Pyramid Solitaire: pairs, passes and a place in the middle
Pyramid works nothing like Spider, and that is what makes it interesting on our difficulty ladder. There are no columns to build. Twenty-eight cards are dealt face up in a triangle seven rows tall, and you remove them in pairs that add up to 13: a 6 with a 7, a Jack (11) with a 2, a Queen (12) with an Ace. Kings count 13 and go on their own. Clear the whole pyramid and you win.
On this site you get three passes through the 24-card stock, and that makes a big difference. Our solver, which knows the order of the stock, proved 62.2% of 4,000 deals winnable and 14.0% impossible. A simple player that sees only the face-up cards won 25.2%. That places Pyramid mid-ladder, next to Golf, far below one-suit Spider for a simple player and far above four-suit Spider.
This page covers where Pyramid ranks, what the extra passes are worth, the rules on this site, and a step-by-step account of the research.
Where Pyramid ranks
| Game | Simple player won | Proven winnable | Proven impossible |
|---|---|---|---|
| Spider, 1 suit | 52.8% | not measured | – |
| Pyramid (this page) | 25.2% (23.9–26.5%) | 62.2% (60.6–63.6%) | 14.0% |
| Golf | 22.4% | 92.7% | 7.3% |
| Spider, 2 suits | 5.7% | not measured | – |
For the remaining 23.9% of Pyramid deals, our solver ran out of search budget before reaching an answer. So the true share of winnable deals lies somewhere between 62.2% and 86.0%. The published study we use as a reference does not cover Pyramid, so these figures have no outside check.
What the extra passes are worth
We also tested a stricter version with only one pass through the stock. The solver could prove just 7.3% of those deals winnable and 34.8% impossible, with the rest undecided. We gave the single-pass test a smaller search budget, so the gap is not exact, but the direction is clear: the second and third passes are what make Pyramid winnable. They let you see which cards the stock holds and come back for them.
Pyramid rules on spidersolitaire.us
- The pyramid: 28 cards in seven rows, from one card at the top to seven at the bottom, all face up. A card is available when no card in the row below overlaps it.
- The stock: 24 cards. Each click flips the next stock card face up onto the waste. You get three passes in total.
- Pairs: remove any two available cards that total 13. Jacks count 11, Queens 12, Aces 1.
- Kings: count 13, so they are removed alone.
- Stock and waste: the top card of the waste can be paired with a pyramid card. On our reading of the game code, the face-up top card of the stock can be paired too.
- Winning: clear the pyramid. Cards left in the stock or waste do not matter.
Playing Pyramid with the numbers in mind
Find the Kings that block you
In 40.8% of our deals, at least one King sat in the top three rows. A King high up cannot be removed until everything beneath it is gone, so it tells you which part of the pyramid you must clear first.
Don't panic at a blank start
Only 3.6% of deals started with no King and no pair available at all. Nearly every deal has somewhere to begin.
Choose which card of a pair to use
When two different 6s could each pair with a 7, take the one that uncovers more of the pyramid. Our simple player did not look ahead like that and won 25.2%; the solver, which plans every step, proved 62.2% winnable.
Treat pass one as a scouting trip
With three passes, your first trip through the stock can be about gathering information. Note which cards are there, and save pyramid cards for partners you know are coming.
Undo is your planning tool
You cannot see the whole stock in advance the way the solver can, but unlimited Undo lets you test a line and back out.
Features on spidersolitaire.us
Pyramid is free to play in any modern browser on computer, tablet or phone. Nothing to download and no account, sign-up or email. Large clear cards with zoom, Hint, unlimited Undo, Restart, Auto Play, and drag-and-drop or tap. Wins, time and moves are tracked for the current game; sound can be switched off; fullscreen and table colors are available.
Behind the numbers: how we ran the study
In September 2026 the spidersolitaire.us team measured Pyramid to place it on the same ladder as Spider and to see what the stock passes are worth.
- Started from the code that runs our game. A 28-card pyramid, a 24-card stock with three passes, pairs that total 13, Kings removed alone, and a win when the pyramid is cleared. We assumed, from reading the code but without testing in a browser, that the face-up top card of the stock can be paired directly.
- Rebuilt Pyramid as a program, with a setting for a single pass as a comparison.
- Dealt numbered hands. Deals 1 to 4,000, each from a fixed seed, used for both the three-pass and one-pass tests.
- Chose two players. A solver that knows the stock order and searches for a way to clear the pyramid, as a ceiling. And a greedy player that sees only face-up cards, as a floor.
- Ran every deal. The solver was allowed 1,000,000 positions per deal for the three-pass game and 200,000 for the one-pass comparison. Deals it could not settle within that were marked undecided.
- Looked for published figures. Blake and Gent (2026) do not report Pyramid, so we have no outside figure to compare with.
- Calculated the margin of error. For 62.2% solved, the 95% range is 60.6% to 63.6%.
- Stated the limits. The solver knows the stock order, which no player does. Almost a quarter of deals stayed undecided. And if the stock-card assumption is wrong, the figures would shift.
The code behind the ladder
The simulation uses Python 3.11 and nothing outside its standard library; Pyramid is the pyramid.py module. The solver is a depth-first search that tracks which pyramid cards are gone, which stock cards have been used, where the stock pointer is and how many passes remain. It remembers positions that already failed so it does not repeat them, and it abandons a line early when some pyramid card has no possible partner left, a test that can never throw away a winnable position. The 4,000 deals ran in about 16 minutes across 19 worker processes on a 20-core machine.
Ranges are Wilson score 95% intervals. Claude, the AI assistant from Anthropic, helped the team write and review the code and draft this page. It did not generate any of the figures; all of them come from running the code, and the team reviewed them before this page went up.
Ladder questions, answered with data
Why do some Pyramid deals feel hopeless?
Some are. Our solver proved 14.0% of deals impossible even knowing the whole stock.
How many stock passes do I get?
Three times on this site. That is a big help: with one pass, far fewer deals can be proven winnable.
Is Pyramid harder than Golf?
For a simple player they are close (25.2% here, 22.4% for Golf). But more Golf deals can be won with perfect play.
How does Pyramid compare with Spider?
Easier than two-suit Spider for a simple player, harder than one suit.
What other games did you test?
All twelve are on the games page, and our study write-ups are on the blog.
By Admin, spidersolitaire.us. Research run September 2026.