Pyramid Solitaire is a card-matching game in which you dismantle a 7-row pyramid by pairing cards whose ranks sum to 13. It is one of the oldest solitaire variants, appearing in published card-game rule books in the early twentieth century, and it remains one of the hardest — well under 10 percent of randomly dealt games are completable even with optimal play. The difficulty comes from circular dependencies that lock the pyramid into positions no amount of clever play can escape.
What is Pyramid Solitaire?
Pyramid Solitaire is a single-player card game played with a standard 52-card deck. Twenty-eight cards are arranged in a 7-row pyramid shape, with 1 card at the apex and 7 cards forming the base. The remaining 24 cards become the stock. The goal in most versions of the game is to remove all 28 pyramid cards by pairing them with other cards whose ranks sum to 13.
Rank values for pairing purposes are: Ace = 1, 2 through 10 at face value, Jack = 11, Queen = 12, King = 13. The valid pairs are therefore: Ace + Queen (1 + 12), 2 + Jack (2 + 11), 3 + 10, 4 + 9, 5 + 8, and 6 + 7. Kings, with a rank of 13 by themselves, are removed alone without needing a partner.
Pyramid Solitaire has appeared in Hoyle's card game books and similar reference collections since the early twentieth century, making it one of the older formalized solitaire variants. Despite — or because of — its brutal win rate, it remains widely played. Microsoft included it in the Microsoft Solitaire Collection alongside Klondike, Spider, FreeCell, and TriPeaks.
How to play Pyramid Solitaire
Step 1 — Deal the pyramid
Deal 28 cards into a 7-row triangle. Row 1 (apex) has 1 card. Row 2 has 2 cards. Row 3 has 3 cards. Continue to row 7 (base), which has 7 cards. Each card in rows 1 through 6 overlaps two cards in the row below it. The 7 base-row cards are all face-up and available from the start. Cards in higher rows are covered and unavailable until both cards below them are removed. The remaining 24 cards form the face-down stock. The waste pile starts empty.
Step 2 — Understand card availability
A pyramid card is available to be paired when no other pyramid cards overlap it from below. In the starting position only the 7 base-row cards are available. As you remove base-row cards, the row-6 cards they were covering become available, and so on upward toward the apex. A card covered on both sides by two uncleaned cards is not available. A card covered on only one side is not available until that one remaining card is also gone.
Step 3 — Remove pairs that sum to 13
Click two available cards whose ranks sum to 13 to remove them both. You can pair any two available pyramid cards with each other, or pair one available pyramid card with the current waste top (the top card of the waste pile). You cannot pair two waste cards together, and you cannot pair a stock card directly with a pyramid card without first drawing it to the waste.
Step 4 — Remove Kings alone
A King has a rank of 13, which means it sums to 13 by itself. Click a single available King to remove it without needing a partner. Kings blocking key paths in the pyramid should usually be removed as soon as they become available.
Step 5 — Draw from stock when needed
Click the stock pile to flip its top card face-up onto the waste pile. The waste top is now available for pairing with any available pyramid card (or with another available pyramid card that sums to 13 — the waste top does not pair with another waste card). Once the stock is exhausted, you can recycle the waste back to stock. Most standard Pyramid rules allow 2 recycles (a total of 3 passes through the stock cards).
Step 6 — Win by clearing the pyramid
The game is won when all 28 pyramid cards have been removed. Stock and waste cards do not need to be cleared. If you exhaust all allowed stock passes and pyramid cards still remain, the game is lost. Because of circular dependencies — situations where removing card A requires removing card B, which is blocked by card A — many deals become unwinnable before the stock runs out.
The Pyramid Solitaire play area
The Pyramid Solitaire play area has three regions. The largest is the pyramid itself, occupying most of the screen, with the 7-row triangle of 28 cards arranged apex-up. Below or beside the pyramid sit the stock pile (face-down) and the waste pile (face-up, showing only the top card). There are no foundation piles — removed pairs disappear from the board entirely.
The pyramid rows are arranged so that each card in rows 1 through 6 visually overlaps the two cards directly below it in the next row. This overlap is what creates the coverage relationship. A card cannot be selected until both of the cards below it are gone. At the start of a deal, only the 7 base-row cards are selectable.
As the pyramid shrinks, more cards become exposed. Removing both base-row cards beneath a row-6 card causes that row-6 card to highlight or animate as available. The apex card in row 1 becomes available only when the two row-2 cards beneath it are both gone, which in turn requires all four row-3 cards beneath those to be gone, and so on. Clearing the final obstacle to the apex is often the hardest part of the game.
