Baker's Game, Nuances in Recent Programming

Every newly created position is converted to a canonical form. To create the canonical form, the Free Cells are sorted ascending according to the representation of the cards that are contained within the Free Cells. The board columns (also called stack columns) are sorted according to the representation of the base card of each column. The use of canonical forms makes it much easier to reduce the size of the search space by eliminating equivalent positions. That is, many equivalent positions are reduced to the same canonical form. However, the use of canonical forms make it difficult to document an exact sequence of moves that will solve a particular game. Indeed, my program does not even try to document the solution it found. The program just counts wins and losses.
Every newly created position is simplified immediately by moving all possible cards to the home cells (also called payoff cells). When the cards are moved to the home cells in this manner, the collection of such moves is treated as all one move. The version of FreeCell that is distributed with Windows does the same thing. However, there are two differences. One difference is that the process of playing off exposed cards to the home cells is easier with Baker's Game than it is with FreeCell. The other difference is that my program does it right, and the FreeCell that comes with Windows fails to make some obvious payoff moves that it really ought to make.
An STL set container is maintained in a particular order, and the position that is processed by my program first for each move is the first position in the container. My program provides a compare routine to the STL so that the positions that are closest to being won will in general be stored closest to the beginning of the container (hopefully!). The compare routine gives preference to positions that have more cards in the home cells and to positions that have fewer cards in the Free Cells.
The program is surprisingly fast. It can solve about eight games per second, rather than taking hours per game as sometimes happened back in 1981.
None of my Baker's Game programs have ever had any graphics capability at all, nor do they have any capability of inputting a particular game to solve. Rather, the programs just generate a bunch of random games and solve them.