Logic

• Introduction
• Players and Cards
• Deal and Layout
• Play
• Declaring
• Variations
• Strategy and Tactics
• Example Game

Introduction

This game from the San Francisco Bay area of the USA, also known as "Logic: THE card game", was explained to me by David Wu. It is a game of questions, answers and deduction, in which the object is to discover or guess and correctly declare the locations of all the cards. It has some affinity with the South Indian game Literature: although the actual game mechanism is different, the objective of finding out the locations of cards by a process of logical reasoning is similar. It seems likely that Logic was inspired at least in part by Literature, especially since some of the Logic players also play Literature, which they know by its alternative name Canadian Fish.

Players and Cards

There are four players in fixed partnerships, each player sitting opposite their partner. The game uses a 24-card deck consisting of the cards from Ace (low) to Queen (high) in one red and one black suit taken from a standard 52-card deck (traditionally hearts and spades are used). It is also useful to have an easily grabbable object, such as a water bottle, that is placed in the centre of the table (see declaration below).

As described by David Wu the game is dealt and played counterclockwise and the description below assumes counterclockwise play, although he believes that some other groups play it clockwise.

Deal and Layout

Since there is a slight advantage in playing first, the first dealer is chosen at random. Any player draws a card from the shuffled deck. If it is an Ace, 5 or 9 the drawing player deals first; if it is a 2, 6 or 10 their right hand opponent deals first; if it is a 3, 7 or J the drawing player's partner deals first; if it is a 4, 8 or Q the drawing player's left hand opponent deals first. In subsequent games the players take turns to deal in anticlockwise order.

The cards are shuffled and the dealer deals six cards face down to each player. Each player independently looks at their cards, arranges them in ascending order from left to right and places the cards in a row in front of them face down on the table. A player who has both cards of a number can choose in which order to place them.

When all players have laid out their row of six cards, each player turns all their red cards sideways so that all players know which cards are red and which cards are black. For example if your six cards are 6 4 J 6 5 A you may arrange them in the order A 4 5 6 6 J and then after you turn the red cards your row will look like this:

Alternatively you could have placed the 6 to the right of the 6 in which case the second and fifth cards of your row would be horizontal.

Players are not allowed to see the arrangement of other players' rows before deciding on their own arrangement: this is the reason that red cards are turned only after everyone has chosen the order of their row. (Of course this is only significant when players have pairs of equal cards: if all your cards have different ranks you have no choice in how to arrange them.)

Play

The players take turns to play in anticlockwise order, beginning with the dealer who has the first turn. Each turn consists of three steps.

1. The Show

The partner of the player on turn privately shows one of their face down cards to the player on turn. The player on turn is not allowed to give their partner any hint about which card they would like to see. The opponents are allowed to know which of the six cards was shown, but not its value. After showing the card, the partner returns it to their row face down.
Players may replace their shown cards slightly offset in their row to help their team to remember which cards have been shown, though this may also help the opponents. A player who does this must do it consistently - players are not allowed to use card offsets to convey extra information.
The partner of the player on turn may choose to omit this step and not show any cards, if for example the player on turn already knows all their cards, or of necessity if all their cards are already face up.

2. The Guess

The player on turn must guess the identity of one of the opponents' face down cards, specifying one card in their layout and stating its rank. (If both opponents have all their cards face up then player on turn cannot guess and must declare at this point - see below.)

3. The Reveal

If the guess is correct the opponent has to flip the correctly guessed card face up. If it is wrong the player on turn must flip one of their own face down cards face up. If the player on turn has no face down cards then an incorrect guess has no consequence for them.

Note that in step 2 it is legal to deliberately make a guess that you know to be incorrect, for example by guessing that the opponent's card you select is a card that is in your own row or a card that your partner has shown you or a card that is face up elsewhere. You might do this in order to mislead the opponents or because you actually wish to expose one of your cards to help your partner.

Declaring

At any time, any player may end the game by declaring. The declaring player must first turn all their own cards face up and then state the identity of each of the face down cards in front of the other three players. As each card is identified it is turned face up. If the declarer correctly identifies all the cards, the declarer's team wins the game. If the declarer makes any mistakes - the turned up card is not what the declarer said it was - the declarer's team loses the game.

The player to the previous dealer's right then shuffles the cards and deals the next hand.

Note you really may declare at any time, including but not limited to: after your partner shows you a card in step 1, after either team reveals a card in step 3, or even in the middle of either team making a guess (step 2), after the player on turn guesses a card but before the other team has responded as to whether the guess was correct or incorrect (step 3). Especially in the last case, there will often be a rush by players from both teams to reveal and be the first to declare, so it is useful to play with an easily grabbable object in the centre of the table, such as a water bottle. To declare, you must say "Declare" or something similar to that effect and grab the object in the middle, then reveal all of your cards to have the right to declare.

There is no fixed length for the session, which may end whenever the players agree to do so. There is no scoring as such, but players normally keep a tally of how many games each team has won.

