Gun #2 (PlayStation 2 2005)
Poker ends 6:10
While the world is map isn't large in comparison to other open world exploration games, it's still fairly chalk full of side quests and other collectables, that being the gold you can mine for extra cash.
The side missions offer a range of activities, such as hunting down bounties, hunting, (once you obtain a bow), ranch help, or doing various peacekeeping missions. That and poker.
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Taken from the Wiki:
Gun is a Western-themed action-adventure video game developed by Neversoft and published by Activision for the PlayStation 2, Xbox, GameCube, Microsoft Windows, and Xbox 360 (as a launch title) in 2005. The PlayStation Portable version was released a year later under the title Gun: Showdown, this version features new side-missions, a multiplayer mode, and other additions that were not available in the console versions.During its first month, the game sold 225,000 copies across the four console systems for which it was initially released. The game had sold over 1.4 million units in the United States as of October 2008. It was well received by game critics and won several awards, including GameSpy's Xbox 360 Action Game of the Year.
Gun is set in the American Old West, specifically in Arizona, Colorado, Kansas and New Mexico in the year 1880. This includes cities and badlands with populated environments that stretch from the mountains to the plains of early Dodge City, Kansas. The story, written by Randall Jahnson, features several veteran actors, including Ron Perlman, Lance Henriksen, Kris Kristofferson, Brad Dourif, Tom Skerritt and the lead, played by Thomas Jane.