Games played
Win percentage
Wins
Loses
Current streak
Best streak
You win! You're awesome.
Calculation is one of the more difficult solitaire card games. It requires a bit of simple math, thus explaining the name “Calculation”. It also requires a great deal of skill, as only a skilled player can average winning this game even half the time. The game is also known as Broken Intervals, Hopscotch, or Four Kings Solitaire.
This game is played with a standard fifty-two card deck. Once the deck is shuffled, remove an Ace, a Two, a Three, and a Four from the deck. These are now the foundation cards and should be placed at the top of the tableau, each starting their own foundation pile. The suit of each card does not matter.
During play, one card is pulled from the stock pile at a time. Every card must be played. You can put the card either on a foundation pile, if it is next in that specific pile’s sequence, or you can put the card into one of four empty piles of cards on the tableau. These are the waste piles. The top card in any of the waste piles can also be added to the foundation piles if it is the next card in that specific sequence.
Each foundation pile has its own rule as to how it can be built up. The Ace pile is added to by adding a card of the next highest sequential value (Ace, Two, Three, etc). The Two pile is added to in twos (Two, Four, Six, etc). The three pile is added to in threes (Three, Six, Nine, etc). The four pile is added to in fours (Four, Eight, Queen, etc).
You cannot move a card once it is in the foundation pile. You also cannot move cards between waste piles.
The game is over when the entire stock pile has been played and there are no more moves left. If all cards are in the foundation piles, the game is won. If there are still cards in the waste piles, the game is lost.
Once the cards have been shuffled and the foundation cards have been laid out, you are ready to play. Begin by pulling the first card from the stock pile. You can place this card in a waste pile of your choosing or in a foundation pile if it is the next sequential card for that specific foundation pile. The next card in the stock pile cannot be dealt until the previous card has been played.
One of the trickiest parts of this game, and where it earned its name, is figuring out the next card for the foundation pile. This requires a little bit of counting or arithmetic. The Ace is both after the king and before the two, so that as you calculate the next card in a pile, the numbers make a consecutive ring. For example, the four pile goes Four, Eight, Queen (12), Three, etc. This is because Three is four cards after Queen – Queen, King, Ace, Two, Three. A chart is given below.
| Foundation | Sequence of Cards in Foundation Pile | |||||||||||
| Ace | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Jack | Queen | King |
| 2 | 4 | 6 | 8 | 10 | Queen | Ace | 3 | 5 | 7 | 9 | Jack | King |
| 3 | 6 | 9 | Queen | 2 | 5 | 8 | Jack | Ace | 4 | 7 | 10 | King |
| 4 | 8 | Queen | 3 | 7 | Jack | 2 | 6 | 10 | Ace | 5 | 9 | King |
The suits are completely irrelevant in Calculation. You can play a Jack of Diamonds the same as a Jack of Spades.
Notice that every row ends with a king. At the end of the game, if the game has been won, every foundation pile will end with a king, and all the cards will be in the foundation piles.
As stated above, every card from the stock pile must be played once it is dealt. It must either be placed in a foundation pile or in one of the four waste piles on the tableau. Once a card is placed in any pile, it cannot be removed, with the exception that the top card of one of the four waste piles can be put into a foundation pile in the proper sequence. You cannot move cards between waste piles on the tableau. Even if a waste pile is empty, you can only move cards into that pile from the stock pile.
Any card within a waste pile must stay in the waste pile until all the cards that have been placed in the waste pile on top of it have been moved to the foundation piles. This means that cards often become “trapped” under other cards that can not be played. Having a large amount of cards “trapped” in the waste piles is the main cause of losing the game.
When a card appears in the stock pile that cannot be played in any of the foundation piles, it is important to choose wisely which waste pile to put it into. We will discuss this more below in the Common Strategies section.
Furthermore, a card may appear in the stock pile or as the top card of a waste pile (if the card on top of it has been played in a foundation pile) which can be used in the next in the sequence of two or more foundation piles. It is entirely up to the player which pile they choose to put the card into, and this is one of the many ways that strategy becomes so important in the playing of this game.
