The present invention relates to computer-based multiplayer games that follow the scoring rules of poker in which players select cards from a second deck of playing cards that is composed of cards randomly selected by the software from a first deck of playing cards for each new hand, where the second deck has fewer cards than the first deck. The introduction of a smaller second deck whose composition and size can vary substantially from hand-to-hand, adds a fascinating and challenging puzzle component to the strategy and chance elements of prior card selection games. The use of a prior art deck that remains unchanged allows each player to tend to rely on a predetermined set of fixed card selection strategies. Whereas, the ever-changing, smaller second deck compels each player to formulate his/her card selection strategy anew for each hand, keeping play fresh and exciting.