A system and method for facilitating play of a poker game utilizing mathematical dealer qualification criteria that impact the manner in which the game proceeds. The player(s) and dealer ante, and starting hands are dealt to the player(s) and dealer. The player may fold and lose the ante, or place a bet. The dealer's starting hand must meet mathematical qualifying criteria, such as a particular sum of point values assigned to each card. If the criteria is not met, the dealer does not qualify, and the player(s) win the dealer's ante amount. If the dealer's starting hand qualifies, the dealer calls the players' bets, and deals a community hand. Using their respective starting hands and the community hand, each of the players and dealer arrives at a resulting hand. If a player's resulting hand beats the dealer's based on poker rank, that player wins.