One of the main strategies for Calculation is to build “reverse” sequences in the waste piles on the tableau. This means trying to put cards in a specific waste pile in the opposite order that you need them so that when you get to that point in a foundation pile, you can just put all the cards up one after another. For example, a reverse sequence for the end of the Four foundation pile would be King – Nine – Five – Ace – Ten. If you put the cards in that order, the Ten will be on top of the tableau pile. Then, when you get to a Six in the Fours foundation pile, you can put, in order, Ten – Ace – Five – Nine – King. Even if you do not have every card in the sequence, placing them in order without extra cards in between will ensure easier play once that section of the foundation pile is ready to be played.
Unfortunately, this strategy of reverse sequencing can be difficult, as you must play every card from the stock pile and thus are dependent on them being in an order that allows this strategy. Some players will thus continue the reverse sequence but “skip” cards that have not appeared, solely so that they can place a stock pile card in the most strategic waste pile. In the example given above, if your waste pile is currently King-Nine-Five, and a Ten appears, it may be strategic to still put it in this pile, knowing that an Ace may later appear, and you are not blocking cards lower in the pile (you will still need the cards in this order).
Overall, however, you want to try to build your piles in a way that cards don’t become “stuck” lower in the pile. As you are learning to play the game, you may want to keep a chart nearby so that you can remember what order the cards will eventually be played in the different foundation piles.
One tip is that if you can play a card into a foundation pile, do it immediately. If you put it in a waste pile, it may become buried, and then you missed a chance to further the game.
If a card appears in the stock pile that can go into more than one foundation pile, consider carefully which foundation pile to put the card into. For example, if an Eight is drawn and the Two pile currently has a Six while the Four pile currently has a Four, you could place the Eight on either the Two or the Four pile and maintain the sequence. Check to see if you have the next card in either sequence as a top card in one of your waste piles. In this particular example, if one of your waste piles has a Queen as the top card, you may choose to put the Eight on the Four foundation pile so that you can then immediately move the Queen into that foundation pile as well.
Kings are always the last card to go in any of the four foundation piles. This means that very commonly a king will “block” everything below it in one of the waste piles. In this way, it is often fortuitous if kings come up early in the game, so that a player can put them at the very bottom of a waste pile.
If the kings do not come up early in the game, many players will try to keep one of the waste piles reserved for the kings.
Do not place a king in a waste pile that already has many cards in it. It is unlikely that you will be able to move the king before requiring all the cards below it.
If you are playing at home with a standard deck, players often find it useful to arrange the waste piles so that they can see all the cards in the pile, thus allowing them to know which cards have already been played. If you are playing an online version, the game may or may not allow you to see the contents of the waste piles, depending on the settings of the game.
The terms used in Calculation are similar to the terms used in classic solitaire. These include:
Foundation Cards: The foundation cards are the four cards pulled out at the beginning of the game. These are one Ace, one Two, one Three, and one Four.
Foundation Piles: Foundation piles are made by putting cards on top of the foundation cards in the required order. See the “How to Play Calculation” section above for a full chart of these sequences.
Stock: The stock is the pile from which cards are dealt. Every card from the stock pile must be used immediately, either placed in a foundation pile or a waste pile, before the next card can be dealt.
Tableau: This is the area where the game is played. It is also sometimes called the “board”.
Waste piles: The four piles in the playing area where you can put cards that are not yet ready for the foundation piles.
If you completely master Calculation, there are two variations that are even more difficult. In one variation, players will not pull out the foundation cards at the beginning of play. Instead, they must wait until they appear in the stock pile.
In another variation, there are only three empty waste piles on the tableau rather than four. This restricts the options on where to place cards and thus makes the game more difficult.
On the other hand, there are some online versions that will allow you to start with a certain number of cards already in the foundation piles. This makes the game much easier to win.
Q: Do you use the jokers
A: No, the jokers are not used in Calculation.
Q: This is hard! Is it just not winnable?
A: There are some games you just can’t win. However, Calculation in generally is solvable; it simply requires a great deal of strategy and skill.
Q: I didn’t mean to do that! Can I take back a mistake?
A: If you’re playing at home alone, that’s up to you. Online versions usually don’t let you undo a mistake.
Q: I want to play! Where can I play Calculation online?
A: You can find Calculation and many other versions of Solitaire at www.playsolitaire-online.com
Calculation is an extremely difficult version of solitaire, requiring skill, strategy, and planning. If you think you are up to the challenge, try your hand here.