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
Last modified: July 1, 1996