Gaming table systems include electronic gaming tables, gaming terminals, and a system server. A system or table can be configured to administer a live wager-based table game involving an initial shared hand that is shared by multiple live players. Each player can make different live game decisions regarding discarding physical playing items from the initial shared hand, and game outcomes include final hands that vary by player depending upon the different decisions. The live table game can be draw poker, which can involve dealing five physical cards face up for the initial shared hand and five additional cards face down for a first set of replacement cards before any live game player decisions. A second set of replacement cards can provide a second play from the same initial shared hand. Methods of providing the draw poker game can include preventing further user inputs prior to revealing the face down cards.