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Tea Party
Inventor: Clark Daniel
Rodeffer, 2001
Ranks: Two
Sowing: Single laps
Region: USA


Tea Party is a two-player game of unequal forces by Clark Daniel Rodeffer, November 2001. Submitted as a first entry for the 2002 Game Design Competition sponsored by About Board Games, the Strategy Gaming Society and Abstract Games Magazine, 2001.

Overview

Tea Party is a small three-dimensional single lap mancala game of unequal forces playable with items likely to be found around the house. In Tea Party, one player controls the movement of the counters, while the other player controls the the movement of the pits. Despite these different modes of play, the object for both players is, as in other mancala games, to capture the most counters.

Equipment

  • Two players designated Cream and Sugar,
  • A four-place tea set, including four teacups, four saucers, one cream pitcher and one sugar bowl (the kettle may be left to simmer),
  • Twenty-three sugar cubes to use as counters, and
  • A cozy table for two.

Preparations

Players decide between themselves by some fair method who will be Cream and who will be Sugar. Cream begins the game with all four cups, all four saucers and the cream pitcher. Sugar begins the game with the sugar bowl and all twenty-three sugar cubes. Cream and Sugar use the cream pitcher and sugar bowl, respectively, to store sugar cubes captured during the second phase of play, Clearing the Table.

For the rest of these instructions, the following ASCII drawings will be used:

   Figure 1.
   ---------
   * Saucer          \_ _ /
   * Inverted Saucer / - -\
   * Cup              c[_]
   * Inverted Cup     c[-]
   * Cream Pitcher    c[_/
   * Sugar Bowl        (_)

The following is an example of how a Tea Party game in progress might appear:

   Figure 2.
   ---------
   2H \_ _ / 8     c[_]  2   c[_/ 0
   2L  c[_]  2    \_ _ / 1
      
   1H  c[_]  0     c[_]  4
   1L \_ _ / 1    \_ _ / 5    (_) 0
          
         A           B

The numbers following a drawing represent the number of sugar cubes in each saucer, cup, sugar bowl or cream pitcher. The numbers and letters along the left and bottom are a coordinate system we'll use to designate example plays: ranks 1 and 2, files A and B, and levels High and Low. For example, the saucer with eight sugar cubes in the upper left is at A2H.

Setting the Table

The first stage of play is called Setting the Table. Beginning with Cream, players alternate between Cream placing cups and saucers onto the table and Sugar dropping sugar cubes into any open saucer or cup. No captures may be made while Setting the Table, and the following rules apply:

Cream

  • May place either a cup or a saucer (open end up) directly onto the table to form any unfilled element of a two by two by two array space, or
  • May place a cup (open end up) on top of a previously played saucer that rests directly on the table, or
  • May place a saucer (open end up) on top of a previously played cup that rests directly on the table, but
  • May not place a cup on top of another cup, and
  • May not place a saucer on top of another saucer, and
  • May not place either a cup or a saucer open end down, and
  • May not place a cup or saucer directly onto the table in such a way as to increase any dimension of the array space beyond two.

In other words, Cream is restricted to a two by two by two space, but may fill it in any order, as long as cups are paired with saucers and they are all played open end up. The following ASCII drawings show some legal and illegal plays for Cream while Setting the Table:

   Figure 3.
   ---------
  c[_]    Legal: cup paired with saucer and
 \_ _ /   both played open end up
  
 \_ _ /   Legal: saucer paired with cup and
  c[_]    both played open end up
  
 \_ _ /   c[_]  Legal: cups paired with
  c[_]   \_ _ / saucers, all are
                played open end
  c[_]    c[_]  up and fit into a
 \_ _ /  \_ _ / two by two by two
                space
       
 / - -\   Illegal: saucer may not be played
  c[_]    upside down while Setting
          the Table
        
  c[-]    Illegal: cup may not be played
 \_ _ /   upside down while Setting
          the Table
        
