Suppose that each node of a search tree has *b* descendants;
this is sometimes called the * average branching
factor*.[Real search trees often have different
numbers of descendants from different nodes.]
Then the number of nodes at the bottom of a tree *d* plies deep
is *b ^{d}*. This number grows exponentially with depth and
can quickly become very large as the search becomes deeper;
this rapid growth is called the

The maximum depth, i.e. maximum number of steps between any two states,
is called the * diameter* of the problem space.

In chess, there may be 30 possible moves from each state.
A chess tree 10 plies
deep would require searching *30 ^{10}* or nearly