Available moves in Pyramid Solitaire
At any point you have three categories of move. First, you can pair two available pyramid cards whose ranks sum to 13 and remove them both. Second, you can pair one available pyramid card with the waste top if their ranks sum to 13, removing the pyramid card and the waste top. Third, you can click the stock to draw one card to the waste, which does not remove any pyramid card but gives you a new waste top to work with.
The waste top is treated as a single available card for pairing. You cannot pair the waste top with another waste card (only the top card of the waste is visible and accessible). You cannot skip the waste top to access a card beneath it — you must pair the top or draw a new stock card, which buries the current top under the new card.
Available pyramid cards are highlighted in most implementations. A card is available if and only if no other pyramid card overlaps it from the rows below. Both the left-side and right-side lower neighbors must be gone. A common mistake is clicking a card that is still half-covered — watch for the coverage indicators to confirm full availability before attempting a pair.
Pyramid Solitaire strategy
Always remove Kings immediately
A King blocks two cards above it and removes itself without needing a partner. Leaving a King on the board when it is available costs you nothing to fix and delays uncovering the cards above it. Make removing available Kings an automatic first step before evaluating pairs.
Prioritize the apex and upper rows
The apex card is the last card you need to remove to win, but it is also the hardest to reach. Work to clear a path toward the apex early. This means identifying which base-row and row-6 cards are directly beneath the apex's chain of coverage and pairing those first when possible.
Identify circular dependencies early
A circular dependency occurs when card A is needed to remove card B, but card B is one of the cards blocking card A. For example, if the only 7 on the pyramid is blocked by the only 6 that would pair with a different 7, you may be stuck. Scanning for these loops early helps you identify unwinnable deals before investing more time, and in borderline cases it shows which stock cards you need to arrive in the right order.
Preserve stock passes for critical unlocks
You have up to 3 passes through the stock (2 recycles). Drawing quickly can help you find a partner for a stubborn pyramid card, but each draw also buries the current waste top. Plan your draws to reach specific needed cards rather than flipping blindly. Sometimes it is better to pair what you can from the pyramid and wait for a better waste top than to draw immediately.
Think about which pairs block other pairs
Two cards might both sum to 13 with the same card. For instance, if a 6 can pair with either of two available 7s, choose the 7 that is blocking more other cards. The other 7 may be paired later with a 6 from the stock. This sequencing matters most on the base row, where multiple options often appear together.
Accept that many deals are unwinnable
Pyramid Solitaire has a win rate of roughly 0.5 to 5 percent on random deals. If a game stalls despite careful play, the deal is likely structurally unwinnable. Identifying this quickly and starting a new game is not giving up — it is good game management. Spending 20 extra minutes on an unwinnable deal produces the same outcome as spending 2 minutes.
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Pyramid Solitaire odds and win rate
Pyramid Solitaire has one of the lowest win rates of any popular solitaire variant. Estimates for the percentage of randomly dealt games that are winnable with optimal play range from roughly 0.5 percent to about 5 percent, depending on the exact rules used (number of stock recycles allowed, whether the win condition requires only the pyramid or the full deck). This means the vast majority of deals — somewhere between 95 and 99.5 percent — cannot be won regardless of how well you play.
The low win rate is a direct consequence of circular dependencies in the pairing structure. Because each rank pairs with exactly one other rank (Ace with Queen, 2 with Jack, and so on), and because both cards of a needed pair must be reachable, it is common for a required card to be buried under a card that needs it. When the same card is both the blocker and the only key to the lock, no play order can resolve the position.
Allowing more stock recycles improves the practical win rate modestly, because you have more chances to cycle the waste top to a needed value. The standard rule of 2 recycles (3 total passes) offers a reasonable balance between accessibility and challenge. Some casual implementations allow unlimited recycles, which raises win rates significantly but reduces the strategic weight of each stock draw.
For perspective, TriPeaks Solitaire wins roughly 80 to 90 percent of random deals, Klondike Solitaire wins theoretically around 82 percent but significantly less in practice, and FreeCell wins approximately 99.999 percent of deals (only one known unwinnable deal exists in the standard Microsoft FreeCell numbering). Pyramid is the outlier — it is fundamentally a harder combinatorial puzzle than the other major variants.
History of Pyramid Solitaire
Pyramid Solitaire is among the oldest formalized solitaire variants. References to games using the 7-row pyramid layout and the pairs-summing-to-13 mechanic appear in Hoyle's card game books and similar rule collections from the early twentieth century. Unlike many solitaire variants whose exact origin is unknown, Pyramid has a documented paper trail through twentieth-century card game literature.
The game reached mainstream computer audiences through Microsoft Solitaire Collection, which launched with Windows 8 in 2012. Before that, Pyramid appeared in various shareware and casual game compilations through the 1990s and 2000s. Its simple visual layout — an obvious triangle of cards — made it easy to implement and immediately recognizable.
