How to Play the Twenty-Four Card Game

Twenty-Four is a card game originally developed in Shanghai, China, which can be both fun and educational for all ages. The game is sometimes used in Mathematics classes as it reinforces the basic arithmetic operations but can also be challenging and very competitive.

The standard game is designed to be played by four players, but variations are provided below for differing number of players. The Twenty-Four card game uses the standard deck with all Jacks, Queens and Kings removed. This makes a 40 card deck. The cards in the deck have no relative ranking, however each card does have a numerical equivalent value. This value is 1 for an Ace and the number marked on the card for all other cards remaining in the deck.

Before beginning, seating positions and the first dealer should be determined. Any method can be used, but the most common is for all players to draw a card from the deck. The player drawing the highest card takes the first choice of seat at the table, the next player the next choice of seats and so on until every player is seated. The player drawing the highest ranked card of all becomes the first dealer. For each subsequent hand, the deal rotates around the table from player to player in a clockwise direction.

Once the first dealer is determined, he should thoroughly shuffle the cards and the player at his left cuts the deck. After the cut, the dealer then begins distributing the cards to the players starting with the player to his immediate right. He deals the cards one by one in clockwise direction around the table, face down in a pile in front of each player. He continues dealing this way in a counter-clockwise direction until the entire deck has been dealt, with each player having a total of 10 cards.

Once the hand's have been dealt the players each square up the pile in front of themselves in preparation for gameplay. Each player should not see any of cards in his own pile or any other player's pile until played. At a signal from the dealer, all four players simultaneously reveal the top card of his pile in front of himself. The players then mentally attempt to determine some type of mathematical equation in which they can form these four numbers to equal exactly 24. They may use any combination of parentheses as well as the four basic mathematical operations to do this; Addition, Subtraction, Multiplication and Division. Players are usually required to perform all the calculations mentally, with paper and pencil usually disallowed. The first player to determine a method to create 24 with some combination of the four exposed cards should knock on the table. He then details the equation and, if his equation does in fact create 24, he then collects all four cards placing them to his side. If he is incorrect, the other players may continue to attempt to find such an equation. The incorrect player may not make further guesses for these particular cards. If no player has found such an equation after a set amount of time (say five minutes) or all players agree there is no possible equation for those particular four cards, the cards are set aside in a discard pile, won by no player.

Each of the four numbers must be used in the equation and no other numbers are allowed. Although the final total must be exactly 24, the intermediary results in the equation may be anything (including fractions). For example, the cards 2, 4, 10 and 10 can form 24 using the following equation: (2 + 4 /10) * 10. Some combinations of four numbers may have no solution, for example, the cards Ace (1), Ace (1), 5 and 9 have no combinations using these standard arithmetic operations that can create 24. Still others have multiple ways in which the numbers can be arranged with the operators to create 24. Any one of the possible solutions for the combination of numbers is acceptable.

After the cards are either won or set aside, the dealer then again gives the signal and all players expose the next top card in their piles and the players again attempt to form an equation that equals exactly 24. This continues until all the cards have been played. At this time, each player counts the cards he was able to win during the hand and the player with the most cards is declared the winner. If two or more players tie for the same number of cards, these players tie for the win. Often, multiple hands are played with each player keeping a sum total of points won during the hand. After a set number of hands are played, the player with the highest point accumulation is declared the overall game winner.

Example of valid combinations equalling 24

There are several proprietary games which have been developed using the same principal. In most of these versions, however, the cards are already prepopulated with four numbers that are known to have at least one solution. Thus, only one card is dealt for each round, with the players attempting to find an equation using the four numbers pre-printed on that card. However, most of these are no longer in common circulation.

Variations and Optional Rules

Additional Operators: Some players prefer to include additional allowed operators in creating a total of 24. The most common additional operators allowed are exponents, roots and factorials. These operators can be combined with any of the usual operators as well as any combination of parenthesis. This version is sometimes done for veteran players of the game, and increases the number of combinations that have at least one valid solution.

Face Cards: A common variant is the inclusion of Face Cards to the deck. In this case, each of these cards has an equivalent value, as shown:

Card	Numeric Equivalent
Jack	11
Queen	12
King	13

In this variant each player would then receive three additional cards each hand. This change can also be combined with any of the other variants of the base game.

One Pile: In the original version of this game, no cards were dealt to the players. Instead, the dealer himself would possess the entire shuffled, face-down deck. He would then quickly deal four face up cards to the center of the table and all players (including the dealer) would then attempt to create an equation equaling 24. In all other aspects this version is played identically to the version described above.

Alternate Totals: Regular veterans of this game can sometimes begin to memorize the specific combinations of cards that can be arranged to equal 24. Thus, some players will make the game fresh by occasionally changing the required total. Thus, on a particular hand, the total might be 23, 26, 50, 34 or any other agreed upon total. This total to be used for the current hand should be clearly written down to prevent any confusion during the hand.

Alternatively, the total to be used for the hand can be dynamically changed for every hand. The cats have developed the following simple method to change this total for each hand. Before each hand begins, the deck should be thoroughly shuffled. Eight cards are then dealt face up from the deck. The two highest ranked cards and two lowest ranked cards should be removed from the set. Then, the remaining cards should be summed and this total will be the requirement for the next hand. This total should be recorded somewhere for all players to see. The eight removed cards are then shuffled back into the pack and the hand dealt as normal.

No More Cards: Another variant is for the first player who successfully announces a valid combination of 24 from the exposed cards to place the four cards at the bottom of his own pile. If a player runs out of cards he remains in the game but does not contribute a card on his turn. In this case, if there are only two players who actually have cards, each of these players exposes two cards in front of himself. If there are three players (of the four) who currently have cards, the player to the immediate right of the player without cards places two and each other player exposes one card. If a player without cards is the first to announce a correct total, he takes the four cards and creates a new, small pile in front of himself. The game continues until only one player has cards remaining, with that player declared the winner.

Last Slap: In this variant, the first player to slap the table does not announce his equation. Instead, the hand continues until three of the four players slap the table. The fourth player, who has not yet slapped the table on the current play, then selects one of the other three to announce his equation. If that player is correct, the player who did not slap the table must add them to the bottom of his own current stack. However, if the player is unable to provide a valid equation equaling 24, he must take the four cards and add them to the bottom of his own stack. If all players agree there is no solution (with no player slapping the table), each player takes his card and adds it back to the bottom of his own stack. If only one or two players slap the table after a sufficient time has passed, indicating those players believe they have discovered a solution, the remaining players decide amongst themselves which of the slapping players should be the one to indicate his solution. If the answer is incorrect, as before the player with that incorrect solution must take all four cards back into his own hand, however if that player is correct, the other players must take the cards into their hands evenly distributed, with any odd cards left on the table (turned face-down) and will be added to the hand of the next player who must take cards from the table. The first player to exhaust his entire stack is declared the winner of the game.