Calculation Solitaire

Calculation is the most mathematically distinctive game in the patience family. Most solitaire games ask you to build foundations in a simple ascending sequence. Calculation asks you to build four foundations at once, each following a different arithmetic progression: by ones, by twos, by threes, and by fours. All sequences wrap around from King back to Ace, treating the 13 ranks as a circular system.

The game begins with one Ace, one 2, one 3, and one 4 placed as foundation starters. The Ace foundation builds: A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K. The 2 foundation builds by twos: 2, 4, 6, 8, 10, Q, A, 3, 5, 7, 9, J, K. The 3 foundation counts by threes: 3, 6, 9, Q, 2, 5, 8, J, A, 4, 7, 10, K. The 4 foundation counts by fours: 4, 8, Q, 3, 7, J, 2, 6, 10, A, 5, 9, K. Every foundation ends on a King.

The arithmetic is the game's great novelty. You must hold all four sequences in mind while managing four waste piles that temporarily park cards that can't go to a foundation yet. The question is never just "where does this card go?" but "which waste pile should hold it so I can reach it in the right order later?"

Players who enjoy numbers will find the sequence logic intuitive and satisfying. Players less comfortable with modular arithmetic should write out the four sequences before their first game — which is entirely recommended and takes nothing away from the enjoyment.

The game is winnable with good play. Waste pile management creates enough agency that skill matters, though the stock order contributes significantly. A skilled Calculation player will win more often than a novice — which is more than can be said for Clock. Tracking four simultaneous arithmetic sequences while managing four waste piles is unique in the solitaire world.

1. Remove one Ace, one 2, one 3, and one 4 from a shuffled 52-card deck. Place them face-up in a row as the four foundation starters. The remaining 48 cards form the stock. Set up four empty waste pile spaces below the foundations.
2. The four foundations build by different intervals, each ending on a King:

• Foundation 1 (Ace): A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K — by 1s
• Foundation 2 (2): 2, 4, 6, 8, 10, Q, A, 3, 5, 7, 9, J, K — by 2s
• Foundation 3 (3): 3, 6, 9, Q, 2, 5, 8, J, A, 4, 7, 10, K — by 3s
• Foundation 4 (4): 4, 8, Q, 3, 7, J, 2, 6, 10, A, 5, 9, K — by 4s Rank sequences wrap around: after King comes Ace.

1. On each turn, flip the top card of the stock. You may place it on the correct foundation if it is the next required card for that pile, or place it face-up on any one of the four waste piles. If it fits no foundation, it must go to a waste pile. The top card of each waste pile is always available to play to a foundation.
2. Continue flipping stock cards one at a time. There is no redeal — the stock is gone through once. Cards may only move from waste piles to foundations, not between waste piles. The game is won when all four foundations are completed through to King. The game is lost when the stock is exhausted and the waste pile cards cannot finish the foundations.

• Write out the sequences first. Knowing all four foundation sequences is not optional. Without them, you cannot make informed decisions about where to place waste pile cards. Write them down before your first game.
• Give each waste pile a purpose. Each waste pile should serve one or two foundations. Designate one pile as the holding area for Foundation 3 cards, for example, and keep it ordered so the next needed card is always on top. Mixing all four sequences into one pile creates an inaccessible mess.
• Keep urgent cards accessible. When you flip a stock card needed by a foundation in two or three turns, place it on a waste pile where it stays easy to reach. Burying an urgently needed card under others is the most common way to lose Calculation.
• Clear constrained waste piles first. When multiple waste piles have exposed cards that fit foundations, prioritize the most constrained pile — the one with one useful card on top of several useless ones. Clear that top card quickly before it gets buried further.
• Accept the luck factor. Even perfect waste pile management cannot overcome a severely unfavorable stock order. The goal is to make the most of each deal, not to win every game.

Calculation is a relatively modern patience game, with documented appearances in English card game anthologies from the mid-20th century. Its arithmetic foundation system is unusual enough that most historians believe it was a deliberate design rather than an organic evolution from earlier games. The inventor is unknown, but the construction — four sequences with intervals of 1, 2, 3, and 4, all ending on King — suggests a mathematically inclined designer who appreciated modular arithmetic.

The name Broken Intervals appears in some European collections, emphasizing the non-sequential nature of the foundation builds. Sir Tommy is a related but distinct game from the British patience tradition with some structural similarities, leading to occasional conflation in older references.

Digital versions of Calculation appeared in comprehensive solitaire collections throughout the 1990s and 2000s, where its mathematical novelty attracted players who found standard ascending-sequence foundations too routine. It remains a favorite among numerically inclined solitaire players and is regularly cited as one of the most intellectually distinctive single-deck patience games.