Pyramid Solitaire: the game where the number of stock passes decides almost everything
On solitaire-turn-3.com we ask the same question of every game: how much does the way you go through the stock change what you can win? For Klondike, the answer is drawing three cards instead of one. For Pyramid, the answer is how many times you may go through the stock at all, and it is the only game on this site where we measured that directly.
The table is a triangle of 28 face-up cards in seven rows, with 24 more cards in the stock. You remove two exposed cards that add up to 13 (a 6 with a 7, a Jack with a 2, a Queen with an Ace), and a King goes on its own. Clear the pyramid and you win. Here you get three passes through the stock. With three passes, a solver that knows the stock order proved 62.2% of 4,000 deals winnable (95% range 60.6–63.6%). Allowed only a single pass, it could prove just 7.3% (6.5–8.2%).
At a glance: three passes against one
| Measure | Result | 95% range | Deals |
|---|---|---|---|
| 3 passes (this site): proven winnable | 62.2% | 60.6–63.6% | 4,000 |
| 3 passes: proven impossible | 14.0% | 12.9–15.1% | 4,000 |
| 3 passes: undecided when the search stopped | 23.9% | 22.6–25.2% | 4,000 |
| 1 pass: proven winnable | 7.3% | 6.5–8.2% | 4,000 |
| 1 pass: proven impossible | 34.8% | 33.4–36.3% | 4,000 |
| 1 pass: undecided | 57.9% | 56.3–59.4% | 4,000 |
| Greedy program, 3 passes, sees only face-up cards: won | 25.2% | 23.9–26.5% | 4,000 |
| No King or pair available at the start | 3.6% | 3.0–4.2% | 4,000 |
Read the pass comparison with care. The three-pass search could look at up to 1,000,000 positions per deal; the one-pass search stopped at 200,000, and it left 57.9% of deals undecided. So the true one-pass share lies somewhere between 7.3% and 65.2%, and the three-pass share between 62.2% and 86.0%. What we can say firmly is that one pass proves far more deals lost: 34.8% against 14.0%.
Passes in Pyramid, draws in Klondike
Klondike Turn 3 and Pyramid hurt you in different ways. In Turn 3 the stock never runs out of passes on this site, but only every third card is in reach on any one lap. In Pyramid every stock card turns up face up, one at a time, but the laps are rationed. Both rules limit how often a card you need is available at the moment you need it. Our Klondike figures show the draw-three cost (a simple bot fell from 42.3% at Turn 1 to 10.6% at Turn 3). Our Pyramid figures show the pass-limit cost. We did not measure a Klondike pass limit, and we did not measure Pyramid with a different number of cards per turn.
Pyramid rules on this site
- Deck: one standard 52-card deck.
- Pyramid: 28 cards in seven overlapping rows, all face up. A card is free when no card covers it.
- Stock: 24 cards, turned one at a time. The top stock card and the top waste card can both be paired.
- Passes: three in total (two redeals).
- Pairs: two free cards totaling 13 are removed. Jack = 11, Queen = 12, King = 13 and goes alone.
- Win: clear the pyramid. Cards left in the stock or waste do not count against you.
Making three passes count
Spend the first pass learning
You cannot see the stock order the way our solver can, but after one lap you know it. Note which partners are in the stock and roughly where, then take pairs that open the pyramid on the second and third laps.
Do not waste a stock card on the stock
Pairing two stock cards with each other clears nothing in the pyramid. Prefer pairs that use a pyramid card, unless a stock pair is the only way to reach a partner underneath.
Watch buried partners
A card whose only possible partners sit underneath it can never be removed. Our solver proves deals lost this way, and 14.0% of deals are lost even with three passes.
Kings early
Kings leave on their own. Clearing a King frees two cards below it at no cost.
Count what is left before the last pass
On the third lap there is no coming back. Before you turn the last card, check that every pyramid card still has a partner somewhere you can reach.
Undo is not a fourth pass, but it helps
Unlimited Undo lets you rewind a bad pairing. It does not bring back a pass you have already used, so the habit of learning the stock early still matters most.
Playing on solitaire-turn-3.com
Pyramid is free in any current browser on computer, tablet or phone, with no download and no account. You get Hint, unlimited Undo, Restart and Auto Play, drag-and-drop or tap-to-move, zoom and fullscreen, a count of wins, time and moves, and sound and table-color settings.
How the figures were made
The solitaire-turn-3.com team ran these tests in September 2026, on the rules read from this site's own Pyramid code, in Python 3.11 with the standard library only.
- Numbered deals: seeds 1 to 4,000, so every deal can be replayed.
- Solver: a memoized search that knows the stock order, up to 1,000,000 positions per deal for three passes and 200,000 for one pass. Each deal ended as solved, proven impossible or undecided.
- Greedy program: sees only face-up cards and takes the first good-looking pair. It is a floor, not a typical human result.
- 95% ranges: Wilson score intervals.
- Published check: the study we compare against, Blake and Gent (2026), does not cover Pyramid, so there is no outside figure.
Claude, an AI assistant by Anthropic, helped write and review the code and draft this page. It produced no figures; every number comes from running the code, and the team checked them.
Pyramid questions
Would four or more passes help?
We did not test more than three, so we cannot say by how much.
Is every deal winnable with three passes?
No. At least 14.0% are proven impossible even for a solver that knows the stock.
How does this compare with Turn 3 Klondike?
Different rule, same lesson: how you get to the stock shapes your chances. See Solitaire Draw 3 and Klondike Turn 3, or browse the games page and the blog.
By Admin, solitaire-turn-3.com (Forty Media). Research run September 2026.