ARCADIA, Calif. — Mike Smith knows plenty about riding undefeated female horses. He was aboard superstar mare Zenyatta for most of her 19-race winning streak.

Now he’s on unbeaten Songbird, who takes an 11-race winning streak into the $2 million Breeders’ Cup Distaff, Friday’s headline race on the opening day of the two-day world championships at Santa Anita, which is hosting for a record ninth time.

She’s got stiff competition from fellow champions Beholder and Stellar Wind.

Songbird is the early 6-5 favorite, with Beholder and Stellar Wind as the co-second choices at 5-2 among the eight fillies and mares chasing the prize in the 1⅛-mile race.

Smith won the 2008 Distaff aboard Zenyatta, and he later guided her to a thrilling victory against males in the 2009 BC Classic at Santa Anita. Her winning streak was snapped in the 2010 Classic at Churchill Downs, where Zenyatta ended her career losing by a head to Blame.

The Hall of Fame jockey took the defeat hard, crying and barely able to speak afterward.

The pressure of Zenyatta’s run of victories kept him awake at night. This time, the 51-year-old rider isn’t carrying the mental burden of Songbird’s streak.

‘‘For some reason I'm more comfortable than I was the last time Zenyatta ran. You learn little things,’’ he said. ‘‘She has to do her job; I have to do mine. If given the opportunity to do that, I think we’re going to see something special.’’

With the exception of fellow 3-year-old Land Over Sea, Songbird is challenging older horses in the Distaff.

‘‘She’s always been above average about everything,’’ Smith said. ‘‘The way she thinks, she gets it. She’s smart. Mentally, she’s ready for it. You hope physically she is. She looks like it.’’

Zenyatta was known for her come-from-behind style, often spotting rivals huge leads before overtaking them down the stretch. Songbird runs at or near the lead. The only time she wasn’t first or second in the early going was in her first two races, when she rallied from fourth and sixth, respectively.

‘‘You really can’t plan for how to run the race, because the moment the gates open it could all change,’’ her Hall of Fame trainer Jerry Hollendorfer said. ‘‘We know she can go to the front or sit off the pace; we’re comfortable with her versatility. This really becomes a riders’ race so you need to have confidence in your jockey. Mike has ridden her in all of her starts and knows her very well.’’

Beholder won the 2013 Distaff at Santa Anita. She has never won outside of her Southern California base, losing both times she traveled to New York and Kentucky, and last year she failed to make her scheduled start in the BC Classic at Keeneland after spiking a fever.

‘‘Everything is right, right now, so my job is to see if there is anything wrong between here and there,’’ Hall of Fame trainer Richard Mandella said. ‘‘Hopefully, I am not going to find it or there is nothing to find.’’

Beholder, a 6-year-old, three-time Eclipse Award winner, will be making her 26th and final career start Friday.

‘‘On paper, this is the best Distaff I've ridden in,’’ her jockey Gary Stevens said. ‘‘Beholder is the best horse I have ever ridden.’’

Trained by John Sadler, Stellar Wind has won seven of 11 career starts. She beat Beholder in her previous two starts under Victor Espinoza.

‘‘She needs a good trip,’’ Sadler said. ‘‘I don’t know what that trip is, but just a nice, smooth one and she should do well.’’