backgammon in education
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Roots of Backgammon in Experimental Education
University of South Florida
A number of games can be traced to ancient beginnings. In education this process may serve to develop understanding of sociql science con- cepts and generalizations as well as develop research skills. Ancient board games and their progeny may be modified for use as multi-player simulations at various levels of abstraction. Backgammon and its history serve as a case in point and further illustrate the notion of man as Homo Lud en s .
A game is often what you make it, and backgammon is no exception. Thousands of Americans and hundreds of thousands of others through- out the world engage in the game. It is played by individuals at all levels of society from prince to pauper. Egyptian President Anwar Sadat finds the game a source of relaxation from the strain of governing a nation, while shopkeepers in the Arab quarter of Jerusalem partake in the game between customers. In the United States, backgammon clubs and socie- ties have been founded. Approximately one hundred such groups are affiliated with the World Backgammon Club (WBC) which was estab- lished by Prince Alexis Obolensky in the mid-sixties [l].
Some play backgammon for the mere enjoyment of the game. There are those who play for both enjoyment and club or tournament cham- pionships. Still others find it a source of wagering. There is no doubt that backgammon can be a serious gambling game. Thousands of dollars may be won or lost in an evening. On the other hand, backgammon may be a learning tool in the classroom.
For young children, the game can be used to improve math skills and assist in understanding sets. However, its greatest contribution in this area lies in the games ability to enhance the understanding of probability
Address correspondence to: Milton Kleg, Suite 307D, College of Education, University of South Florida, Tampo, Florida 33620
Journal of Experiential Learning and Simulation 1, 179-194 (1979) @ 1979 Ann R. Kleg
180 M. Kleg
Milton Kleg, Associate Professor, has been at the University of South Florida since 1970. He was a Visiting Associate Professor at the University of Tel Aviv from 1976 to 1978, and served as social studies program director of the NETA Project in Israel. Although his main work has been in ethnic relations (Race, Caste, and Prejudice, Handbook for Teaching Multi-ethnic Relations Using a Multi-media Approach), he has written two previous articles on ancient games and two inter- national simulations, Survival and Dominance and Rush to Peace.
theory at a rudimentary level. For example, let us say that a player must decide whether to move hidher piece two, six, or eight places (called points) from an opposing piece. Since dice are used to determine move- ment, the chance of being attacked by an opponents piece is 33 % if two points away and 47% if six points away. There is a 17% change of being attacked if a piece is eight points from an opposing piece. Jacoby and Crawford present a chapter on basic probability in their publication, The Backgammon Book [Z].
Two other uses of backgammon are as a simulation game to teach social concepts, and as a lesson in history to illustrate cultural diffusion as well as to learn something about the role of games in cultures. This article relates an attempt to trace the ancient roots of backgammon. Fur- thermore, a multiplayer simulation design using backgammon to teach certain concepts is presented. However, before engaging in these topics, it may be best to provided a general description of the game as it is played today.
Backgammon is a rather simple contest involving luck and skill. The material consists of a board with twenty four triangular points divided into groups of six. Each of two players has fifteen playing pieces referred to as men which are placed on predetermined points at the beginning of the game as shown in Figure 1. Using dice to determine movement factors per turn, the players attempt to get all fifteen of their men into their respective inner table. The inner table is the last six points on the board side of each player. Once all fifteen men are in a players inner table, the player seeks to move hidher men off the board. The first player to succeed in removing all fifteen men is declared the winner.
Figure 1. Backgammon board.
BLACKS INNER TABL.
WHITES I N N E R TARL:
Roots of Backgammon in Experimental Education 181
Figure 2. Senat board.
The men are moved in opposing directions. In Figure 1, the white player must move hidher men clockwise until they reach the inner table of white. The black player must move hidher men counterclockwise. When a piece or man stops on a point which contains one opposing piece, the opposing piece is bumped off the board and must reenter on one of the first six points in the opponents inner table. Two or more men of the same side are safe from bumping when they occupy the same point. Finally, each die counts independently when determining a move- ment factor. A roll of 3-5 allows a player to move one piece 3 and then 5, or one piece 3 and another piece 5. One piece moving 3 and then 5 may bump at 3 and again at 5. A throw of doubles (2-2, 4-4, etc.) allows for double movement. For example, a roll of 5-5 is equivalent to four 5s. In this case, a piece may move 20 points; two pieces may move 1 0 and 1 0 or 5 and 15; four pieces may move 5 points each; or three pieces may move 10-5-5. These rules are not complete but are presented here in order to provide a general understanding of the game prior to proceeding along the ancient trail of backgammon and the simulated model pre- sented at the conclusion of the article. An inexpensive game with rules is readily available in most game or department stores in the United States, Middle East, Europe, and elsewhere.
