An improvement to two groups of wagering games with at least one player hand and a dealer hand. In one group, the gaming pieces in a hand are divided into two or more sub-hands. In the other group the games include a Reverse Bet and/or a Push Bet. Games may be in both groups. In the improved versions of these games, at least one type of wager has a minimum hand value, known as a qualifier. When a pre-specified hand has that hand value or higher, one method of settling wagers is used. Otherwise, a different method is used for settling at least one type of wager. Introducing this qualifier allows a casino to adjust the advantage for the dealer, making several desirable options practical for these games.