Calculation Solitaire

TSBy The Strategy Desk·Published April 5, 2026

Calculation is a unique math-based solitaire where suit doesn't matter — only rank. Four foundations build up using different counting intervals: by 1s, 2s, 3s, and 4s, wrapping around from King back to Ace. The challenge lies entirely in managing your four waste piles to access cards in the right order.

How Calculation Works

Start with an Ace, 2, 3, and 4 as foundation bases. Draw cards one at a time from the stock. Each drawn card must go to a foundation (if it matches the next expected rank) or a waste pile. The top card of each waste pile is available to play to foundations at any time. There is no redeal — once the stock is empty, you can only play from waste pile tops.

The Sequences

Strategy Tips

• Dedicate each waste pile to a specific range of ranks — don't mix randomly.
• Keep one waste pile empty or nearly empty as a “buffer” for unexpected cards.
• Learn the sequences! Knowing what's coming next on each foundation is crucial.
• Kings are always last — plan to bury them deep in waste piles early.
• Watch all four foundations simultaneously — a card might fit one you didn't expect.

History & Origins

Calculation holds an unusual place in the patience literature: it is one of the only classical solitaires whose foundations are built on arithmetic sequences rather than suit or rank adjacency. Documented in nineteenth-century German patience books under names such as Sir Tommy's Variant and Broken Intervals, Calculation reached English-speaking players through translations and Hoyle revisions in the late 1800s. The game's mathematical DNA — four foundations built with the four increments +1, +2, +3, +4 — reflects an era when patience was considered a mental discipline rather than a casual amusement. Edwardian manuals sometimes printed the four sequences as a memorisation drill for young players, and the word “calculation” stuck because that is literally what the game demands. Today it survives as the purest example of rank-only, suit-indifferent solitaire still widely played.

Strategic Principles

Calculation is a routing puzzle more than a card game. Because suit is irrelevant and every card has exactly four possible foundation targets, our job is to bury cards in waste piles we can recover from — and the four foundation sequences demand four different mental models. We memorise the +1 sequence instantly (it is just A through K in order). The +2 sequence alters at seven cards in (2, 4, 6, 8, 10, Q, A, 3, 5, 7, 9, J, K), and we hold the wrap point A→3 in our heads. The +3 and +4 sequences reorder the ranks completely, and strong players simply learn them by heart.

Because each foundation wants a different “next card,” every drawn card could be a foundation play right now or a future foundation play buried in a waste pile. We assign each of the four waste piles a loose character: one pile absorbs cards needed soon by the +1 foundation, one pile hoards cards for the +3 and +4 foundations, one pile collects Kings and other late-sequence cards, and one pile stays deliberately shallow as a buffer for surprise cards. Mixing ranks randomly across piles is a slow-motion disaster: we will bury a card that we need next only to discover the card sitting on top of it is not needed for another ten plays.

The mental math matters because each play forces recomputation of all four “next needed” targets. After we place the 6 on the +2 foundation, the next needed card there is 8, but 6 may also be an active bury target for the +3 pile. We narrate these recalculations aloud during learning, then internalise them. Players who track the foundations as a constant four-way lookup win roughly twice as often as players who watch only one foundation at a time.

A practical rule of thumb: after foundation plays, the four “next needed” ranks across the four piles rarely repeat. In a typical mid-game state, we might be watching for an 8, a Queen, a 5, and a 3 — four distinct ranks that cover a substantial portion of the deck. That distribution is what keeps Calculation interesting; no single card becomes worthless. Every rank in the deck is valuable somewhere, which is why losing cards to a careless bury feels so expensive. Expert players also learn to predict when a foundation is about to become “sticky” — meaning the next-needed card is sitting on the wrong waste pile, and several plays elsewhere must happen before it becomes accessible.

Difficulty & Win Rate

Calculation is famously skill-dependent: estimates place the win rate around 25-30% with disciplined waste-pile management, and under 10% with careless play. The gap between novice and expert is enormous. There is no redeal and no reserve, so a single sloppy waste-pile assignment can end a deal we were winning half a minute earlier.

Compared to most patience games, Calculation rewards practice much more consistently. Because suit is removed from the puzzle, the game distils down to pure routing, and a player who sees the same deal twice will play it much better the second time. That repeatability is part of the appeal: unlike games where luck dominates, skill visibly compounds in Calculation.

Common Mistakes

The biggest mistake in Calculation is mixing ranks across waste piles without a plan. Players grab the nearest pile because it feels natural, and twenty cards later they have burned a winnable deal. The second biggest mistake is neglecting the +3 and +4 sequences — novices watch the +1 and +2 foundations carefully but treat the harder sequences as background noise, only to find themselves unable to play a Queen that was the next needed card on the +3 pile for six moves.

A third common blunder is refusing to keep a buffer pile. Players greedily load all four waste piles with useful cards and then have no safe place to drop a wild card when one arrives. A shallow buffer, even if it seems to waste capacity, is what prevents deadlock. Finally, new players often forget that the top card of a waste pile is playable to any foundation, not just the one they originally had in mind — they miss legal plays simply because they are not scanning all four foundations each turn.

Another recurring error is moving a card to a waste pile when it could go directly to a foundation. Because we have memorised the four sequences, we sometimes get locked into the “sort to pile” rhythm and forget to check foundation legality first. Every turn starts with the same question: can this card play to any foundation right now? Only if the answer is no do we route it to a waste pile — and even then we choose the pile that best matches its future foundation target.

How This Game Compares

Calculation is closest in structure to Sir Tommy, which also uses four waste piles but with a single +1 sequence per foundation — Sir Tommy is the simpler cousin, and Calculation is the mathematically demanding extension. Compared to Baker's Dozen, Calculation removes suit entirely and replaces cascade management with waste-pile management — a different skill, but with similar demands on foresight. Compared to Clock, Calculation is vastly more interactive: Clock is essentially automatic, while Calculation requires deliberate decisions on every single card.

Players who enjoy Calculation often gravitate toward Accordion (another pure-skill, low-luck patience) or toward Gaps for its rank-focused, routing-heavy puzzle. Players looking for a break after a streak of Calculation losses usually cross over to FreeCell, where skill is still decisive but the win rate is an order of magnitude kinder.

Variant Notes

The most common Calculation variant allows a single redeal of the waste piles after the stock is exhausted, usually by gathering all four piles in order and redealing them as a new stock. This one-pass redeal variant lifts the win rate closer to 50% but blunts the game's intense skill demands — we prefer the classical no-redeal form here. Another variant opens with foundations pre-stocked at 2-3-4-5 instead of A-2-3-4, shifting all four sequences by one rank; this “German Calculation” version appears in some older patience compendiums. A rarer variant permits cards to move between waste piles before playing, dramatically increasing flexibility but diluting the puzzle's distinctive constraint.

Learn More

• How to Play Calculation — Complete rules and strategy guide
• Calculation Strategy Guide — Tips and winning tactics
• Play Baker's Dozen — Another foundation-building solitaire
• Play FreeCell — The classic free cell solitaire
• Types of Solitaire — Explore 20+ solitaire variants