Study
Solitaire odds: what our solver found
Before a deal reaches you, our solver has won it. Making those lists showed how often each solitaire can be won.
Card games
Deals our solver won
Deals tried in a row from our shuffle (deal 1, 2, 3 …) until the solver had won 1000.
| Game | Tried | Won | Share won | Search |
|---|---|---|---|---|
| Klondike, draw 1 | 1,402 | 1,000 | at least 71.3 % | a guided search (most promising position first) of up to 100,000 positions |
| Klondike, draw 3 | 1,357 | 1,000 | at least 73.7 % | a guided search (most promising position first) of up to 100,000 positions |
| Spider, 1 suit | 1,008 | 1,000 | at least 99.2 % | a beam search of up to 3,000 positions |
| Spider, 2 suits | 1,024 | 1,000 | at least 97.7 % | a beam search of up to 5,000 positions |
| Spider, 4 suits | 1,319 | 1,000 | at least 75.8 % | a beam search of up to 10,000 positions |
| FreeCell | 1,004 | 1,000 | at least 99.6 % | a guided search (most promising position first) of up to 50,000 positions |
| Yukon | 1,610 | 1,000 | at least 62.1 % | a guided search (most promising position first) of up to 60,000 positions |
| Golf | 2,290 | 1,000 | 43.7 % | a complete depth-first search |
| TriPeaks | 1,038 | 1,000 | at least 96.3 % | a depth-first search of up to 3 million positions |
| Pyramid | 1,536 | 1,000 | at least 65.1 % | a depth-first search of up to 3 million positions |
How we measured
Every deal here comes from a number: the same number always shuffles the same cards on every device. To build a game's deal list we took deal 1, 2, 3 and so on, and ran our solver on each. A deal goes on the list only when the solver wins it and its winning line replays move by move through the same rules you play with.
The solvers differ by game. Golf is small enough to search completely, so its share is exact for our rules. The others stop at a limit of positions; a deal they didn't finish might still be winnable, so their share is a lower bound.
The numbers are checked by a test against the deal lists each time the site is built.
What stands out
- FreeCell and 1-suit Spider are almost always winnable: our solver lost fewer than 1 deal in 100.
- 4-suit Spider is far harder: about one deal in four beat our solver.
- Golf is the hardest here: fewer than half of all deals can be won at all under our rules.
- Draw-1 and draw-3 Klondike come out close; with unlimited passes through the stock, drawing three is not much worse for a careful solver.
Minesweeper
Boards that need no guess
Share of random boards (with a start square) our step solver cleared using sure steps only.
| Level | Boards tried | No guess needed | Share |
|---|---|---|---|
| Minesweeper, beginner | 1,119 | 1,000 | 89.4 % |
| Minesweeper, intermediate | 1,430 | 1,000 | 69.9 % |
| Minesweeper, expert | 6,733 | 1,000 | 14.9 % |
Questions
- What share of Klondike games can be won?
- Our solver won 71.3 % of the first 1,402 draw-1 deals it tried and 73.7 % of draw-3 deals, within a search of 100,000 positions per deal. Deals it gave up on may still be winnable, so these are lower bounds for our rules, not exact odds.
- Why are some numbers exact and others only "at least"?
- For Golf our search tries every line of play, so a deal it can't win can't be won. Klondike, Spider, FreeCell, Yukon, TriPeaks and Pyramid have far too many lines to try them all, so the solver stops at a limit. A deal it didn't finish might still have a winning line it never reached.
- Can I check the numbers?
- Yes. The table can be downloaded as a CSV file, and every deal can be played here: the deal lists are the deals our solver won, numbered from 1 to 1000 per game.