Deriving Optimum Suit Plays
Within the simplified setting, declarer's optimal play of a suit combination may be derived using well-established game theory, namely the theory of two-person zero-sum games. Crowhurst generally covers two alternative objective functions for every suit combination in the catalog. One is the (maximum) expected number of tricks won, or tricks expectation. Another is the (maximum) probability of winning a salient specific number of tricks such as three for a combination with four cards in each hand.
This means that an objective function to be maximised is specified. For suit play purposes, this objective function (or goal) is usually taken to be the likelihood of making a specified minimum number of tricks.
Given this objective, all lines of play are checked against all possible defenses for each distribution of opponent's cards, and the objective function is determined for each of these cases. Each line of play combined with each distribution of opponent's cards can then be assigned a minimum value of the objective function resulting from the best defense for that layout. The optimum line of play is selected as the line that maximises the minimum value of the objective function averaged over all possible layouts. As a result, the optimum solution to the suit combination takes into account all lines of defense (including all forms of falsecarding), and guards against the best lines of defense, but is not necessarily optimal in terms of exploiting errors made by the defense.
Read more about this topic: Suit Combinations
Famous quotes containing the words deriving, optimum, suit and/or plays:
“Beware thoughts that come in the night. They aren’t turned properly; they come in askew, free of sense and restriction, deriving from the most remote of sources.”
—William Least Heat Moon [William Trogdon] (b. 1939)
“Everywhere—all over Africa and South America ... you see these suburbs springing up. They represent the optimum of what people want. There’s a certain sort of logic leading towards these immaculate suburbs. And they’re terrifying, because they are the death of the soul.... This is the prison this planet is being turned into.”
—J.G. (James Graham)
“How are we to know that a Dracula is a key-pounding pianist who lifts his hands up to his face, or that a bass fiddle is the doghouse, or that shmaltz musicians are four-button suit guys and long underwear boys?”
—In New York City, U.S. public relief program (1935-1943)
“In the game of “Whist for two,” usually called “Correspondence,” the lady plays what card she likes: the gentleman simply follows suit. If she leads with “Queen of Diamonds,” however, he may, if he likes, offer the “Ace of Hearts”: and, if she plays “Queen of Hearts,” and he happens to have no Heart left, he usually plays “Knave of Clubs.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)