# Which Pyramid pairs make 13, and which should you take first?

In Pyramid you will often see two or three possible pairs at once. Which one should you take first? First, be sure which pairs exist and which cards you may use.

## The pairs that make 13

You remove two available cards whose ranks add up to 13:

- Ace and Queen (1 + 12)
- 2 and Jack (2 + 11)
- 3 and 10
- 4 and 9
- 5 and 8
- 6 and 7

A King counts as 13 and is removed on its own. Suits do not matter, and because 13 is odd, no card pairs with another of its own rank. Every rank except the King has exactly four possible partners: the four cards of the matching rank.

## Which cards are available

The pyramid has 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, and every card above the bottom row is overlapped by the two cards beneath it. At the start, only the seven cards of the bottom row are available. The other 24 cards form the stock; Draw turns one onto the waste, and the top waste card is also available.

Two consequences are easy to miss:

- **A card can never pair with a card that overlaps it.** The covered card only becomes available once the card on top of it has gone, so the two can never be removed together.
- **Two waste cards can never pair,** because only the top one is available.

## Worked example: the bottom two rows

Here are the two bottom rows of a pyramid, left to right:

- Row 7 (bottom): 5♣ 8♦ K♠ 4♥ 9♣ 6♦ Q♥
- Row 6: 7♠ J♦ 2♣ 10♥ 3♠ A♦

Each row-6 card is overlapped by the two row-7 cards below it: 7♠ by 5♣ and 8♦, J♦ by 8♦ and K♠, 2♣ by K♠ and 4♥, 10♥ by 4♥ and 9♣, 3♠ by 9♣ and 6♦, and A♦ by 6♦ and Q♥. Without touching the stock:

1. **K♠ on its own.** A King needs no partner, so removing it never costs you anything.
2. **5♣ and 8♦.** With both gone, 7♠ is available, and so is J♦, since the K♠ has already gone.
3. **4♥ and 9♣.** This frees 2♣ (K♠ and 4♥ gone) and 10♥ (4♥ and 9♣ gone).
4. **7♠ and 6♦.** The 6♦ could have waited for a 7 from the waste, but the 7♠ has to leave the pyramid anyway, so pairing two pyramid cards does two jobs in one move. Removing the 6♦ also frees the 3♠.
5. **2♣ and J♦.**
6. **10♥ and 3♠.**

That is 11 of the 13 cards gone, and the row above has started to open up. Two are left: Q♥ and A♦. They add up to 13, but the Q♥ overlaps the A♦, so they can never be paired with each other. The Q♥ needs one of the other three Aces, and only then does the A♦ become available, needing a Queen of its own.

## Choosing which pair to take first

1. **Kings at once.** They need no partner and only ever uncover cards.
2. **Usually, pyramid pairs before waste pairs.** You win by clearing the pyramid, so a move that removes two pyramid cards does twice the work of one that uses a waste card.
3. **When two cards want the same partner, pick the one that uncovers more.** Removing the last card covering another card is worth more than removing one that leaves its neighbours still covered.
4. **Keep pairs from locking.** Every removal takes one card of each rank in the pair, so the number of 6s left always equals the number of 7s left, and the same holds for Aces and Queens and every other pair. If the last 6 ends up covering the last 7, directly or through the cards between them, that pair can never be made and the pyramid cannot be cleared. When you choose which 7 to use, think about which 6 it leaves behind.

## Three passes through the stock

The stock holds 24 cards, and Draw turns them one at a time onto the waste. You may go through the stock three times in total, which means two recycles of the waste. Each stock card can therefore come up at most three times, and once the third pass is over, nothing new will come.

On every pass, use a waste card whenever it removes a pyramid card that has no partner available in the pyramid. On the third pass be especially thorough, because skipped cards will not be back. And remember the goal: you win as soon as the whole pyramid is gone, even if cards remain in the stock and waste.

## Try it

The left end of the bottom two rows:

- Row 7: 4♣ 9♦ 6♠, with more cards to the right.
- Row 6: 10♥ (overlapped by 4♣ and 9♦) and 7♣ (overlapped by 9♦ and 6♠).
- Top waste card: 9♠.

Which pair do you take, and why can the 6♠ not pair with the 7♣?

**Answer:** Take 4♣ and 9♦. That removes two pyramid cards and leaves the 10♥ uncovered. Pairing the 4♣ with the waste 9♠ instead would leave the 9♦ in place, still covering both the 10♥ and the 7♣. The 6♠ and 7♣ do add up to 13, but the 6♠ overlaps the 7♣, so the 7♣ is not available until the 6♠ has gone: the 6♠ needs a different 7.

Try it in [Pyramid](../play/pyramid.html). For two related games where you play cards one rank up or down instead of in pairs, see the notes on [TriPeaks chains](tripeaks-chains.html) and [Golf](golf-no-kings.html), and the [how to play page](../how-to-play.html) has the full rules of each.