The present invention provides gambling games that are fast to play, easy to learn, and have a high likelihood of a winning Player for each play. Additionally, the games may be operated so as to have a large and growing bonus for each play. Additionally, certain embodiments of the gambling games offer a sequence of decision points to accept an accrued payout or risk the payout in further play to obtain an even larger payout, in some embodiments, exceeding a billion dollars. After a first successful wager in such a game, a Player is offered the opportunity to accept accrued winnings, i.e., accept 'The Deal,' or decline to accept the accrued winnings i.e. decide 'No Deal,' and risk the accrued winnings in an additional play of the game. The gaming method comprises: a) defining collections of objects to be used in playing a game according to the method; b) assigning a first collection of the objects to a dealer party, and a second collection of the objects to a first wagering party, the second collection of the objects comprising at least the same objects as the first collection of objects; c) accepting a first wager of funds of a defined value from the first wagering party, the wager contingent upon the outcome of random selections of objects from the first and second collections of objects; d) making a random selection of a subset of objects from the first collection of objects and a random selection of a subset of objects from the second collection of objects; e) comparing the subset of objects from the first collection of objects with the subset of objects from the second collection of objects; f) if the subset of objects from the first collection of objects does not correspond to one of a predefined set of matching relationships with the subset of objects from the second collection of objects, transferring the defined value of the first wager of funds to the dealer party; g) if the subset of objects from the first collection of objects has a matching relationship to the subset of objects from the second collection of objects that corresponds to one of the predefined set of matching relationships, transferring a payout of X times the defined value of the funds of the first wager from the dealer party to the first wagering party, wherein X is a function of the probability of occurrence of the corresponding one of the predefined set of matching relationships. WO 2016/205708 PCT/US2016/038175 PROVIDE PLAYER'S DEFINE COLLECTION OF COLLECTION I PROVIDEDEALER'S OBJECTS OF OBJECTS COLLECTION OF PLAYER OBJECTS WAGER | 406 RANDOM SELECTION 408 OF SUBSET OF PLAYER'S COLLECTION -------- 410 ------- ----- END RANDOM RANDOM GAME- ANY 412 SELECTION SELECTION 414- HOUSE MATCH? OF SUBSET |OF SUBSET KEEPS OF PLAYER'S |OF DEALER'S COLLECTION COLLECTION MATCH 4440----- NO EXCEEDS QUALITY 432 END THRESHOLD? ANY NO GAME HOUSEPAYS MATCH? HOUSE PLAYERFOR KEEPS FIRST TIER WIN Y 438 4 YES WAGER HOUSE OFFERS TO END YES MAXIMUM CONTINUE PLAY GAME JACKPOT? NO PLAYER HOUSE OFFERS TO CONTINUES PLAY? CONTINUE PLAY PLAYER WAGERS CONTINUES PLAY? ACCRUED WINNINGS 422 I PLAYER ACCRUED YES WINNINGS 446 PLAYER WAGERS ACCRUED WINNINGS
Games of chance