MIT OpenCourseWare http://ocw.mit.edu CMS.608 / CMS.864 Game Design Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.The “All-Trump” Bridge Variant Charles Tam March 17, 2008 Bridge is a trick-taking card game. Play occurs between two pairs of players, with the members of each pair seated across from one another. The goal of the game is to score as many points as possible, or to be the first to reach a certain number of points, depending on which scoring variant of bridge one is playing. Before any card play occurs, there is an auction for a contract. During this auction, players guess how many tricks they can take during play. One team, the offense, will successfully bid the contract and will have to make a prescribed number of tricks out of thirteen in order to score points. The other team, the defense, scores points for preventing the offense from completing their contract. In addition to defining the critical number of tricks for the offense to take, the contract also indicates what the trump suit is; or, in the case of “no trump,” that there is no trump suit. Contracts consist of a level, which is a number between 1 and 7 inclusive, and a suit. Suits are arranged in increasing order as “Clubs, Diamonds, Hearts, Spades, No Trump.” It is important to note that each player makes his bids without any explicit knowledge of his partner’s hand. Instead, during the course of bidding, partners may agree to attach meaning to certain bids to convey information about their hand. For example, a player may open with “1♠” to indicate that he has a certain number of the honors (Ace, King, Queen, Jack), and at least five of the Spades. The amount of expression viable using these systems is constrained by always bidding a higher contract, unless one chooses to pass. Using the complex bidding conventions that have come from this usage of the auction, a player may ascertain with a surprising amount of precision the holdings of his partner. Players may indicate important features of their hand, such as strength, a good holding of honors; length, a large number of cards in one suit; or shortness, a dearth of cards in a suit that may be exploited for trumping. The auction terminates when three consecutive players pass. Once the contract has been determined, play starts. One person in the offensive pair is the declarer, the person who first named the contract suit. The other person is the dummy, whose hand is played face-up by the declarer. The first trick is led by the person to the left of the declarer. Play proceeds clockwise around the table, where each trick is led by the winner of the previous trick until players are out of cards. The “All Trump” bridge variant introduces a sixth possible contract suit, “All Trump,” so that the ranking of the contract suits in increasing order is Clubs, Diamonds, Hearts, Spades, No Trump, All Trump. The initial rule was that if one is unable to play the led suit, one may play any other suit and it is automatically trump. After the first trump suit is played, one must follow the trump suit if unable to follow the led suit; if one is also unable to follow the trump suit, then one may play a second trump suit, which is regarded as beating the first trump suit. For example, suppose that South leads ♠9. West, who is void in Spades (that is, he has no Spades), plays ♦5 as a trump. North now must follow South’s suit if his is able; if his is unable, then he should follow West’s suit; if he is also unable to do that, only then may he play a new suit as trump. Thus we might have N ♦3, E ♠K, in which case West wins with ♦5; or N ♣T, E ♦8, where North wins; or N ♠A, E ♦Q, in which East wins. 1This first version was playtested by people who had experience in trick-taking games, but not with contract bridge proper. Players ignored the auction phase of the game, under the assumption that contract was always 1 All-Trump (7 tricks required to fulfill contract), in order to ensure the testing of the variant mechanics. An illustrative example of play is given in the Appendix. Testers observed that the person to lead the last trick would lose it. In that particular trick, in which each player as one card, the pair that has off-suit cards wins. In particular, this means that the lead has one chance to mismatch his own suit (that is, his partner’s card), whereas the leader’s opposition has two chances to do so. This principle actually extends frequently through the couple hands preceding the last, and indeed through the whole game it is felt that the team of the person leading has a disadvantage. This was observed as tricks frequently went back and forth. In other words, this formulation of the All Trump rules actually punishes players for winning tricks! A simple thought experiment suffices to show that it’s also impossible for one team to take all 13 tricks. Testers also tended to lead from their shortest suits whenever possible, in order to create voids quickly. Testers that went beyond this simplistic strategy and counted cards to predict other players’ holdings were not rewarded for their higher understanding of the game, since the player that won a trick brought a disadvantage to his team in the next trick. As there was little that could be done to influence the outcome of a game beyond happening to have an extra honor, testers reached consensus that the game favored luck over skill too heavily. The second iteration was played with the additional rule that when trumping, the card being trumped may not be any more than n = 5 values above the trumping card. Therefore in ♠4 – ♥8 – ♠Q – ♠5, the heart wins because the Queen is only four values above the 8. However, in ♠4 – ♥6 – ♠Q – ♠5, the Queen wins. Multi-suit trumping still applies, as in ♦6 – ♥J – ♠9 – ♣2, in which the Spade wins because it is close enough to the ♥J, but the Club does not because it is trying to trump the ♠9. This alteration only slightly fixed the aforementioned problems of excess trumping. In addition, testers felt that too much mental figuring was required, since they would have to do arithmetic and track 7’s, 8’s, and 9’s as potential trumps in addition to the usual honors T, J, Q, K, A. Testing low