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 is dominated by the strategy of truthfully bidding. The strategy of underbidding is dominated by bidding truthfully. Assume that bidder i bids formula_8. If formula_9 then the bidder would lose the item with a truthful bid as well as an underbid, so the strategies have equal payoffs for this case. If formula_10 then the bidder would win the item either way so the strategies have equal payoffs in this case. If formula_11 then only the strategy of truthfully bidding would win the auction. The payoff for the truthful strategy would be positive as they paid less than their value of