Roots of Backgammon
In search for the genesis of backgammon, we are led beyond the shadows of Egypts ancient pyramids. Its trail winds to and fro from Egypt through Palistine to Sumer. Paths of other games are crossed, and each must be examined as a possible progenitor of backgammon. Some of these games have fallen to disuse; others are still played daily in villages and Bedouin camps as well as highrise modern apartment complexes. In a previous article, it was mentioned that Sir Leonard Wooley described what may have been a backgammon board on the reverse side of the gaming board found at Ur . It was also mentioned that Williams and others have taken the basic structure of backgammon and applied it to the board game found on top of the same board described by Wooley . Seeking the origins from Egypt and Palistine resulted in the examination of a number of games. Three of these games are presented in detail. They are senat (sent), thau (tau), and seega (seejah, segi). The latter game is cur- rently played while the other two have faded into disuse. Senat and thau seein to have a direct bearing on backgammon; seega may have a con- nection with backgammon, but at a more abstract level.
Senat (Sent) Senat was a game of the nobility and the Pharoah. It was generally played on a board of thirty squares, three by ten (Figure 2), Each player had six pieces according to Petrie , five pieces according to the finds of Carter at the tomb of Tut-Ankh-Amen , and ten pieces according to Faulke-
1 8 2 M. Kleg
Figure 3. Throwing sticks.
ner . Williams and others provide a modern version which appears to be based on Carters find [ 8 ] . Differences of opinion have led each ob- server to arrive at somewhat different interpretations of the game.
The third component was the chance factor for movement. The game found in Tut-Ankh-Amens tomb had four throwing sticks. These throw- ing sticks consisted of ebony on one side and ivory on the other . The combination of the sides facing up after a throw determined the move- ment factor (Figure 3A). Petrie examined rectangular sticks with mark- ings indicating an elongated die. The value of the sides was either 0, 1, 2, or 3 [lo] (Figure 3B). Petrie suggests that only two sticks were used by each player. Using the numbered sticks, this would allow for a range of 0 through 6 per turn. Using four ebony-ivory sticks per roll, Williams and others present five possible counts ranging from 1 through 6 but without 5. In this case, a roll of all black or all white would result in either a 4 or 6 count [ I l l . Eliminating the 5 count may be arbitrary, but a 6 count is necessary. Inscriptions clearly indicate that rolls of 3 and 6 were made in the game .
The players sat at the narrow sides of the board. According to Car- ter, the game was pure chance, purely a game of hazard . Carter does not attempt to reconstruct the game, but offers the following opinion:
I would even go so far as to say that modern games of skill, like seega, or draughts, and chess, were in all probabilities evolved from the games of hazard, such as we find from time to time in ancient Egyptian Tombs, and so well represented in this burial .
Carters comment might be more accurate than he imagined. Gadd pre- sented evidence that chess may have originated in Babylon . How- ever, the basis for Gadds thesis is literally fragmentary, being based upon an inscription and design from a portion of the Stele of the Vultures as well as the Sumerian chariot. There is no doubt that the Sumerian chariot has a similar design to the rook chessman of the 12th Century. Todays rook or castle was originally a chariot, as it remains in Chinese Chess. In an earlier article, Gadd presents very strong evidence that an Egyptian game diffused to Assyria . My own observations of finds throughout Palestine indicate a definite trail of games between Egypt and Assyria. Furthermore, the similarity between the Ur gaming board and the boards used for senat and thau is too great to be considered mere chance.
Rules of Senat There are two general interpretations of the game. The more generally accepted version reflects Petries view that pieces begin in a mixed man- ner.
Roots of Backgammon in Experimental Education 183
The game seems to have been one of position, beginning mixed, and then segregating. This resembles English backgammon, where pieces are set in mixed order and then separated into the table of each player [141.
Based on inscriptions, Petrie suggests that the playing board be viewed as having three rows of ten squares each. A player moves hidher pieces along one row and then to the next. However, a roll of 6 or 3 with the throwing sticks allows a move directly from one row to the next or third row. It appears that such a movement is optional. As for the symbols on the board, Petrie holds that they merely indicate the number of the groups of three squares across the width of the board. However, the board at Saqqara seems to indicate that the symbols refer to individual squares . The symbols in squares 1, 2, 3 , 4, 10, and 20 in Figure 2 are easily associated with numbers. Square 20 has the same symbol as square 10, and that symbol is of the number 10. It is my suggestion that the two 10s indicate the direction of movement. The player beginning on squares 1 through 5 would move hidher pieces to 10, from 10 to 11, from 11 to 20 (the square with the second symbol of lo), and then over to 21. From 21, the player would move along this last column until the final five squares. The opposing player would follow the same route but in the opposite direction. The reason for the second 10 symbol indicates the tenth square in the middle column (row according to Petrie, who uses row interchangably with column). Although most observers tend to set the pieces in a mixed or alternate position at the beginning of the game, drawings in tombs may also suggest that pieces begin and end in a segregated fashion. Finally, it should be pointed out that boards vary in terms of symbols found on squares 1 through 5. Square 4 has either water (on four boards), a boat (on one), or the symbol for 4 (on four boards). Carter  and Williams and others  suggest that the presence of water may indicate a danger or penalty square. In the following rules, spe- cial meaning to this square is ignored since water is not universal on square 4. 1. The object of the game is to be the first player to move hislher pieces
to the last five squares on the players near left. 1.1 Player X begins with five pieces on square 1-5. 1 .2 Player Y begins with five pieces on squares 26-30.
