## some amenities for alpha-beta

The *order* in which the possibilities at a node
are investigated can have a dramatic effect
on the total time complexity of the search.
If a good solution is found relatively early on,
then a relatively larger number of not-as-good subtrees
may be pruned.
In the context of the bridge hand evaluation problem,
the set of possibilities at a node is just the set of
cards that may be played at that turn.
*Suit-ordering* specifies the order in which
the 4 suits are considered as a source for the card to be next played.
*Dynamic suit-ordering* redefines the order of the suits
at each turn, thereby taking advantage of the knowledge
of the current suit distribution.
*Rank-ordering* specifies the order of the cards
within a suit.
*Dynamic rank-ordering* takes into account which
cards have already been played during this trick
and/or which cards might yet be played during the subsequent
plays of this trick.

If two possibilities, *p1* and *p2*,
lead to the exact same set of leaf values
then, after determining the results of choosing *p1*,
there is no need to expand the subtree of possibility *p2*.
In the bridge problem, *rank equivalence*
refers to the fact that playing either one of two cards
will have exactly the same effect.
For example, if North has the 9 and 8 of Clubs, then
playing the 9 will have the same effect as playing the 8.
*Dynamic rank equivalence* refers to the fact that
some cards might initially not be equivalent yet
might subsequently become equivalent.
For example, if initially North has the 9 and 7 of Clubs and East has
the 8 of Clubs then initially the 9 and 7 of Clubs are not equivalent.
However, if East plays the 8 of Clubs on the first trick and
North retains the 9 and 7 of Clubs then the 9 and 7 of Clubs
will be equivalent during the second trick.

Dan Hirschberg

Computer Science Department

University of California, Irvine, CA 92697-3425

`dan at ics.uci.edu`

Last modified: July 1, 1996