How deterministic is execution plan creation in SQL Server?

Question

Given the following constants:

• The same database with the same structure (tables, indexes, etc)
• The same data
• The same SQL Server and hardware configuration
• The same statistics
• The same SET options in the client
• The same SQL Server versions
• The same trace flags

Given these constants, will SQL Server always produce the same plan for a given query?

If not, are there other considerations? Is there also an element of nondeterminism to consider as well?