Variations

Different card backs

Some players prefer to use a red suit from one deck and a black suit from another deck with a different back design. This ensures that players don't make a mistake when orienting their red and black cards at the start of the game. However, in this case it is necessary for players to conceal their cards completely when arranging their rows at the start of the game so that other players do not get any hint of the other players' arrangements until they have committed to the arrangement of their own cards.

Agreeing a draw

During a declaration, after revealing their own cards, the declarer usually names the cards that their partner has already shown them, then moves onto the rest of partner's cards or opponent's cards that are easily deducible, and finishes with a guess as to the position of the last two or three cards, if necessary. If the game comes down to a 50-50 guess by the declarer about the positions of the last two cards, both teams can agree to record the game as a draw instead of leaving it up to fate (or psychology and mind reading!) as to whether declarer gets the positions of the two remaining cards right.

Logic with Jokers

David Wu recommends the following variant for players who have mastered the basic game and are ready for a more difficult challenge.

28 cards are needed: two full suits of 13 cards from Ace (low) to King (high) plus two Jokers. Seven cards are dealt to each player. A Joker can be placed in any position in the owner's row. During your partner's turn you can show a Joker to your partner as usual, and you can also guess an opponent's card as a Joker during your guessing phase.

There are two versions:

1. Jokers can be placed upright or sideways at the player's choice. In this case if both Jokers happen to be oriented the same way there will appear to be 15 cards of one colour and only 13 of the other.
2. If your deck has distinguishable Jokers, you can treat the red or coloured Joker as a red card which must be placed sideways and the black or uncoloured Joker as a black card which must be placed upright, so that there are always 14 cards of each colour.

Note that rather than showing a Joker to your partner there is also the possibility to indicate to your partner where it is by showing cards that would imply an illegal arrangement in the basic game. For example, if you have an Ace you can place the Joker at the very left in the same orientation as the Ace next to it, so that when you show the Ace to your partner they immediately know about your Joker because no other card in the same suit could be in that position. Similarly you could place the Joker between a pair of equal cards or between two consecutive cards of the same suit, so that when you show both the flanking cards your partner knows you have a Joker between them. Of course the opponents may catch on to this tactic and thereby guess the location of your Joker.

Strategy and Tactics

David Wu provides the following advice for the basic game (without Jokers).

1. Often it matters in which order you place your pair. For example, if you are dealt A, A, 2 and arrange your cards from the left as A, A, 2, once you show your partner the 2 your partner knows for sure what your two cards to the left are, whereas with the other arrangement, your partner could not be sure if the red card was the Ace or the Deuce. Similarly, with A, 2, 2, rearranging it as A, 2, 2 gives more efficient information. The downside is that if the card you show to your partner gets guessed by the opponents then the other two cards will be all but revealed. So it is a double edged sword.

2. Your first show can sometimes be very powerful in terms of information. For example, if your lowest card is an unpaired 5 and you start by showing it to your partner, your partner knows you have no cards ranked 4 or lower and can guess those low cards of the opponents without fear of accidentally guessing your cards, which is almost always something to be avoided in this game. Again, the downside is by starting off by showing this 5 from the very left edge, your opponents will rightfully suspect that this card is unusually high, and may have an easier time guessing it. Once it is guessed, now your opponents have the same information your partner does, which could jeopardize the safety of your partner's low cards. A weaker variation of this is when you have some high red cards, but your highest black card is a 6. By showing the 6 to your partner, your partner knows you do not have any of the black cards ranked 7 or higher, and can focus on teasing out those high black cards from the opponents.

3. There is a concept called "protection". Cards held by you and your partner are said to "protect each other" or "have good protection" when they create ambiguity about their actual positions for your opponents. For example, if your two highest cards are the 9 and Q and your partner's two highest cards are the 10 and J, then these cards protect each other well, since from your opponents' perspective, any one of 6 possible permutations could be the actual permutation of the cards. They might need to waste several guesses to narrow down the possibilities. On the other hand, if your two lowest cards are the A and 2 and your partner's two lowest cards are the A and 2, then these cards do not protect each other at all, since it will be readily apparent to the opponents what these cards are once they have exchanged information about their own low cards. For this reason, when it comes time for your team to reveal a card after an incorrect guess, you should prefer to reveal a card with bad protection and keep your opponents in the dark about cards with good protection.

4. Since only one person from your team needs to successfully declare in order to win, you should usually play so that one team member gets maximum information. This means that if you were dealt many "bad" cards, such as outside cards like A, 2, J, Q, with little protection from your partner, you should play a supporting role to help your partner be the first to get enough information to declare. You should undertake all the risky guesses that stand to gain lots of information for your team, since you will only have to reveal a "bad" card if you guess incorrectly, while your partner should make safe guesses in order to not risk revealing their "good" cards to the opponents. This is a prime example of when later in the game you can use the "guess wrong on purpose" tactic. If you have a card that the opponents probably already know, but would be a key card for your partner to see, you can guess wrong in order to reveal it sooner than if you were to wait until your partner's next turn to show them, as a declaration from either team could be imminent.

