
## 2.5 Experimental Results

Partition search was tested by analyzing 1000 randomly generated bridge deals and comparing the number of nodes expanded using partition search and conventional methods.

In addition to our general interest in bridge, there are two reasons why it can be expected that partition search will be useful for this game. First, partition search requires that the functions R 0 and C 0 support a partition-like analysis; it must be the case that an analysis of one situation will apply equally well to a variety of similar ones.  Second, it must be possible to build approximating functions R and C that are reasonably accurate representatives of Ro and Co.

Bridge satisfies both of these properties. Expert discussion of a particular deal often will refer to small cards as x's, indicating that it is indeed the case that the exact ranks of these cards are irrelevant. Second, it is possible to "back up" x's from one position to its predecessors. If, for example, one player plays a club with no chance of having it impact the rest of the game, and by doing so reaches a position in which subsequent analysis shows him to have two small clubs, then he clearly must have had three small clubs originally.

Finally, the fact that cards are simply being replaced by x's means that it is possible to construct data structures for which the time per node expanded is virtually unchanged from that using conventional methods.

Perhaps an example will make this clearer. Consider the following partial bridge deal in which East is to lead and there are no trumps:

![0_image_0.png](0_image_0.png)

An analysis of this situation shows that in the main line, the only cards that win tricks by virtue of their ranks are the spade Ace, King and Queen. This sanctions the replacement of the above figure by the following more general one: