. But pity the poor Brad Garrett fan. If the former Everybody Loves Raymond star doesn't make it to the Brooks Atkinson Theater for his supporting part in the same play you might be out of luck. Why? Because the Emmy-winning actor is listed below title. That's not to say you couldn't plead your case to the box office manager - presenting your Official Brad Garrett Fan Club I.D. card might scare any box office manager into submission - but he or she has less of an obligation to accommodate your request.
At a restaurant, you usually can't get your money back for an undercooked steak if you wait until dessert to tell your waiter. The same general rule applies to Broadway. If you arrive at the theater and discover that your favorite star won't be performing, talk to someone in the box office before the curtain goes up as a refund can usually be honored if there is a chance that your ticket can be resold. You don't have to wait until you sit down to listen for any "at this performance..." announcements; check the status of the person you came to see by looking for the understudy board in the lobby.
Understudies are not necessarily a bad thing. In fact, you might see a future star. In the early nineties, Laura Bell Bundy was understudied by Natalie Portman and Britney Spears in the Off Broadway Show Ruthless! and while we're sure Bundy has her own following in Broadway circles, she never went on to act in the Star Wars prequels or marry Kevin Federline. In the most famous case, Shirley MacLaine went on as an understudy in the 1954 show The Pajama Game when leading lady Carol Haney broke her leg. MacLaine's performance attracted the attention of a Hollywood producer and she went on to become a famous psychic.