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 payment in the sealed second-price auction. Vickrey considered the case of two buyers and assumed that each buyer's value was an independent draw from a uniform distribution with support formula_15. With buyers bidding according to their dominant strategies, a buyer with valuation formula_12 wins if his opponent's value formula_17. Suppose that formula_12 is the high value. Then the winning payment is uniformly distributed on the interval formula_19 and so the expected payment of the winner is We now argue that in the sealed first price auction the equilibrium bid of a buyer with valuation formula_12 is That is, the payment