2.1 Player X moves from hislher starting squares in order to the last
2.2 Player Y moves from hidher starting squares in reverse direction
3. Throwing sticks, rectangular in shape, with numbers 0, 1, 2, and 3
2. Players move in opposite directions.
five squares (26-30).
to the last five squares (1-5).
are used. Each player throws two sticks per turn as with dice. 3.1 A throw of sticks may be used separately.
(e.g. A throw of 1-2 may be used to move one piece one square and a second piece two squares.)
(e.g. A throw of 2-3 may be used as a five count for one piece.)
4.1 A throw of 3 allows a piece to move immediately to another col-
4.2 A throw of 6 allows for a jump of two columns. (e.g. from 29 to
3.2 The result of a throw may be applied to one piece.
4. A throw of 3 or two 3s (6) allows the following option:
umn. (e.g. from square 16 to 5, 1 to 20, etc.)
9 or from 3 to 23, etc.)
1 I 184
I M. Kleg
5. Pieces may jump over their own or opposing pieces if the throw count allows for a jump. A piece cannot end its move in an occupied square.
Two optional rules or conditions which may have a historical basis are as follows: 1. The initial placement of pieces is along the middle column with op-
posing pieces alternating from one square to the next. 2. Any stick throw in which 3 appears requires that a player move to
another column. It is interesting to note that, in using this rule, a 5 count is eliminated as in the game suggested by Williams and others. A double 3 would still allow for movement of one piece two columns or two pieces one column.
These versions of the game appear to be reasonable reconstructions. HQwever, the game remains largely one of chance with a touch of block- ing-timing strategy, For those interested in developing a more sophis- ticated game, the above may be viewed as a starting point for further development. The above reconstruction does seem to indicate a strong resemblance with backgammon. Both games involve chance through dice or throwing sticks. Both are race games with different degrees of block- ing. Although senat does not have bumping, it should be noted that Turkish backgammon has neither bumping nor stacking and thus resem- bles senat to a greater degree. In addition, Greek backgammon calls for the initial set up of all pieces of each side at opposite ends and nQt in alternating fashion as in backgammon. Finally, backgammon is undoubt- edly more sophisticated as we might expect. Before leaving senat, some mention of the works of Faulkener is warranted since his Games Ancient and Oriental is currently available.
It appears that Faulkener mistook a fragment of B senat board for something which did not exist. He is led to conjecture that this fragment was part of a 144 square board played with 120 pieces . As for his examination of a complete senat board, he suggests that it is played in the same fashion as thau, and he offers the judgment that it is called the game of the sacred way. Notwithstanding his apparent error regarding the senat board, Faulkeners analysis of thau seems somewhat reasonable.
Thap (Tau) Thau may have been more common in ancient Egypt and Palestine than senat, Although thau boards have been found on the opposite side of senat boards in Egypt, most thau boards have a different game or no game on their reverse side in Palestine. I did notice a possible design cut into a stone in the food storage (or stables, archaeologists are currently at odds QD the nature of the place) ruins at Megiddo (Armageddon), which could have been a senat board, but it was impossible to tell for certain. A thau board found in Bet Mirshim, south of Hebron, was ac- companied by a cube resembling a modern die . The playing pieces were cone shaped which is more similar to senat pieces than thau pieces found in Egyptian tombs. This find was dated as belonging to the middle bronze age of Palestine (1750-1550 BCE). qlthough the Bet Mirshim board is cut in stone and rather rough, as is the same type of board found at Hazor, north of the Galilee, the thau boards found at Megiddo are made from wood and are quite elaborate.
The thau board consists of twenty squares. At one end it has twelve
Roots of Backgammon in Experimental Education 185
Figure 4. Thau board.
squares, 4 x 3. From the center square there extend eight squares in a column. Each of the two players is allotted five pieces. These resemble a modern thread spool. The top flat surfaces are white, and the bottoms are black. This allows a piece to be either white or black depending upon which end is up. Tombs with both senat and thau games have separate sets of playing pieces for each game. Because one could not play both games simultaneously, it appears that the invertable thau pieces had a special function.
As in backgammon and senat, the use of dice or throwing sticks was part of the thau game. Faulkener recommends the use of a throwing stick with a range count of 1 through 4. Although this seems reasonable, the same 0 through 3 range as in senat is recommended in the reconstruction of thau given below.
Rules of Thau Thau is another game of chance with a very slight degree of strategy. However, the strategy is unique in that a player may desire to capture hidher own piece.
1. The object of the game is to be the first player to exit five pieces from the board via square 20 (Figure 4). Should a player capture all five of the opponents pieces, the game ends in victory since removal of five would be unhampered.
2. Each player begins with four pieces on hisher opening squares. 2.1. Player X places one piece each on squares 1 through 4. 2.2. Player Y places one piece each on squares 5 through 8. 2.3. The additional piece of each player is kept in reserve at point
3. The stick throw determines the movement factor of a turn. 3.1. A player must use all of hisher movement count in a turn unless
it is impossible, in which case the player must use what is pos- sible.