 \_ _ /   Illegal: saucers must always be
 \_ _ /   paired with cups
          
  c[_]    Illegal: cups must always be
  c[_]    paired with saucers
           
  c[_]    Illegal: all pieces must fit into
 \_ _ /   a two by two by two space
  c[_]
        
 \_ _ /    c[_]
  c[_]    \_ _ /    \_ _ /    c[_]
         
  c[_]    Illegal: all pieces must fit into
 \_ _ /    a two by two by two space

Sugar

  • May drop from one to three sugar cubes into any saucer in play, or
  • May drop from one to three sugar cubes into any uncovered cup in play, but
  • May not drop any more sugar cubes into a cup that has been covered with a saucer (even if that cup already contains some sugar cubes), and
  • Must, on the final turn during Setting the Table, drop all remaining sugar cubes into any one saucer or uncovered cup, even if doing so means that one or more other containers remain empty.

In other words, Sugar can drop from one to three sugar cubes into any open container. (Anyone who makes more than three sugars with tea could quite fairly be accused of having a sweet tooth.) Then, on the last play of Setting the Table, Sugar puts all of the remaining sugar cubes into a single open container.

Clearing the Table

Once the table has been set, the second stage of play, Clearing the Table, begins. In this stage, Cream and Sugar each use different methods to try to capture sugar cubes, storing them in the cream pitcher and sugar bowl, respectively. Since there are only twenty-three sugar cubes available for capture, the first player to capture at least twelve sugar cubes wins. Again, Cream starts, then Sugar and Cream take turns. The following rules apply while Clearing the Table:

Cream

  • May invert any empty cup or saucer, or
  • May exchange one cup for an orthogonally adjacent cup, or
  • May exchange one saucer for an orthogonally adjacent saucer, or
  • May exchange a cup with the saucer beneath it, or
  • May exchange a saucer with the cup beneath it, or
  • May pour one sugar cube from the cream pitcher back into a open cup or saucer, but
  • May not invert a cup or saucer that contains any sugar cubes, and
  • May not exchange containers that are only adjacent along a diagonal, and
  • May not make any exchange that would result in two cups or two saucers being paired together.
  • If a move causes any sugar cubes to become trapped inside a cup closed on top by a saucer, or on a saucer closed on top by an inverted cup, those sugar cubes are captured and stored in the cream pitcher.

Examples:

   Figure 4.
   ---------
   2H   \_ _ / 8     c[_]  2   c[_/ 0
   2L    c[_]  2    \_ _ / 1
   
   1H    c[_]  0     c[_]  4
   1L   \_ _ / 1    \_ _ / 5   (_) 0
   
            A           B

Cream has several legal moves from this position, which is typical for the beginning of Clearing the Table. Cream could invert the cup at A1H to prevent Sugar from capturing the 8 sugar cubes in A2H and simultaneously capture the 1 sugar cube at A1L:

   Figure 5.
   ---------
   2H   \_ _ / 8     c[_]  2   c[_/ 1
   2L    c[_]  2    \_ _ / 1
    
   1H    c[-]  0     c[_]  4
   1L   \_ _ / 0    \_ _ / 5   (_) 0
   
           A           B

From Figure 4., Cream could exchange the cups at B1H and B2H. No capture is made during this exchange, but Cream may find such an exchange to be a useful tactic in defending against captures:

   Figure 6.
   ---------
   2H   \_ _ / 8     c[_]  4   c[_/ 0
   2L    c[_]  2    \_ _ / 1
   
   1H    c[_]  0     c[_]  2
   1L   \_ _ / 1    \_ _ / 5   (_) 0
   
           A           B

Cream may not, however, exchange cups A2L and B2H because they are not orthogonally adjacent.

