According to an MS press release from a few weeks back, Rainbow Six 3: BA will officially drop to $19.99 on November 3rd.
Edit....
Here is the press release....and the price changes start on Oct 31, not November 3rd.
Touchdown! Microsoft Announces Winning Holiday Offer
Holiday Shoppers to Score Xbox Console, Two Premium Games and Xbox Live Trial for $149.99!
Microsoft today unveiled a special holiday offer that will provide gift-givers, sports fans and gamers of all ages an unparalleled experience. Beginning October 31 at retail stores nationwide, consumers can purchase the Xbox® video game console, two full premium sports games and a two-month trial subscription to Xbox™ Live™ for just $149.99.
The specially priced holiday package offers an amazing value to consumers who are looking to spread the holiday love by giving family and friends a full Xbox game experience out of the box with full versions of "NCAA® Football 2005" from the powerhouse EA SPORTS™ brand and "Top Spin" featuring tennis star Anna Kournikova by Microsoft Game Studios, both playable on Xbox Live, and the two-month trial subscription to the highly-acclaimed Xbox Live service. The fully loaded console comes equipped with a built-in Ethernet port, enabling online gameplay.
"This is the most exciting holiday season yet for video gamers and Xbox fans," says Mitch Koch, vice president, worldwide retail sales and marketing for Microsoft's home & entertainment division. "Not only are we offering a tremendous value to gamers with the holiday offer, but Xbox has the most expansive and entertaining library of games this season on any platform, with titles like 'Halo 2,' 'Fable,' and 'MechAssault 2' from MGS, 'Need for Speed™ Underground 2' from EA, and 'Dead or Alive Ultimate' from Tecmo."
Xbox is making a 100-yard dash to the top of holiday must-have lists, with the fastest growing market share of any video game console and its strongest games line-up ever. More than 450 games will be available on Xbox this holiday season, including the critically acclaimed "Fable" and the most-anticipated game of the year on any platform, "Halo 2," both by Microsoft Game Studios. Parents will also be thrilled about the incredible value of the new games for the Xbox Platinum Hits collection, each available for only $19.99 at retail, and the fact that Xbox is the only console with built-in parental controls. Several new titles in the collection include "Teenage Mutant Ninja Turtles" from Konami, "The Simpsons: Hit and Run" from Vivendi Universal Games, "Project Gotham Racing 2" from MGS, and "Tom Clancy's Rainbow Six 3 Black Arrow" from Ubisoft.