In Eyes Wide Shut, Domino chances upon a wandering Bill, and lures him into her apartment for a good time. His wife interrupts him with a call, and he decides against it. In the second half of the movie, Bill arrives at her apartment with some sweet pastries, only to be disappointed in being told that Domino is HIV-positive, and that she "may not even be coming back."
Now, Eyes Wide Shut being long enough as it is, you can cut these two scenes out of the movie altogether, and it'll have no impact on the overall story. You can have Bill walk straight from visiting Marion over to the jazz club where his friend Nick is performing at, and also have Bill go from his clinic over to being stalked. You wouldn't miss anything if Domino's scenes are cut. Anti-paranoia is that eerie thought that nothing is connected to anything.
At the Somerton Manor, during the opening ritual, the lead woman bypasses all the other men and chooses Bill. The way she walks is like how Domino first greets Bill with her swaying hips, and the slow, lingering "kiss" is like how Domino slowly kisses Bill at her bedroom. This is how you know who the masked woman is.
It goes against the common view that the woman is Amanda. But to know Kubrick is to know his penchant for mis-directing an audience who has a hard time deciphering ambiguity, exhaustively considering the possibilities. There are other analysis which highlight how, for example, Alex DeLarge was never brainwashed by the Ludovico technique (which wouldn't work in reality), instead faking his state of docility in exchange for freedom.
As Bill wanders through the halls of Somerton, the masked Ziegler brings a woman over through the doorway. The woman's areolae and pubic hair changes between shots. Bill and the general audience are going to confuse the identities, but this is Amanda. As Ziegler brought Bill earlier over to his washroom for her, he brings Amanda over to Bill.
With the lead woman's sacrifice, Domino is absent. There is no reason given why Domino "may not even be coming back." However, a subtle clue reveals the connection with the Somerton manor: as Bill goes up to Domino's door, the shot changes to a close-up. By the stairs, blue light, which is absent just before. The same blue which silhouetted the lead woman on the balcony.
This changes the meaning of the film. In Kubrick's filmography, there is always someone who is killed, without exception. Here, there is a murder dressed up like an accident, but there is more than one murder.
When Bill is called over to the Nathansons' apartment, Lou rests dead on the bed. Bill and the audience are misled into believing that it was a natural death, "[dying] peacefully in his sleep."
"It's so unreal. Daddy had such a good day. His mind was clear, and he remembered so many things. Then he had a little dinner.. and he said he felt like taking a nap. I went into the kitchen and talked to Rosa for half an hour at most.. and when I went back in to see how he was, I just thought he was asleep. Then I realised he wasn't breathing."
Through Lou's poisoning by the higher-ups, Bill is lured out for an unforgettable night. It is reminiscent of how Alex consumes drugged spaghetti and wine in the later scenes of Clockwork Orange, where he eventually collapses onto the plate.
The night progresses in such a manner as to guide Bill over to the mansion itself; a place he would never have discovered otherwise. It's suggested that an invisible hand has coralled Bill: as Bill is stalked, the taxi driver so happens to be off-duty, but you'll see as the stalker vanishes around the corner of Wren St., a taxi passes by at the same time.
As well, Domino happens to be by the intersection where Bill walks – when you link how the masked woman walks from the ritual circle to this innoceous moment, Domino has been summoned over to Bill.
She is well-dressed, intelligent, and incredibly sweet to him. An irresistable offer as a street hooker. The only thing is that you don't know Domino's real identity, let alone her name. In the original script:
Bill: "By the way, what's your name?"
Domino: "Domino."
Bill: "Domino. That's an unusual name."
Domino: "Well, it's my, uh.. professional name."
What about Amanda's death? The newspaper "Lucky To Be Alive" which leads Bill over to Amanda is a plant. As a conspiracy theorist today would tell you, the media is controlled by the higher-ups to keep the public misled by false narratives, doing public hitpieces on figures they want to damn, while remaining silent on news events which go against their agenda. Why should this be any different back then? In other words, Amanda and the newspaper article are red herrings, used to fool Bill and the audience into mistaking the masked woman's identity for her.
In Ziegler's last meeting with Bill, he tries to take Bill in with the idea that the whole scenario played out for him at the house is a charade – an idea which is not entirely untrue, if you substitute "night" for "house."
However, Bill – by happy accident – mixes up Ziegler's party with the Somerton ball:
Bill: "I saw her body at the morgue.. was she the woman at the party?"
Ziegler: "Yes, she was."
Bill: "The woman lying dead in the morgue.. was the woman at the party?"
Ziegler: "Yes."
Bill: "Maybe I'm missing something here. You called it a fake, a charade. What kind of fucking charade ends with somebody turning up dead?"
Ziegler gets visibly nervous as Bill touches upon the truth: Amanda had been murdered, to distract from Domino. He covers the latter part up by lying about Amanda's death. When you're left asking the wrong questions, nobody has to worry about your answers.
Ziegler: "Listen Bill, nobody killed anybody. Someone died. It happens all the time. But life goes on. It always does.. until it doesn't. But you know that, don't you?"
As a result, Bill's eyes are kept wide shut over Domino's disappearance, along with the audience's.