3.2. Rectangular sticks are used with a 0 through 3 count per stick. Two sticks are used by a player in hidher turn.
3.3. A movement count may be a combination of stick totals for one piece or it may be divided with a stick count for one piece, and a stick count for another piece. (It is impossible to move more than two pieces in a given turn.)
4. Movement proceeds from starting squares to the middle column via square 9. 4.1. From square 9, the track leads to square twenty. A players piece
travels up the middle column until it moves off the board via square 20, is captured, or enters the retrograde square.
4.2. A piece must return to its owning players reserve area when it ends its turn on square 16!
A in Figure 4.
186 M. Kleg
Thau and Backgammon
4.3. A piece is safe from capture on square 12 . 4.4. Movement from the reserve area requires a count of 1 through 4. 4.5. No more than one piece can be located in a square at the same
5. A piece is captured when an opposing piece ends a stick count on the same square. (e.g. if X has pieces on 9 and 11 and Ys sticks are 3-2, then Y may move a piece from 6 to 9 capturing one X piece. Y may then continue to use the stick with the 2 count to capture Xs piece on 11.) 5.1. Once a piece is captured, it is turned over and becomes a member
of the opposing side. The captured piece is placed in reserve on the side of its captor.
5.2. Again, a piece landing in square 16 is not captured but retreats to its owners reserve area.
6. Leaving the board requires an exact count. (e.g. if a piece is on square 19, it must have a stick throw count of two in order to exit: 2 , 1-1; a throw of three-3, 3+3, 3+1-would not be sufficient.)
Only Faulkener seems to be concerned with thau to any great extent. In general, his version and the one which I have reconstructed above are in agreement. Although Faulkener did not have the advantage of living to see the playing pieces found by Carter, he did manage to fit together the notion of capture although for reasons of making a more interesting game rather than attempting to fit together the evidence of the spool type playing pieces with different colors at opposite ends. Unfortunately, he was apparently unaware of the inscriptions in square 1 2 and 16. In square 1 2 , one board shows the inscription there is nothing. My interpretation is that there is nothing to capture, hence a safe square. In square 16 we read, I carry away. Again, I risk the possibility of error in interpreting this to mean that a player carries away hislher own piece. It would seem useless to interpret it to mean that the players piece is carried away by the opponent. First, all squares in the middle column aside from twelve are open to attacks. Second, if square 16 called for capture by the op- ponent, then it should refd he carries away. However, this second point can be debated. One may argue that square 12s inscription indi- cates that I cannot take my opponent here. Likewise, 16 may indicate that I carry away my opponent. Notwithstanding this counterargument, the former interpretation was made. It should be noted that virtually every other board has an X in squares 8, 4, 1 2 and 16. The Xs in squares 4 and 8 seem to indicate the number four or the gate through which pieces pass into the middle column.
Thaus relationship with backgammon may not be as striking as in the case of senat. Nevertheless, there are some similarities which deserve consideration. As in senat, thau is a race game in which pieces cover common squares. This same condition exists with backgammon. Unlike senat but similar to backgammon, thau does allow for bumping an op- ponent. The difference between the backgammon bump and the thau bump is that the former is merely a bump and the latter is a capture. A similarity which thau has with backgammon, but which may not have existed in senat, is the movement off the board in order to win. It may be possible that backgammon is a cross between thau and senat.
Roots of Backgammon in Experimental Education
Seega (Segi, Seejah)
Description and Rules of Seega
187 The notion of crossing in the evolutionary development of games is
given some basis in the game of seega which reflects the development of a thought game with traces of senat and thau. These traces involve the possible mixing condition of senat and the notion of capture of thau. Seega begins in a very mixed state, and the nature of capture concep- tually reflects a form of servitude rather than kill as is found in most games save shogi or Japanese chess.
Although seega is considered by many to be a modern game, a seega board has been found cut in the side of a stone from a pyramid. This would indicate that the cut was made prior to setting the stone in po- sition since it would be impossible to play with the board in a vertical position. Furthermore, seega playing pieces were apparently referred to as dogs and were viewed as objects to be captured for the purpose being placed in a state of servitude. This notion of servitude is suggested based upon the following.
In seega a piece is captured when two opposing pieces are occupying adjacent squares on a vertical or horizontal axis. Symbolically, this may indicate a locking or chaining of a piece where one side is blocked and cannot move. Furthermore, the game can easily develop into a stalemate. In order to break the stalemate, the player who started the game removes two pieces from the board, and the other player removes one. This con- tinues until the stalemate is broken. Todays Bedouins, who engage in the game and who may very well be the more original remnants of the ancient Hebrews, refer to this system of stalemate breaking as a marriage in which two friends leave the board with one friend. On this point, one must be reminded that servitude of bondsman and bondswomen in an- cient times did not always reflect or indicate a pure slave-master rela- tionship. For example, a child of a master and bondswoman was often ascribed a legitimate birthright. Furthermore, cliental relationships among groups were quite common as is reflected in the relationships between some of the ancient Hebrews and Canaanites. The captured pieces in seega do not return to action as in the case of thau, but the concept of the capture may be somewhat similar in that captured pieces are viewed as having a service, be it only in the end game counting. Hence, they are referred to as friends. As for the relationship between seega and backgammon, it may be that they are cousins, one of which evolved as primarily a chance game and the other as a thought game.
