Experimental Analysis of
Fortress Solitaire

Jan Wolter
Jan 24, 2014

[General Introduction]

The Game

Fortress Solitaire is a quite old one deck solitaire where all the cards start out dealt faceup, and you must re-arrange them to get them to the foundations. You start out with all cards dealt to ten tableau columns. Two columns will have six cards and the other eight columns will have five. You can move only the top cards of tableau stack, moving them either to the foundation, or to another tableau stack, if they are the same suit as the card that is already there and either one rank higher or one rank lower. You can read the rules or play the game on politaire.com or many other places.

Michael Keller has written a useful discussion of Fortress strategy.


The depth-first-search solver that I built for Indefatigable was readily adapted to play Fortress, mostly by throwing out all the redeal logic. Otherwise the games are very similar.

This is a fairly easy game for computers to solve, as the search tree doesn't tend to branch much until you get to the point where nearly all paths lead to a solution. The depth-first search algorithm usually completed with less than twenty backtracks and hardly ever require more than a thousand or so.

Random Deals

I ran the solver on the first million Politaire Fortress games, seeds zero through 999999. It was able to solve 202,396 games, for a win rate of 20.2%. An average of 12.12 cards were removed.

The histogram below shows the full distribution of the numbers of cards which could be removed.

Numbers of Removable Cards in One Million Random Fortress Games
Note that while about 20% of games were winnable, there were also 19% of games where not a single card could be moved to the foundation, and another 20% where only one card could be. It is quite rare to be able to remove any significant number of cards and still not be able to win the game.