Simplified Setting
Optimal strategy in the play of one deal at the bridge table varies along with variation in declarer's objective; the opponents' information, skill, and objective; the contract and vulnerability; and the lie of the cards in four hands, which includes four suit combinations and their arrangement. In bridge exposition it is routine to suppose two partnerships with opposite objectives that incorporate the conditions of contest (scoring variant and tournament variant) and the contract and vulnerability. In terms of game theory, then, the play of any deal is a zero-sum game.
At least since Crowhurst (1964), the analysis of suit combinations routinely makes further simplifications along the same lines. Most fundamental, the play of any suit combination is a zero-sum game. In effect, the two sides agree on the relation of the suit to the entire hand so that their opposite entire objectives reduce to opposite objectives in the suit. (The double-dummy nature of the defense, below, makes this an important unexplored objective.*) The bottom line is that their opposite objectives can be expressed in terms of the number of tricks won and lost in the featured suit.
It is common to go two steps further with Crowhurst. First, a suit combination is a two-person zero-sum game. That means the two defenders play as one; they are of one mind. They know each other's cards and thereby, knowing the dummy, they know declarer's hand too. (That particular is properly called double-dummy defense.) One plan governs both their plays. If they choose to randomize their plays (see "Mixed strategy" below), they are able to randomize together.
Second, play of a suit combination amounts to a sequence of tricks with the lead always from dummy or from the closed hand at declarer's option. In effect, the defenders always switch to a side suit when they win a trick, and declarer stops those side suits at least before discarding from the featured suit. Declarer is able to cross between hands using side suits; i.e. communication or entry management is no problem.
Read more about this topic: Suit Combinations
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