Seega is played on a board of 5 x 5 , 7 x 7, or 9 x 9 squares. The standard size is 7 x 7 or 49 squares, shown in Figure 5. Each player has 24 pieces (for the 7 x 7 game). At the village of Qalanswa, the head of the El Natour family, a Haj with three wives, twenty children, and between forty and eighty grandchildren (no one is quite certain) demonstrated a series of games with his son (Figure 6). They used stones and bottle caps and drew the board in the sand. The games lasted between five and ten minutes. Each time, the Haj defeated his son, Muhammed Ismail Salem, with apparent ease. As each game neared the end, the Haj would exclaim, I am strong; I am strong. Muhammed was somewhat humiliated, as his wife and children observed the games. He suggested a game of edris-a form of nine man Morris-which was his forte. Following Mu-
Figure 5. Seega board.
hammeds face-saving victories in edris, we visited a group of elders playing at seega (Figure 7). They used stones and little balls apparently made from manure and mud. I recommend the stones and bottle caps!
The game has two stages. Stage one consists of placing pieces on the board. Stage two consists of movement and capture. The winner is the player who can capture more pieces. The following rules are quite sim- ple, but skill in the game is another story.
Stage One Rules 1. The first player places two of hisher pieces on the board. 2. The second player does likewise. 3. This continues until each player has placed all of hidher pieces. 4. The marked center square is left vacant. Otherwise placement is free. 5. Once the total of 48 pieces is placed, stage one is completed.
Stage Two Rules 1. The player who started the first stage begins the second stage. 2. A player must move one piece one square either vertically or hori-
3. A piece is captured when the following occurs: zontally. The first move of the game i s to the center.
3.1. The piece to be captured has an enemy piece in a vertically or horizontally adjacent square (x = piece to be captured; o = op- posing piece).
Roots of Backgammon in Experimental Education 189
3.2. Another opposing piece moves to the opposite adjacent square, creating a locking situation or envelopment. 0x0 = capture of x. ox is not a capture.
t 0 t
3.3. A piece which moves between two opposing pieces is not cap- tured. 0x0, x is NOT captured. t
3.4. Below is an example of two pieces (x,x) being captured at one time.
t OR :xo t
3.5. The following is hot a capture.
4. A piece which captures may move again if the move will result in another capture. The same piece continues to move until it can no longer execute a capture. There are two versions: 4.1. A piece which captures may move one square (as normal) to any
adjacent square in order to execute a second, third, etc. capture. 4.2. Any piece involved in a capture may move only into the square
vacated by the capture. (This version is less common today.) 5. When a stalemate occurs, the player who started the game must re-
move two pieces (hisher choice), and the other player must remove one. This repeats until the stalemate is broken.
0 0 0 0 x x x x o
xo = A stalemate until x opens up. xo
x x xo
(note: x is completely closed; if o retreats a piece, x mdst come out. If o does not, then its a stalemate situation.)
Seega is a fast-moving game. The first stage is critical. Placement of pieces must be made in termgof the probable outcomes in the second stage. In other words, a player must develop an overall strategy and adjust the strategy to new developments. The second stage involves the application of tactics designed to complement the strategy developed during the first stage. Creating or preventing a stalemate is a tactic which might be employed during the second stage.
A modern version of the game is produced in Israel. The pieces are plastic and the gameboard is cardboard. Nevertheless, the Arabs still use the ground. Ersatz has yet to penetrate the natural state of the art of seega. In leaving seega, the following anecdbte may serve as a word of
Figure 6. The Haj forsees an easy seega victory against his son while some of his grandchildren look on.
caution to those who see the game as unchallenging. When I first intro- duced the game to an Israeli graduate research assistant who is a fair chess player, he commented, Well, it is for sure a Bedouin game, in- dicating a slightly condescending attitude. About a month later, he men- tioned that he had been playing the game, and it was definitely more complex than it originally appeared. Another month passed, and during a discussion of ancient warfare, he commented, You know, seega re- flects a mode of combat in which horsemen engage. If you are attacked from both sides, you cannot defend. As for his stereotype of Bedouins, the game apparently created more than a slight dissonance.
Figure 7. Adult villagers playing seega.
Roots of Backgammon in Experimental Education 191
Back to Backgammon
Backgammon: An Educational Simulation
Aside from its possible relationships with senat, thau, and seega, back- gammon may also be related to wari via other Egyptian games. The back- gammon-wari connection, if there is one, is vague. Wari reflects thau in that it involves the use of the same pieces by both players. The ancestors of wari are called hole games. These games often appear on the reverse side of thau boards. Some have been cut in stone. The game kadmon is an Israeli version of such a game found in the Golan Heights and pro- duced by Hagal Hachadash, Ltd. (Tel Aviv). A comparison between the various ancient hole games and kadrnon indicates that kadmon is defi- nitely a modern version although the board is based on ancient finds. Arabs in Jatt, Israel, use seven pods, each with seven peas, and regard the game as more complex than seega. The significance of this game lies in its ancient physical design and the application of more modern rules. Basically, what we may have is the progenitor combined with its des- cendant. This situation provides a novel cross in the evolution and de- velopment of games. The impact of this cross is more readily felt if we thrust ourselves a few centuries or more into the future.
