## node isomorphism and equivalence

Consider the following two scenarios. Scenario A: spades are played during trick 1 and hearts are played during trick 2. Scenario B: the same cards are played as in scenario A except that the hearts are played during trick 1 and the spades are played during trick 2. The hand configuration is identical after the partial sequences described in scenarios A and B. If, in addition, the same number of tricks are taken by N/S during both of these scenarios then, even though the actions of the two scenarios differ, the ultimate set of obtainable results are identical. Node isomorphism refers to the situation in which two nodes correspond to identical hand configurations with equal number of tricks taken by N/S.

Consider the situation after 3 rounds of spades have been played with everybody following suit each time. Only one spade remains, say in South's hand. Which spade card remains in South's hand is irrelevant to the future trick-taking ability of either side. This is a simple example of node equivalence, which refers to the situation in which two nodes correspond to equivalent hand configurations with equal number of tricks taken by N/S.

Node A is said to be superior to node B if nodes A and B correspond to equivalent hand configurations but N/S have taken a greater number of tricks at node A then at node B.

Dan Hirschberg
Computer Science Department
University of California, Irvine, CA 92697-3425
dan at ics.uci.edu