A method and apparatus for casino slot games in which at least two and preferably three games are linked together by displaying the two or three games on one video display device. The games are linked through the initial cards displayed for each game, and their bets and their outcomes. A computer calculates the probabilities of all bets and outcomes during the betting rounds in real time. As a result of the so chained games the player makes decisions in multiple betting rounds in insufficient information about the game outcomes. At any time during the game play the player can evaluate the game outcomes as presented to him by the computer and either play the next successive game or simply finish the game with no penalty.