Other Egyptian games, such as the snake game, seem to have little or no connection with backgammon except for traces reflected via thau. Once leaving the Egyptian period or area, the tracing of backgammon may lead the investigator toward the Greeks and Romans or in the di- rection of India. Eventually, however, one must arrive at medieval Eu- rope. From this point, the developments and tracing of backgammon become more certain but not less interesting. The major tasks of library and field research, analysis, synthesis, and evaluation remain. Where archaeologists leave off, historians and art work begin to present indi- cations of the game. The game sweeps through the American continent through time and space from statesmen to riverboat gambler to Las Vegas. Whether the game finds a place in education depends upon its use and value in this area. If it does, another chapter will be scratched out in the history of the game.
On returning to backgammon and its possible uses in the classroom, we might consider its potential as a simulation game. The following rules are suggested as a means of presenting a backgammon simulation de- signed to teach such concepts as cooperation, use of power, shared de- cision making, and the conflict between group and individual interests. The rules appear more complex than they are. This is primarily because of their length. In setting down rules for a game, one must attempt to balance the principles of KIS (keep it simple) with CCC (clear, complete, and concise). Furthermore, within the CCC principle, there is a problem of maintaining a concise and simultaneously complete presentation. In the following I have chosen completeness over brevity when necessary.
1. Divide students into teams of five players each, with two teams per game. The normal rules of backgammon apply except as modified by the following. (Boards and pieces may be constructed by stu- dents .)
2. Each student is assigned three playing pieces. 2.1. Pieces are numbered 1-15 for each team. 2.2. Each piece represents a life support value (LSV).
2.2.1. Fiece at start of game-2 points LSV
192 M. Kleg
2.2.2. Piece after being bumped one time-1 point LSV 2.2.3. Piece after two bumps-0 points LSV
2.3.1. 1-2 points-poor, low subsistance level. 2.3.2. 3-4 points-moderate subsistance level. 2.3.3. 5-6 points-high moderate level. 2.3.4. 7-8 points-affluent. 2.3.5. Above 8 points-superaffluent.
2.3. The meaning of life support values.
These levels are simulated but may be converted into tangible rewards by the teacher. If this is done, the reward for points should be explained at the beginning of the simulation.
2.4. In order to survive, a player must have at least one piece with a value of one.
3. When a piece is reduced to zero points (after being bumped for the second time), the piece is removed from the board and placed in the dead stack. However, a piece may be kept alive if the owner or a team member loans a point (or more) from another piece to the piece which is at zero. This must be done immediately and announced. Once a loan is given, it can only be returned at the will of the player who received the loan. Records of all transactions and the values of pieces must be kept and open to inspection by the opposing team.
4. When a team loses a piece or pieces from the game, it must exit remaining pieces as in backgammon. However, in order to win by exiting from the board, a team must have the same number or more pieces in play than the opposing team.
4.1. Team X has only ten pieces remaining. Five have been killed. In order to win by exiting, Team X must reduce the opposing team to ten pieces.
4.2. A team cannot exit pieces as long as the opposing team has more pieces than values (living pieces). 4.2.1. Team X has ten pieces. Team Y has twelve pieces. Team
X must reduce Team Y to ten or fewer before X can begin to exit.
4.2.2. Team X began to exit pieces when the two teams had ten pieces each. After exiting three pieces, Y attacks and kills one X piece. Can X continue to exit the board? The answer is yes. Once a side has exited at least one piece, it may continue to exit regardless of future imbalances due to enemy attacks.
5. A team may win by two means. 5.1. By exiting all living pieces before the opposing team (as de-
5.2. By killing all the pieces of the opposing team. scribed above in 4).
The following rules apply to the internal structure of a team.
6. Each team forms a governmental or decision-making structure.
6.1. Students determine a means for selecting a chief decision maker who will make the final decision as to which piece will move and where it will move. 6.1.1. If the owner of a piece refuses to abide by the decision
of the CDM (Chief Decision Maker), then the owner
Two suggestions are presented below.
Roots of Backgammon in Experimental Education 193
must provide at least one other player to support h i d her. If no fellow team member is found to support the player, he/she must submit to the will of the CDM.
6.1.2. If one member is found to support the owner, then the CDM may change the decision or appeal to the entire team. A vote of confidence is held. If in favor of the CDM, the owner must move his or her piece; if in favor of the owner, then the CDM must resign, and a new CDM is elected. (The original CDM may be reelected.)
6.1.3. The same procedure is followed when a CDM orders a player to loan another player a value point for a piece which has been reduced to zero. When a CDM orders such a loan, he may take over ownership of the piece to receive the loan, allocate it to the public domain, or allow the original owner to maintain control. Once a decision is recorded, it is binding.
