Calculation

Full rules

1. Overview
2. Card values
3. The parts of the layout
4. The four sequences
5. Setup
6. Playing
7. Winning
8. Tips for beginners
9. Variants

Overview

Calculation is a patience (a card game for one player, also called solitaire) for people who like to think ahead. You build four piles at once: the first counts up in ones, the second in twos, the third in threes and the fourth in fours – and all four must end with a King. Suits don't matter at all. The whole skill lies in choosing where to put the cards you can't use yet.

• Players: 1
• You need: one standard 52-card deck, no jokers.
• Time: about 15 minutes per game.

Card values

For counting, Ace = 1, 2–10 count their number, Jack = 11, Queen = 12, King = 13.

When a count goes past 13, you start again from the beginning: subtract 13. For example, counting in twos from the Queen (12) you reach 14, and 14 − 13 = 1, so the next card is an Ace.

The parts of the layout

• Foundations: four piles in a row, started with an Ace, a 2, a 3 and a 4 (any suits). You build on them in fixed steps – see the table below. Each ends with a King.
• Waste piles: four piles below the foundations, empty at the start, where you put cards you can't use yet. Spread each pile downwards so you can see all its cards, but only the top (last placed) card of each can be played.
• Stock: the face-down rest of the deck, which you hold in your hand.

The four sequences

Suits don't matter – any card of the right rank will do.

Setup

1. Take any Ace, any 2, any 3 and any 4 out of the deck and lay them in a row, left to right. They are the foundations.
2. Shuffle the remaining 48 cards and hold them face down as the stock.
3. Leave room below the foundations for four waste piles.

Playing

Turn over the top card of the stock. You must place it straight away:

• on a foundation, if it is the next card that foundation needs, or
• on any one of the four waste piles – any card may go on any waste pile, in any order.

At any time you may also move the top card of a waste pile to a foundation, if it fits there. Moving that card uncovers the one below, which may then fit too.

Cards can never be moved from one waste pile to another, or from a foundation back to a waste pile. Once a card is on a waste pile, it can only leave it by going to a foundation.

Example: You start with A, 2, 3, 4. You turn up a 6 – it goes on the 3 (3, 6, 9 …). Next an 8 – it goes on the 4 (4, 8, 12 …). Then a King: no foundation wants a King yet, so it goes on a waste pile. You decide to keep that pile for Kings only. Next comes a 5: the A-foundation needs a 2, the 2-foundation a 4 – so the 5 also goes on a waste pile, but not on the Kings.

Winning

There is only one pass through the stock – no redeal. When the stock is used up, keep moving waste-pile cards to the foundations for as long as you can. You win when all 52 cards lie on the four foundations, each topped by a King. If cards are left on the waste piles and none of them fits, the game is lost. Morehead and Mott-Smith estimated a chance of about one game in five.

Tips for beginners

• Keep one waste pile for Kings: a King on top of a low card blocks it until a whole foundation is finished. Once three Kings (maybe two) are down, you may risk using all four piles for other cards.
• Try to build waste piles in descending steps that match a foundation – for example 9, 7, 5 on one pile for the 2-foundation. Even two or three cards in the right order help a lot.
• Avoid putting two cards of the same rank on the same pile.
• Keep an eye on how soon each card will be needed, and cover cards needed soon only with cards needed even sooner.

Variants

All of these are optional – choose one before you start.

• No foundations in advance: don't take out A, 2, 3, 4 at the start; start each foundation when a suitable Ace, 2, 3 or 4 turns up in play. William B. Dick (1883) already described this as more interesting but harder – "it seldom succeeds".
• Three waste piles: play with only three waste piles instead of four. Much harder.