Three passes through the Pyramid stock: how to plan each one

You have 24 cards in the Pyramid stock and three passes to use them. Should you take every pair the waste offers on the first pass, or hold something back? Two details of how the stock and waste behave make the planning much easier.

How the stock and waste work

In Pyramid the 24 cards that are not in the pyramid form the stock. Each Draw turns one card face up onto the waste. The top waste card is available: it can pair with an available pyramid card to make 13, and a King on the waste is removed on its own. Two waste cards can never pair with each other, because only the top one is available.

When the stock is empty, Draw turns the whole waste back over into the stock. That is a recycle, and you get two, so the stock may be gone through three times in total. The status line shows the pass, from Pass 1/3 to Pass 3/3, and when the third pass runs out, Draw stops working. A recycle counts as a move: a full pass of 24 draws plus a recycle adds 25 moves.

Two details matter most:

• The waste is a stack, not a bin. When you pair the top waste card away, or remove a King from it, the card beneath comes back to the top and is available again. A card you have drawn past is buried, not gone.
• Every pass comes round in the same order. A recycle turns the waste over as a whole, so the next pass repeats the last one, minus the cards you removed. What you see on pass 1 tells you what is coming on passes 2 and 3.

Pass 1: scout and take the easy pairs

On the first pass every stock card is new. Use the waste card whenever it removes a pyramid card that has no partner available in the pyramid itself, and take any King that turns up; every stock card you remove shortens the later passes.

Meanwhile, note what you cannot use yet: if a 3 sits high in the pyramid, notice roughly where the 10s come in the stock, because they will come in the same order next time.

Passes 2 and 3: play to the order you know

From the second pass on, you know what is coming, so prepare the pyramid before the card arrives. If a Jack is due in three draws and the 2 that needs it is still covered, use the pairs you can make before then to uncover the 2.

On the third pass nothing comes back. Before each draw, ask whether the current waste card is still needed. If it is, the next draw buries it, and it returns to the top only if every card drawn after it is removed.

Worked example: the waste card that waits

It is Pass 3/3 and three pyramid cards are left: 3♣ at the top, with 9♥ and 5♠ beneath it. The waste shows 10♦. From the earlier passes you know the next two stock cards are 4♦ and then 8♣.

      3♣
   9♥    5♠

Waste: 10♦    Next: 4♦, 8♣

The 10♦ is exactly what the 3♣ needs, but the 3♣ is covered, and neither 9♥ nor 5♠ pairs with the 10♦. You must draw and bury the 10♦. Here that is no problem:

1. Draw. 4♦ + 9♥ = 13, so remove them, and the 10♦ is back on top.
2. Draw. 8♣ + 5♠ = 13, so remove them, and the 10♦ is on top again.
3. Remove 3♣ and 10♦. The pyramid is gone and the round is won.

That takes five moves, with cards still left in the stock. They do not matter: Pyramid is won when the whole pyramid has been removed.

Now suppose the second stock card were J♠, with the 8♣ after it. The J♠ lands on the 10♦ and pairs with nothing, so you draw again: the 8♣ removes the 5♠, but the waste now shows J♠, and the 3♣ needs a 10. On the last pass that means "No moves left". You could have known this order from passes 1 and 2, so the job on pass 2 was to uncover the 3♣ in time for the 10♦, or to find it another 10.

How the round ends

The round is lost when no pair can be made and no draw or recycle remains. A recycle needs cards in the waste, so this can happen before the third pass if you have removed every stock card. Near the end, name the partner each remaining pyramid card needs and check that one is still in the stock or waste.

Try it

It is the start of Pass 2/3. The stock holds 15 cards and the waste is empty.

1. If you made no pairs at all, how many more times could you press Draw?
2. The waste shows Q♣ with 6♥ just beneath it. A 7♠ is available in the pyramid, but no Ace is. Can you pair the 6♥ with the 7♠?

Answers: (1) Thirty-one: 15 draws, one recycle and 15 more draws, adding 31 moves. (2) Not now. Only the top waste card is available, and the Q♣ can only leave with an Ace. If you draw instead, both stay buried unless the cards above them are removed, and they come round again after the recycle in the same order.

For the pairs themselves, read Which Pyramid pairs make 13; the full rules are on how to play.