6.2. Have one team set up as above in 6.1. Have another team es- tablished upon an absolute CDM who can rule without re- straints until all remaining team members refuse to accept his or her leadership at which time they must choose a new leader or change the structure of their government. Changes in gov- ernment must be recorded explaining what happened and why. Have another team develop a decision-making body without guidance.
7. Dice rolls should be made by players in alternating fashion. 8. In order to assist in postsimulation analysis (debriefing, feedback,
generalizing, etc.), records should be kept. It is also important to keep records of moves and changes in value points of pieces.
9. Time limits for a teams turn can be imposed. The following are suggested:
9.1. Forty seconds for a turn without conflict. 9.2. Three minutes should a vote of no confidence or a change of
government structure be initiated. 10. Students should have probability charts available for use:
10.1. Showing the probability of being bumped at various points from opposing pieces.
10.2. Showing the probability of being able to enter (after being bumped) on available points. (See Jacoby and Crawfords The Backgammon Book, also in paperback edition.)
The following is the end game simulation.
11. At the end of the game, the winning team may distribute points gained from the losing team in any manner as the victors chose. 11.1. Points are gained as follows:
11.1.1. Each surviving piece of the winning team receives a
11.1.2. Each surviving piece of the losing team has its points
11.2. The winning team may use points to rebuild killed pieces. 11.3. The winning team may allow the defeated team to have points
in order to survive. But such a condition may be tied to a treaty or conditions of surrender and must be agreed upon by both sides. Should the losing team be given some points in order to exist after its defeat, it may rebuild killed pieces.
bonus of three points which may be redistributed.
given to the winning team.
194 M. Kleg
The above aspect of the simulation is designed to examine the treat- ment of the vanquished after a conflict or competitive situation. After completion of the simulation, students can examine problems of conflict of interests between individuals and the group. If different organizational or decision-making structures are employed, the students may compare differences between structures in terms of group morale, feelings of ef- ficacy, efficiency, respect for individuals, and the attainment, use, and relinquishment of power. The rules of the simulation are not unalterable. Teachers and students may find it valuable to redesign the rules in order to improve the simulation. For example, they might create conditions which allow for defection or the development of agreements or treaties between teams during the game. A key factor of course lies in the ability of the simulation game to serve as a model of aspects of real life. Com- parisons should not be limited to national and international situations but should include small social units such as the family, clubs, etc.
Does backgammon as a simulation work? Does it or can it assist in developing math concepts and skills? Are the roots of backgammon ca- pable of enabling students to understand the intricate patterns woven by people as makers of history? These questions rest with teachers and students. Their willingness to experiment and the results of such exper- iments will not only answer these questions but also the more general and probably least important question: will backgammons history have a novel chapter entitled, Backgammon, Ancestors, and Simulation in Education?
REFERENCES 1. Obolensky, Prince Alexis, Backgammon, in Britannica Book of the Year, Chi- cago: Britannica, 1977, p. 174.
2. Jacoby, Oswald and Crawford, John R., The Backgammon Book, New York Viking, 1970, pp. 87-92.
3. Wooley, Sir Leonard, Ur Excavations: The Royal Cemetery, A Report on the Predynastic and Sargonid Graves Excavated between 1926 and 1931, Vol. 11. New York: Text, 1934, pp. 274-277.
4. Ibid. 5. Petrie, Flinder, Objects of Daily Use. London: British School of Archaeology
in Egypt-University College, 1927, p. 51. 6. Carter, Howard, The Tomb of Tut-Ankh-Amen, Vol. 111, New York: Cooper
Square, 1963, pp. 232-233. 7. Falkener, Edward, Games Ancient and Oriental and How to Play Them, New
York: Dover, 1961, pp. 358-359. 8. Williams, Gerald et al., Games of the World, New York: Holt, Rinehart, and
Winston, 1975, p. 53. 9. Carter, op. cit., p. 231.
10. Petrie, op. cit., p. 52. 11. Williams et al., op. cit., p. 54. 12. Gadd, C. J., Babylonian Chess? Iraq, VIII:66-73 (1946). 13. Gadd, C. J., An Egyptian Game in Assyria, Iraq, I:45-50 (1933). 14. Petrie, op. cit., p. 51. 15. Quibell, J. E., Excavations at Saqqareh: 1906-1907. Le Caire: Imprimerie De
16. Faulkener, op. cit. pp. 38-62. 17. Encyclopedia ofArchaeologica1 Excavations in the Holyland (M. Avi-Yonah,
LInstitut Francais, DArcheologie Orientale, 1908.
ed.). Jerusalem: Massada Press, 1975, Vol. I. p. 41.