Pyramid's place in Microsoft Solitaire Collection alongside Klondike, Spider, FreeCell, and TriPeaks gave it a consistent, large player base. Microsoft's version uses the standard pyramid-only win condition (clearing all 28 pyramid cards wins regardless of the stock) and 2 stock recycles. These have become the de-facto standard rules, though earlier published versions varied on both points.
The game's extreme difficulty has made it a subject of interest for computational card game analysis. Because win rates are so low, researchers studying the game needed to analyze very large samples of dealt hands to get stable win-rate estimates. This difficulty is also why Pyramid retains a dedicated player base despite — perhaps because of — the rarity of a successful clear. A won game of Pyramid feels earned in a way that most solitaire victories do not.
Frequently asked questions
What is the goal of Pyramid Solitaire?
- The goal is to remove all 28 cards from the 7-row pyramid by pairing cards whose ranks sum to 13. Kings (rank 13) are removed alone. You can pair two available pyramid cards together, or pair one available pyramid card with the top card of the waste pile. The game is won when the last pyramid card is removed. Stock and waste cards do not need to be cleared.
Which card pairs sum to 13 in Pyramid Solitaire?
- The valid pairs are: Ace (1) + Queen (12), 2 + Jack (11), 3 + 10, 4 + 9, 5 + 8, and 6 + 7. Kings have a rank of 13 and are removed alone without a partner. Suit and color are irrelevant — only the rank values matter. Each rank has exactly one partner rank, which is part of what makes the game so difficult: every card depends on a specific counterpart.
When is a pyramid card available to be played?
- A pyramid card is available when no other pyramid cards overlap it from the rows below. In the starting position, only the 7 base-row cards are available. Each row-6 card becomes available once both base-row cards below it are removed. This continues up to the apex: the row-1 card is not available until the two row-2 cards beneath it are both gone. The waste top is also always available for pairing with any valid pyramid card.
How does the stock work in Pyramid Solitaire?
- The 24 stock cards are drawn one at a time to the waste pile. Click the stock to flip the top card face-up onto the waste. The new waste top is now available for pairing with any available pyramid card whose rank, combined with the waste top's rank, equals 13. Once the stock is empty, you can recycle the waste back into the stock. Most standard rules allow 2 recycles, giving you 3 total passes through the 24 stock cards.
Can you pair two waste cards together?
- No. You can only access the top card of the waste pile. You cannot pair the waste top with the card beneath it, and you cannot pair two waste cards directly. To pair a waste card with a pyramid card, the pyramid card must be available (uncovered). When you draw a new stock card, the previous waste top is buried and is no longer accessible unless you cycle back through the stock.
What percentage of Pyramid Solitaire games are winnable?
- Estimates range from roughly 0.5 to 5 percent, depending on the exact rules used. This is one of the lowest win rates of any major solitaire variant. The low rate is caused by circular dependencies: in most random deals, some needed pairing card is covered by the very card that needs it, creating an unresolvable loop. The majority of Pyramid deals are structurally unwinnable regardless of how well you play.
What is a circular dependency in Pyramid Solitaire?
- A circular dependency occurs when card A is needed to remove card B, but card B is blocking access to card A. For example, if the only available pairing for an exposed 6 is a 7 that is covered by another 6 — and that 6 cannot be removed without first removing the 7 beneath it — the game is locked. These circular locks are the main reason Pyramid Solitaire has such a low win rate.
Is Pyramid Solitaire harder than Klondike?
- Yes, significantly. Pyramid Solitaire is one of the hardest popular solitaire variants, with a win rate estimated at 0.5 to 5 percent of random deals. Klondike Solitaire is theoretically winnable in around 82 percent of deals (though the practical player win rate is much lower due to face-down cards and limited information). Pyramid's difficulty comes from its rigid pairing structure and the frequency of circular dependencies rather than from hidden information.
Do I need to clear the stock and waste to win Pyramid Solitaire?
- No. In the standard win condition, you only need to remove all 28 pyramid cards. Stock and waste cards can remain when you win. Some older or alternative versions of the rules require clearing all 52 cards, which raises the difficulty even further. On this site the standard pyramid-only win condition is used: clear the 28 pyramid cards and the game is won.
How many stock recycles are allowed in Pyramid Solitaire?
- The standard rules allow 2 recycles — meaning you can pass through the 24 stock cards a total of 3 times. When the stock is empty, clicking it shuffles the waste back into a new stock. After the third pass is exhausted, no more draws are possible. If pyramid cards still remain at that point, the game is lost. Some casual or beginner implementations allow unlimited recycles, which makes the game considerably easier.
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