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 Combination
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)
“The people needed to be rehoused, but I feel disgusted and depressed when I see how they have done it. It did not suit the planners to think how they might deal with the community, or the individuals that made up the community. All they could think was, “Sweep it away!” The bureaucrats put their heads together, and if anyone had told them, “A community is people,” they would not have known what they were on about.”
—May Hobbs (b. 1938)
“The hare grows old as she plays in the sun
And gazes around her with eyes of brightness;
Before the swift things that she dreamed of were done
She limps along in an aged whiteness....”
—William Butler Yeats (1865–1939)