5. Beginners often wait until they know every card's location with obvious certainty before declaring, which is usually much too late. Most of the time you can rely on sound logical deductions, or even speculative inferences from the cards your opponents have chosen to show each other, as well as records of incorrect guesses by both sides, to help you figure out the correct layout of the cards. For example, let's say you have come down to a 50-50 guess between the last two hidden cards, which are the 4 and the 5. You see that your left hand opponent's lowest three cards are the A, 2, and 3, which are followed by a hidden card. Moreover, you just so happen to remember that, on your right hand opponent's first turn, your left hand opponent chose to show the 3. Aha! If your left hand opponent had the 4, wouldn't they have shown that card first, so as to give more information? Therefore, you conclude that your left hand opponent must have the 5, and it is your right hand opponent that has the 4. So you guess that way, and most of the time, you would be right. Of course, a tricky left hand opponent may very well have set a trap for you, by making what would normally be an inferior play of showing the 3 from 2 3 4, and by guessing this way, you will have walked right into it! This is what makes this game so exciting as a true psychological battle.

6. Suppose you know that your opponents are about to find out the location of all the cards, and that only your 7 and your partner's 8, which are your team's last two cards protecting each other, are standing in their way. It is your opponent's turn, and they decide to guess your card. Regardless of whether they guessed right or wrong, you must not tell them so! For if you do, then they will declare with certainty, and your team will surely lose. Wait, but surely the rules don't just let you sit there in silence and stall out the game, right? Well remember, the rules say that you can declare at any time. So, without answering their guess, you should grab the object in the center of the table and declare! You may not know the location of all the cards, indeed you might not have even a 10% chance to guess the location of all the cards correctly. Yet in this case, whatever miniscule chance you have at winning the game from your Hail Mary declaration, is better than the guaranteed loss you'll get if you answer your opponent's question as to the location of the 7 and 8 and let them have a 100% declaration. By the way, if you believe your partner has a better chance at declaring successfully, you should just sit there and say nothing. Hopefully, your partner will pick up on your predicament and declare for you, or even better, your opponents might be tricked into declaring early and settling for a 50-50 instead of their much higher chances of winning if they force your team to declare. Of course, if no one else declares, please don't hold up the game any longer. Just declare yourself or answer their guess and hope they somehow mess up when declaring.

Example Game

Here is an actual game recorded by David Wu. They played the version with Jokers (shown as $ in the game record) that can be used as either red or black at the player's choice. In this game both were Jokers placed as red cards.

	Q 7 6 6 4 4 A
3 7 $ 8 8 9 K	Michael Eric                      Vincent David	Q J 10 10 $ 5 5
	A 2 2 3 9 J K

1. Michael shows David #4 (6)
1. David guesses Vincent #7 (Q) as K
1. David reveals #1 A

2. Eric shows Vincent #6 (9)
2. Vincent guesses Michael #1 (A) as A
2. Michael reveals #1 A

3. David shows Michael #3 (2)
3. Michael guesses Eric #7 (K) as K
3. Eric reveals #7 K

4. Vincent shows Eric #1 (5)
4. Eric guesses David #3 (2) as 4
4. Eric reveals #1 3 

5. Michael shows David #6 (7)
5. David guesses Vincent #7 (Q) as Q
5. Vincent reveals #7 Q

6. Eric shows Vincent #2 (7)
6. Vincent guesses Michael #3 (4) as 4
6. Michael reveals #3 4

7. David shows Michael #5 (9)
7. Michael guesses Eric #4 (8) as 8
7. Eric reveals #4 8

8. Vincent shows Eric #5 (10)
8. Eric guesses David #3 (2) as 2
8. David reveals #3 2 

9. Michael shows David #2 (4)
9. David guesses Eric #6 (9) as 10
9. David reveals #2 2

10. Eric shows Vincent #5 (8)
10. Vincent guesses David #7 (K) as K
10. David reveals #7 K

11. David shows Michael #4 (3)
11. Michael guesses Eric #3 ($) as 8
11. Michael reveals #7 Q

12. Vincent shows Eric #3 ($)
12. Eric guesses David #6 (J) as J
12. David reveals #6 J

13. Michael shows David #5 (7)
13. David guesses Vincent #5 (10) as 10
13. Vincent reveals #5 10

14. Eric shows Vincent #3 ($)
14. Vincent guesses David #4 (3) as 6
14. Vincent reveals #6 J

15. David shows Michael nothing
15. Michael guesses Eric #6 (9) as 9
15. Eric reveals #6 9

16. Vincent shows Eric #4 (10) (or was it #2 5? doesn't matter too much)
16. Eric guesses Michael #4 (6) as 6
16. Michael reveals #4 6

17. Michael shows David nothing
17. David guesses Eric #3 ($) as 7

Vincent declares
Vincent knows all of Eric’s cards
Vincent guesses 7, 6, and 9 correctly
Vincent guesses 3 and 4 incorrectly

David & Michael win!