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In contract bridge, various bidding systems have been devised to enable partners to describe their hands so that they may reach the optimum contract.Key to this process is that players evaluate and re-evaluate the trick-taking potential of their hands as the auction proceeds and additional information about partner's hand and the opponent's hands becomes available.
Their values depend on the suit (or notrump) and whether the contract is doubled or redoubled; they are not affected by vulnerability. Tricks won beyond that necessary to fulfill the contract are referred to as overtricks and their scoring points are accounted for separately because their values are dependent upon declarer's vulnerability.
In the game of bridge mathematical probabilities play a significant role. Different declarer play strategies lead to success depending on the distribution of opponent's cards. To decide which strategy has highest likelihood of success, the declarer needs to have at least an elementary knowledge of probabilities.
As a declarer, an efficient way of counting the trump cards is: instead of counting the number of trump rounds and cards trumped in, count the number of trumps in the opponents' hands. Once the dummy hand appears, calculate the number of trumps which the opponents have, then reduce this number mentally as they are played from the opponents' hands.
A common practice is to assign values to the four higher honors, called High Card Points (HCP) which are a rough estimate of the real value of those cards in a notrump contract: Ace = 4 HCP; King = 3 HCP; Queen = 2 HCP; Jack = 1 HCP
Zar Points (ZP) is a statistically derived method for evaluating contract bridge hands developed by Zar Petkov. The statistical research Petkov conducted in the areas of hand evaluation and bidding is useful to bridge players, regardless of their bidding or hand evaluation system.
In the card game contract bridge, the Losing-Trick Count (LTC) is a method of hand evaluation that is generally only considered suitable to be used in situations where a trump suit has been established and when shape and fit are more significant than high card points (HCP) in determining the optimum level of the contract.
In the card game bridge, the law or principle of vacant places is a simple method for estimating the probable location of any particular card in the two unseen hands. It can be used both to aid in a decision at the table and to derive the entire suit division probability table.