Table of ContentsAuthor IndexJournal of Experiential Learning and SimulationThe Natural Learning ProjectCognitive Complexity Development In Lecture Vs. Experiential Organizational Behavior ClassesCan Learning Styles Be Used As Curriculum Aids? An Experiential Evaluation Of A Didactic-Experiential Approach For Teaching Personnel ManagementIntegrating Schools Of Management Thought: A Principles Of Management Experiential Exercise"Hop In Bed With Me.": Posture Purre-Fect Bedding Company: An Industrial Advertising ExerciseWhat's In It For Me? Over, Under, And Around Using A Computerized Business SimulationDebriefing Experiential Learning ExercisesThe Use Of Program BAYAUD In The Teaching Of Audit SamplingSimulation Vs Cases Vs Text: An Analysis Of Student OpinionAn Experimental Evaluation Of A Cognitive-Experiential Learning Methodology In The Basic Management CourseExperiencing Confrontation In Marketing: The Press Release ExerciseThe Banana GameDevelopment And Utilization Of The Diffusion GameAppendix: The Diffusion GameDynamic Marketing: A New Marketing Decision GameRoots Of Backgammon In Experimental EducationRetention: The Real Power Of Simulation/Gaming?The Business Simulation An Effective Learning InstrumentThe Impact Of Three Pedagogue Techniques On LearningThe Use Of A Live Case In Teaching Organization Theory And Management Principles To Graduate StudentsAn Interactive Simulation Approach To Teaching The Management Of Physical Distribution ServiceDevelopmental Prospects For Space Heating Applications Of Geothermal Resources In The United StatesUsing An Experimental Approach To Experiential Learning: A Leadership ExampleConsiderations In Design Of Learning SituationsThe Impact Of An In-Service Course On Teachers BehaviorSex-Role Stereotypes And Management Potential: An ExerciseLearning How To Evaluate Advertising Performance: Marketing Tourism DestinationsA Modular Business Game DesignCoping With Future Uncertainties Through Probabilistic BudgetingAn Investigation Of Bias Within The Learning Styles Inventory Through Factor AnalysisThe Teacher - Student Relationship In Experiential Classes And The Students Perception Of Course EffectivenessRealism And Adult Education: An Analysis Of The Consequences Of Two Design Approaches For Simulation In Continuing Medical EducationExperiential Live-Case Projects: Some Potential Legal Issues Affecting Instructors And CollegesIs It Real?An Experiential Exercise In Which Task Interdependencies And Noise Levels Are VariedGaming Performance: The Influence Of Quantitative Training And Environmental ConditionsOrganization Roles, Cognitive Roles And Problem Solving StylesCBID: Cognitive, Behavioral, And Interpersonal Development A Social Learning Approach To Skill DevelopmentAn Experiential Approach To Teaching Business Policy Through General Systems Theory And SimulationPersonality And Problem Solving: Making The Link VisibleThe Effect Of Assessment Ability On Performance In Executive GamesCognition Simulation And LearningThe Experiential Learning Model And The Learning Style Inventory: An Assessment Of Current FindingsExperiential Exercise: Unblocking Perceptual Barriers To Pygmalion EffectsThe Warm - Cold Variable As An Experiential ExerciseGame Simulations As Economic Research ToolsInjecting Interest And Enthusiasm Into The Marketing Management Course: A Simulation Game ApproachThe Role Of Simulation Games, Supplement Or Central Delivery Vehicle?Evaluation Of Experiential Learning In Management EducationThe Mystery Of Organization Discovery: Learning With Less That A Full Deck Using A Case-Exercise HybridA Simulation Investigation Of The Markov Stationarity AssumptionA Decision Support System To Enhance Rationality Of Simulation Game PlayMarkup On Retail: A Self-Administered Simulation In Pricing For ProfitThe Investment Decision Game: A Computer-Assisted Learning Approach To Stock Market DecisionsThe Exercise Of Effective LeadershipJob Redesign: Improving The Quality Of Work LifeTraining For Androgynous Behavior In OrganizationsDiagnosing Organizations: Identifying And Interpreting Internal Environment CluesCharacterizing An Organization: A Metaphor Technique For Initial AssessmentThe Floating Crap Game"The Academic Game" As A Frame GameFraming Power: Authority And Control In A Classroom OrganizationThe Pinto Exercise - Debating Costly Recall"Nuclear Deterrence" As An Adaptive Game Frame For Crisis Decision-MakingFrame Game - MULTRIX: The Multiple Choice Matrix GameAn Interactive Case Pedagogy For Strategy Formulation TrainingDiagnosing And Changing Organizational Learning Through The Use Of Experimental Simulation And Process AnalysisThe PAPCO Company - A Decision Making Role PlayLeadership Styles And Their ConsequencesThe Value Of Conjoint Analysis In Enhancing Experiential LearningUsing Simulation To Study The Effects Of Team CompatibilityIncreasing Student Involvement In Large Lecture Courses: Two Case StudiesApplication Of Organizational Behavior Concepts Through Student WorkshopsIncorporating MIS/DSS Into Policy Courses Via SimulationIntroducing Decision Support Systems Into Business School CurriculaPERMASIM: A New Personal Management SimulationA Microcomputer Simulation For Teaching Retail Location StrategyA Structured Approach To The Simulation Of Labor NegotiationAn Inventory Management SimulationGaming-Simulation: A Mode Of Communication For Conveying Systemic Research