Given the position in Figure 4., another possibility for Cream would be to exchange the cup at B2H with the saucer beneath it at B2L. In this case, two sugar cubes are captured by closing the cup beneath the saucer. (Note that the two sugar cubes in A2L are still safe, since the saucer at A2H was placed there while Setting the Table.) The result of this move would be:

   Figure 7.
   ---------
   2H   \_ _ / 8   \_ _ / 1   c[_/ 2
   2L    c[_]  2    c[_]  0
   
   1H    c[_]  0    c[_]  4
   1L   \_ _ / 1   \_ _ / 5   (_) 0
 
          A          B

Cream's one exception to the rule about controlling the cups and saucers rather than the sugar cubes directly is the defensive maneuver of returning a single sugar cube to an open empty container. Unlike when Sugar drops the last sugar cube into an empty cup or saucer, when Cream does this, no pieces are captured, but it leaves one less empty container for Sugar to use in making a capture. Consider how Cream could pour a sugar cube into cup A1H as a defensive follow-up move from the position shown in Figure 7.:

   Figure 8. 
   ---------
   2H   \_ _ / 8   \_ _ / 1   c[_/ 1
   2L    c[_]  2    c[_]  0
   
   1H    c[_]  1    c[_]  4
   1L   \_ _ / 1   \_ _ / 5   (_) 0
   
          A          B

The value of such a defensive move will become more clear in next section.

Sugar

  • May remove all of the sugar cubes from any one open container and redistribute them one at a time clockwise into open coplanar containers. (Closed and/or inverted containers, including saucers that have inverted cups on them, are skipped.) The redistribution plane must include and start immediately after the source cup or saucer, but may be in any one of the orthogonal planes.
  • If the last sugar cube falls into an empty cup or saucer, any sugar cubes in the Right Hand Rule adjacent container are captured and stored in the sugar bowl, and
  • If Sugar made a capture using the next-to-last sugar cube in play, then Sugar captures the last sugar cube as well.

If all this seems less than obvious, sit back, take a sip of tea, and trust than it's a lot easier than it sounds. Here's a detailed example with diagrams:

   Figure 9.
   ---------
   2H   \_ _ / 8     c[_]  2   c[_/ 0
   2L    c[_]  2    \_ _ / 1
   
   1H    c[_]  0     c[_]  4
   1L   \_ _ / 1    \_ _ / 5   (_) 0
  
          A           B

Suppose Sugar wants to redistribute the five sugar cubes in saucer B1L. There are three legal ways to do so as shown below.

First, they could be distributed clockwise in the B plane as B1H B2H B2L B1L B1H. The last sugar cube drops into cup B1H, but since that cup wasn't empty, no capture takes place. The position after this distribution is shown below:

   Figure 10.
   ----------
   2H   \_ _ / 8     c[_]  3   c[_/ 0
   2L    c[_]  2    \_ _ / 2
   
   1H    c[_]  0     c[_]  6
   1L   \_ _ / 1    \_ _ / 1   (_) 0
 
          A           B

Second, given the position in Figure 9, the five sugar cubes in B1L could be distributed clockwise in the 1 plane as A1L A1H B1H B1L A1L. Again, the last sugar cube drops into saucer A1L, but since that saucer wasn't empty, no capture takes place. The position after this distribution is shown below:

   Figure 11.
   ----------
   2H   \_ _ / 8     c[_]  2   c[_/ 0
   2L    c[_]  2    \_ _ / 1
 
   1H    c[_]  1    c[_]  5
   1L   \_ _ / 3   \_ _ / 1   (_) 0
      
          A          B

Third and finally, given the position in Figure 9., the five sugar cubes in B1L could be distributed clockwise in the L plane. Since the cup at A2L is covered with a saucer, that container is skipped. (Saucers with open end up cups sitting on them are not covered, but any cups with saucers sitting on them, whether the saucers are inverted or not, are covered, as are saucers with inverted cups sitting on them.) Note that clockwise with respect to the L plane looks like counterclockwise when viewed from above. This is necessary to make the Right Hand Rule consistent. So the distribution from B1L would be B2L A1L B1L B2L A1L. The last sugar cube drops into saucer A1L, but again, since that saucer wasn't empty, no capture takes place. The position after this distribution is shown below:

   Figure 12.
   ----------
   2H   \_ _ / 8     c[_]  2   c[_/ 0
   2L    c[_]  2    \_ _ / 3
      
