Peter chose The Mirage, because it was the first of the Definitive Dozen (the massive construction boom of the 90s).
Zoe chose Circus Circus to follow The Mirage, because it was another film location in Leaving Las Vegas.
Peter chose Excalibur to follow Circus Circus because it was Bill Bennett's next casino.
Zoe chose Bally's to follow Excalibur because it's next down in the Megabucks jackpots league table (ignoring Desert Inn (imploded), and Palace Station (not on list)).
Peter chose MGM Grand to follow Bally's because Bally's originally opened as MGM Grand.
Zoe chose Bellagio to follow MGM Grand because it's another MGM Resorts International property.
Peter chose Mandalay Bay to follow Bellagio because it was the next resort to open.
Zoe chose The Venetian to follow Mandalay Bay because it was the next resort to open.
Peter chose Palazzo to follow The Venetian because it's the sister property.