Five-card majors for offensive purposes. However, if the trump cards break 4-1 or 1-4, then drawing trump will result in no trumps left for offensive purposes. The value of five-card majors can be understood then on two levels: But five-card majors have several drawbacks: Both partners must agree to follow the five-card major bidding treatment on their opening bid. Opener must have at least five cards in hearts or spades to start the bidding with that suit. Responder is expected to show support with three-card support, indicating an eight-card fit. With only four cards in a major suit, the opening bidder is
Vickrey auction make $2 instead of $0. Because the seller's revenue can go up when bids are either increased or decreased, the seller's revenues are non-monotonic with respect to bids. The dominant strategy in a Vickrey auction with a single, indivisible item is for each bidder to bid their true value of the item. Let formula_1 be bidder i's value for the item. Let formula_2 be bidder i's bid for the item. The payoff for bidder i is formula_3 The strategy of overbidding is dominated by bidding truthfully. Assume that bidder i bids formula_4. If formula_5 then the bidder would win the