   1H    c[_]  0     c[_]  4
   1L   \_ _ / 3    \_ _ / 1   (_) 0
  
          A           B

Referring again to Figure 9., unfortunately, in choosing to redistribute the five sugar cubes in B1L, Sugar overlooked a chance for a high-scoring capture. Suppose instead that Sugar had chosen to distribute the one sugar cube in A1L in the 1 plane as A1H. Since the cup at A1H was empty when the last sugar cube was dropped into it, all of the sugar cubes in the Right Hand Rule adjacent container are captured. (This is not the place for a lengthy discourse on the topic, but suffice it to say that, in some cultures, the use of the right hand is considered polite.) To determine which sugar cubes to capture, Sugar puts the right hand near the last container (in this case A1H) and curls the fingers in the clockwise plane of distribution (in this case the 1 plane) and looks which adjacent container the right thumb is pointing to (in this case, A2H). Sugar captures all eight sugar cubes in saucer A2H. The position after this is shown below:

   Figure 13.
   ----------
   2H   \_ _ / 0     c[_]  2   c[_/ 0
   2L    c[_]  2    \_ _ / 1
     
   1H    c[_]  1     c[_]  4
   1L   \_ _ / 0    \_ _ / 5   (_) 8
      
          A           B

From Figure 13., a great follow-up move by Sugar, distributing the one sugar cube from A1H in the A plane, would capture all five sugar cubes in B1L for an immediate win.

   Figure 14.
   ----------
   2H   \_ _ / 0     c[_]  2   c[_/ 0
   2L    c[_]  2    \_ _ / 1
    
   1H    c[_]  0     c[_]  4
   1L   \_ _ / 1    \_ _ / 0   (_) 13
   
          A           B

Right Hand Rule Reference Table

   Last Container  Distribution Plane  Target
   --------------  ------------------  ------
A1L ................... A .............. B1L
                        1 .............. A2L
                        L .............. A1H
A1H ................... A .............. B1H
                        1 .............. A2H
                        H .............. A1L
A2L ................... A .............. B2L
                        2 .............. A1L
                        L .............. A2H
A2H ................... A .............. B2H
                        2 .............. A1H
                        H .............. A2L
B1L ................... B .............. A1L
                        1 .............. B2L
                        L .............. B1H
B1H ................... B .............. A1H
                        1 .............. B2H
                        H .............. B1L
B2L ................... B .............. A2L
                        2 .............. B1L
                        L .............. B2H
B2H ................... B .............. A2H
                        2 .............. B1H
                        H .............. B2L

Variants

While not part of the standard Tea Party game, any of the following additional rules can be added for variety.

Whistle Stop Variant

For those who like an even shorter game, leave the kettle to simmer, and play as usual. When the kettle whistles, the game ends immediately, and whoever has captured more sugar cubes is declared the winner.

Pinky Extension Variant

Games of unequal forces are not easy to balance, so if you find that Cream wins too many games, the Pinky Extension Variant can be used in addition to the standard Right Hand Rule. The only difference is, when the last sugar cube is dropped into an empty container, the sugar cubes in the cup or saucer that the extended pinky would point to (always the next clockwise container in the current plane of rotation) are captured in addition to any that would be captured by the Right Hand Rule.

Tea For Two Couples Variant

Four players can participate in teams with partners sitting opposite each other. Conversation topics of social interest are allowed, of course, and even expected. But out of courtesy, players should refrain from offering game-related advice or criticism to their partners.

Spotted Sugar Cubes Variant

For those who like a bit more chance, standard six-sided dice may be used in place of sugar cubes. (This also helps keep the fingers from getting sticky when handling the sugar cubes.) When all twenty-three dice have been captured, Cream and Sugar roll them out of their cream pitcher and sugar bowl. The player with the higher total number of pips showing on the dice (which may be different than the player with the most dice) wins.

References

Rodeffer, C. D. 
Tea Party (e-mail to Yahoo's Mancala Games mailing list). June 16, 2004.

Copyright

© Wikimanqala.
By: Clark D. Rodeffer
Under the CC by-sa 2.5 license.

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