While a human might spend twenty minutes agonized over a single move, an AI can solve a complicated game of Klondike Turn One in milliseconds. Modern solitaire solvers don't just "play" the game; they map out every possible future state to find the most efficient path to victory. My guide explores the primary algorithms that power the world's most advanced solitaire solvers.
1. Recursive Backtracking (DFS)
The most fundamental algorithm for Solitaire is Depth-First Search (DFS) with recursive backtracking. Depth-first search is inherently sequential. The computer treats the game like a maze. It takes a move, follows that path to the end, and if it hits a deadlock, it "backtracks" to the last successful move and tries a different branch.
Efficiency and Pruning
Because there are so many possible moves, a raw DFS would take years to run. Computers use "pruning" to instantly discard paths that are mathematically doomed.
| Technique | Function | Result |
|---|---|---|
| State Hashing | Remembers previously seen board states | Avoids infinite loops |
| Transposition Tables | Stores the result of board positions | Instant lookup for common states |
| Heuristic Scoring | Assigns values to specific moves | Prioritizes high-value branches |
2. Monte Carlo Tree Search (MCTS)
For variants like "Turn Three" where information is hidden, AI uses Monte Carlo simulations. This algorithm doesn't try to look at every move. Instead, it plays thousands of random games from the current position to see which move leads to the most wins.
The Power of Statistics
If a computer plays 10,000 random simulations from "Move A" and wins 40% of the time, but only wins 10% of the time from "Move B," it will choose Move A. This is the same logic used by high-end Chess and Go AIs.
3. Heuristic Priorities: The Human-Like AI
To make solvers even faster, developers program in "heuristics" – rules of thumb that prioritize specific actions. These often mirror expert human strategies.
- Rule 1: Always prioritize moves that reveal hidden tableau cards.
- Rule 2: Prefer moving cards to foundations only when both cards of the next lower rank of the opposite color are already in the foundations.
- Rule 3: Prioritize clearing columns that have the most hidden cards.
Why is Perfect Information Solvable?
When we give an AI "Perfect Information" (letting it see the hidden cards), it becomes a P-Space Complete mathematical problem. With all cards visible, the computer can build a directed acyclic graph (DAG) of the entire game. This allows it to find not just any win, but the shortest possible win.
The Modern Solitaire Assistant
The hint engine in many modern solitaire games is actually a mini-version of these solvers. When you click "Hint," the computer runs a quick DFS to find the nearest winning state and suggests the first move of that sequence.
Algorithm Facts
- Speed: A modern C++ solver can analyze over 1 million board states per second on a standard laptop.
- State of the Art: The "ShootMe" solitaire solver is currently the gold standard for verifying winnability in random decks.
- AI vs. Humans: While humans enjoy the process, AI has proven that Turn One Solitaire is a solved game – we just haven't memorized the solution yet!