# 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.

## Solver

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.