Pyramid Solitaire: a short game in three laps

Pyramid is quick to learn and quick to play. Twenty-eight cards are laid out in a pyramid of seven rows, and the other 24 sit in the stock. You remove cards in pairs that add up to 13: a 6 with a 7, a Jack (11) with a 2, a Queen (12) with an Ace. A King counts as 13 and goes on its own. Clear the pyramid and you win.

On this site you get three trips through the stock, and that is the number that matters most. With perfect knowledge of the stock, our solver proved 62.2% of deals winnable in three laps. Held to a single lap, it could prove only 7.3%. So if you usually play Pyramid in a few spare minutes, the second and third laps are where most wins happen.

What three laps buy you

With three laps, somewhere between 62.2% and 86.0% of deals can be won with perfect play. The one-lap figures come from a smaller search limit and leave most deals undecided, so read them as "far fewer", not as an exact share. Even so, the drop is huge.

How Pyramid works here

• Layout. A pyramid of 28 cards in seven rows, with each row overlapping the one above. A card is free when no card covers it.
• Pairs. Remove any two free cards that add up to 13. An Ace is worth 1, a Jack 11 and a Queen 12.
• Kings. A free King is removed on its own.
• Stock. The 24 remaining cards. The top card of the stock is face up, and turning it moves it to the waste. Free cards can pair with the waste top, and we understand from the game code that the face-up stock card can be paired too.
• Laps. When the stock runs out you can turn the waste back over. You get three trips through the stock in all.
• Winning. Clear the pyramid. Cards left in the stock or waste do not count against you.

Using your three laps well

Lap one: learn the stock

You will see all 24 stock cards on the first lap. Take the obvious pairs, but also notice where the stock cards fall, because the same order comes round again.

Lap two: go for the blockers

Now you know what is coming. Aim at the cards that cover the most others, especially in the upper rows.

Find the Kings early

In 40.8% of our deals, at least one King sat in the top three rows. A King up there can only be removed once the cards beneath it are gone, so plan your route to it from the start.

Choose between equal pairs with care

If two different cards could pair with a 7, take the one that frees more of the pyramid. Our simple player that just took what it saw won 25.2%; planning is where the rest comes from.

Some deals are stuck from the start

In 3.6% of deals, there was no King and no pair available at all among the bottom row and the top stock card. That does not mean the deal is lost, since the stock still turns, but it is a slow start.

On your phone or computer

Pyramid runs in any modern browser, with no download and no account. Tap two cards to pair them, or drag one onto the other. Zoom in if the pyramid feels small. Hint, unlimited Undo and Restart are always available, and the game tracks moves and time. You can turn off the sound, go fullscreen and choose your table colour.

What a Pyramid session looks like

A Pyramid game has three clear parts, one for each lap. The first lap is quick: you take the easy pairs and see every stock card once. The second lap is where most of the planning happens, because you now know what the stock holds. The third lap is the last chance to clear the top of the pyramid.

That structure makes Pyramid a neat fit for a short break. Each lap takes a couple of dozen turns of the stock, and by the end of the third you know whether the pyramid is clear.

If you often run out of laps with a few cards left near the top, the usual cause is taking pairs too greedily early on. Our simple player, which took what it saw, won 25.2% of deals; the solver, which planned ahead, proved at least 62.2% winnable.

How we did the research, step by step

The solitaire-online.nz team ran this study in September 2026 to see how much the extra trips through the stock help in Pyramid on this site.

1. We began with this site's game code. A 28-card pyramid and a 24-card stock with three passes, pairs that sum to 13, Kings removed alone, and the game won when the pyramid is cleared. We assumed that the face-up top card of the stock can be paired directly; that is how we read the game code, but we did not test it in a browser.
2. The game as a program. We wrote those rules into a simulation, with a setting for the number of laps.
3. Numbered deals. 4,000 deals, each from a numbered seed, played once with three laps and once with one.
4. Two players. A solver that knows the stock order and searches for a winning line; and a simple player that sees only face-up cards and takes the pairs it sees.
5. The run. The three-lap solver was allowed up to 1,000,000 positions per deal; the one-lap run was limited to 200,000.
6. Published figures. We did not find a published winnability figure for Pyramid under this site's rules, so the figures here are our own.
7. Error bars. A 95% range contains the answer 19 times in 20 if the test were repeated. For three laps, the proven-winnable share is 60.6% to 63.6%.
8. Limits. The solver knows the stock order, so it is a ceiling, not what you should expect. It left 23.9% of three-lap deals undecided, which is why we quote a range. If our reading of the stock-card rule is wrong, the figures would change.

The technical side

The simulation is Python 3.11, standard library only, in pyramid.py. The solver is a depth-first search that remembers positions it has already found to fail, keyed on which pyramid cards remain, which stock cards are gone, where it is in the stock and how many laps are left. It also cuts off a line as soon as some pyramid card has no possible partner left outside the cards covering it, which is a safe proof that the line cannot win. runner.py spread the 4,000 deals across 19 worker processes, and the three-lap run took about 16 minutes.

Each 95% range is a Wilson score interval. Anthropic's AI assistant, Claude, helped us put the Pyramid code together, review it and draft this page. The AI did not produce the figures: they are the program's output, checked by the team before publishing.

By Admin, solitaire-online.nz. Study date: 18 September 2026.

Short answers before your next deal

What if no pair shows up at the start?

That happened in 3.6% of our deals: no King and no pair among the bottom row and the top stock card. Turn the stock and keep going. You still have three laps, and the order of the stock gives you new chances as you go.

How many laps of the stock do I get?

You get three passes here. That makes a big difference: 62.2% of deals proven winnable in three laps, against 7.3% in one.

What do the picture cards count as?

Jack 11, Queen 12, King 13. Aces are 1.

Is the game over if cards are left in the stock?

Not at all. Once the pyramid is gone you have won, whatever is still in the stock or waste.

Is Pyramid good for a quick game on a phone?

Yes. It is short, and pairing cards with a tap suits a touchscreen.

Another game in the same spirit?

Golf is another quick game built around a single pile. For something longer, try Klondike or browse the games page.