Number Crunchers

Full rules

1. Overview
2. Card values
3. The parts of the layout
4. The four sequences
5. Setup
6. Your turn
7. Free plays
8. No talking
9. When your stock is empty
10. Winning and losing
11. Difficulty
12. Tips for beginners
13. Variants

Overview

Number Crunchers is a cooperative patience for two players: you form one team and win or lose together. (A patience, also called solitaire, is a card game in which you sort a shuffled deck into order.) Together you build four shared piles: 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. Each of you turns up cards from your own stock, and the cards that don't fit yet must go on your own few waste piles. The catch: you may not talk about your plans.

• Players: 2
• You need: one standard 52-card deck, no jokers.

Number Crunchers is a new game written for this site and not yet playtested. It is our own cooperative version of the classic patience Calculation. The number of waste piles is the first thing to tune: if your games are won or lost too easily, change it before anything else (see "Difficulty").

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 in the middle of the table, started with an Ace, a 2, a 3 and a 4 (any suits). They belong to both of you. Each one builds up in fixed steps – see the table below – and ends with a King.
• Your stock: a face-down pile of 24 cards in front of you. Each turn you turn up its top card. Nobody knows which card comes next – not even you.
• Your waste piles: three places in front of you, empty at the start, for cards that can't go on a foundation yet. Spread each pile towards you so that both of you can see all its cards; only the top card (the one placed last) can be played. Only you may put cards on your own waste piles.

The four sequences

Any card of the right rank will do, whatever its suit. Each foundation takes every rank exactly once, so together they take the whole deck.

Setup

1. Take any Ace, any 2, any 3 and any 4 out of the deck and lay them in a row between you, from left to right. They are the foundations.
2. Shuffle the other 48 cards and deal them one at a time, 24 to each player. Put your cards face down in front of you as your stock.
3. Leave room next to your stock for three waste piles. Sit opposite or next to each other, so that both of you can see all the cards on the table.
4. The younger player begins. After that you take turns.

Your turn

1. Free plays, if you like (see below).
2. Turn up the top card of your stock and place it at once: - on a foundation, if it is the next card that foundation needs, or - on one of your own three waste piles – any card may go on any of them, in any order.
3. Free plays again, if you like.

Then it's your partner's turn. You may put a card on a waste pile even if it would fit on a foundation, but it's rarely wise.

Free plays

In your turn – before you turn up your card and again after you have placed it – you may move the top card of any waste pile, your own or your partner's, onto a foundation if it fits there. That uncovers the card below, which may fit too. Make as many free plays as you like.

Cards never move 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.

No talking

During the game you may not talk about your plans: no "I'm keeping this pile for Kings", no "leave that 5 for me", no pointing, no sighing. All foundations and waste piles are face up for both of you, and neither of you knows the next card of any stock – what your partner intends, you have to read from their piles. You may talk about the rules, whose turn it is and how many cards are left in the stocks.

When your stock is empty

The player who began runs out of cards one turn before the other. When your stock is empty, you keep taking turns, but you only make free plays – or pass.

Winning and losing

• You win together when all 52 cards lie on the foundations, each topped by a King.
• You lose when both stocks are empty and no top card of a waste pile fits any more.

Example: The foundations are A♣, 2♥, 3♠ and 4♦, so they need a 2, a 4, a 6 and an 8. Anna begins and turns up the 6♦: it goes on the 3-foundation (3, 6 – now it needs a 9). Ben turns up the K♥. No foundation wants a King yet, so it goes on one of his waste piles; he will keep that pile for Kings, and Anna can see it without a word. Anna turns up the 3♥: the foundations want a 2, a 4, a 9 and an 8, so the 3♥ goes on one of her waste piles. Ben turns up the 2♦ and puts it on the Ace (A, 2). Now Anna's 3♥ fits there: as a free play, Ben moves it from her waste pile onto the A-foundation as well (A, 2, 3). That foundation now needs a 4, and it's Anna's turn.

Difficulty

The budget. What you spend in this game is room on the waste piles. In the patience, one player puts 48 cards on four piles. Here each of you puts 24 cards on three piles – six piles for the team, but each pile takes only its owner's cards, however badly your partner might need the space. In a computer simulation with a simple strategy (play whatever fits, keep Kings apart, cover a card only with one that is needed sooner), the patience alone was won about 2% of the time, Normal about 8%, and Hard only about 0.5% – although Hard gives the team four piles, as many as the patience. So for the same strategy Normal is won about four times as often as the patience, and Hard far less often. In Expert, a fitting card on your partner's pile has to wait for their turn. Humans play much better than this strategy – for the patience, Morehead and Mott-Smith estimated one win in five – so expect better results at the table. The game hasn't been playtested: if you win easily, play Hard; if you keep losing, play Easy or try "Four waste piles each" (see "Variants").

Tips for beginners

• Free plays first. Once you have turned up your card, it must be placed at once – so make every free play before you turn it. One of them may be just what your next card needs.
• Keep Kings apart. As in Calculation, a King on top of a low card blocks that card until a whole foundation is finished. Start a Kings pile with your first King and put later Kings there too. You can't use your partner's Kings pile, so each of you may need one.
• Build descending steps. Try to build waste piles that go down in the steps of a foundation – for example 9, 7, 5 on one pile for the 2-foundation – and cover a card only with one that is needed sooner.
• Watch your partner's piles. Their top cards are free plays for you too. When your card fits two foundations (a 4 may fit both the A- and the 2-foundation), choose the one that lets a waiting top card follow. And before you put a card on a pile, check whether your partner's last play has made its top card fit – play it rather than bury it.

Variants

All optional – agree before you start.

• Four waste piles each: much easier – good for a first game or for younger players.
• No foundations in advance: don't take out an Ace, 2, 3 and 4; deal all 52 cards, 26 each. An Ace, 2, 3 or 4 may start its missing foundation when it turns up or as a free play from a waste pile. Much harder, as in Calculation.