Aseb is the Egyptian version of the ancient Middle Eastern game called The Game of 20 Squares. According to some historians the Egyptian name of this game was Tjau, which in the ancient Egyptian slang meant “got it” or “bingo”, but other claim that this name is a mistake. Aseb is related to the Royal Game of Ur in its more archaic forms, and probably arrived in Egypt from ancient Sumer, during the 17th Dynasty. Versions of Aseb have been found in Egypt, Sudan, Crete, and even in India.

Wooden Aseb Game of 18th Dynasty – Brooklyn Museum – 37.93E, 37.94E

It is a race game, in the same category as Senet and the Royal Game of Ur, but is much shorter, quicker and simpler.

Aseb game box with playing pieces and knucklebones dice. 1635–1458 BCE. Egypt, Thebes. Ivory, copper alloy, modern wood. The Metropolitan Museum of Art, New York- 16.10.475a-k

The original rules of the game are unknown. I have presented here a hybrid set of rules, which are most interesting and challenging set of rules for Aseb, which I developed myself based on a different set of rules developed by a Russian game re-constructor Dmitriy Skiryuk (Дмитрий Скирюк) and originally published on his blog in Russian. I have included aspects from Skiryuk’s rules for Senet in my rules for Aseb.

**Aseb Rules:**

- Number of players is 2.
- The game includes the board of 20 squares arranged into 3 rows of 4 columns and a line of 8 cells, 5 conoid pieces, 5 round spindle pieces, and 4, two sided, throwing sticks are included in the game to serve as dice, with one side rounded and the other side flat.

- In some versions of Aseb, a single 4 sided knucklebone, a single 4 sided stick, or a single 4 sided conoid dice is used instead of the throwing sticks. This slightly changes the game, because such a dice has an equal probability of any of the dice values, where as the throwing sticks do not.
- The game starts with all of the pieces located off the board, on the long fields adjacent to the line cells.

- All 4 throwing sticks are thrown at the same time. The score is determined as follows:
- If one throwing stick landed on the flat side and the other three landed on the round side the score is 1.
- If two throwing sticks landed on the flat side and the other two landed on the round side the score is 2.
- If three throwing sticks landed on the flat side and the fourth one landed on the round side the score is 3.
- If all four throwing sticks landed on the flat side the score is 4, which is the maximum obtainable score.
- If all four throwing sticks landed on the rounded side the score does not count and the player needs to throw the sticks again.

- Additional throws of the sticks by a player in a single turn are not allowed.
- To determine which player starts the game, both players throw the sticks. Whoever scores 1 first moves first.
- The player who gets the first move throws the sticks again to determine how many cells they will move.
- Each score of the dice determines how many cells the player moves from 1 to 4.
- A player can chose to move any of his pieces on any move, as long as the move is allowed.
- With each throw of the sticks the players can either add a piece to the board or move a piece which is already on the board.
- The players begin by moving pieces into cells #1-4 and #17-20, depending on what their initial dice score was.

- All cells can be occupied by only one piece at any time.
- Pieces are not allowed to pass their own pieces. So if a player’s piece is standing in the path of the next piece the following piece must stop on an empty cell preceding the blocking piece, even if the dice score would have placed it further down the path.
- If a player’s piece lands on a cell with the opponent’s piece in it then the opponent’s piece gets knocked off the board and goes back to the beginning of the game.
- All pieces can move only forward.
- If a player cannot make a move due to all available cells being occupied then they skip a turn.
- There are 5 cells that are marked: 4, 20, 13, 9, and 5. Those cells are called “houses”, and if a player lands on any of them they get a second turn.
- There are no safe cells in Aseb, from where a piece cannot be knocked off the board, except or the first four cells of the path on short rows (1, 2, 3, 4 and 17, 18, 19, 20) where the opponent’s pieces do not go.
- To move off the board the player must score on the dice the exact number needed to move off the board. For example, if the piece is located on cell #5, the player must score 1, if the piece is located on cell #6, the player must score 2, if the piece is located on cell #7, the player must score 3, and if the piece is located on cell #8, the player must score 4. If the player scores a different dice score and they cannot make any other moves or move off the board, then they skip a turn and wait for the next turn.
- The player who moves all of their 5 pieces off the board first wins the game.

**On Game Strategy**

- Aseb is mostly a game of chance and does not have much strategy.
- However, if the players use 4 throwing sticks as their dice, instead of a single 4 sided knucklebone, a single 4 sided throwing stick, or a single 4 sided pyramidal dice, this creates some minor strategical options.
- The throwing sticks have uneven probability for different scores, as compared to a four sided pyramidal dice, which makes them more frustrating and exciting at the same time.
- The most frequent dice score on throwing sticks is 2 (probability is 6/16).
- The next most frequent dice scores are 1 and 3 (probability is 4/16).
- The least frequent dice scores are 4 and 5 (probability is 1/16).
- Due to this uneven probability of scoring it is advantageous to the player to keep gaps between theirs and opponent’s pieces of either 1 or 3 cells. Gaps of 4 or 5 are even better. However, gaps of 2 are more dangerous since the probability of the opponent scoring a 2 is highest and therefore the piece can get easily knocked out.

**Bibliography:**

- Crist, Walter, Anne-Elizabeth Dunn-Vaturi, and Alex de Voogt.
*Ancient Egyptians at Play: Board Games Across Borders*. Bloomsbury Publishing, 2016. - Bell, R. C.
*Board and Table Games from Many Civilizations*. Courier Corporation, 2012. - Botermans, Jack.
*The book of games: strategy, tactics & history*. Sterling Publishing Company, 2008.

Kirk Mathews says

Here is an analysis of the influence of the asymmetry of the throwing sticks.

As per the scoring rules, the possible scores are 1, 2, 3, and 4; and 5 is not possible. Let p be the probability of a stick being flat side down. Then q = 1-p is the probability of flat side up. You have assumed that p = q. However, that seems unlikely because a stick can roll from the round side down to stop on the flat side down, but going from the flat side down to the round side down requires bouncing, rather than simply rolling. Thus, I anticipate that p is greater than q. How much difference there is depends on the actual shape of the rounded side. For any one toss of the sticks, the probabilities of the scores are:

Zero (reject and try again): 1 * q * q * q * q = q^4

One: 4 * p * q * q * q = 4 * p * q^3

Two: (4 * 3 / 2) * p * p * q * q = 6 * p^2 * q^2

Three: (4 * 3 * 2) / (3 * 2) * p * p * p * q = 4 * p^3 * q

Four: 1 * p * p * p * p = p^4

If the sticks are symmetrical (like popsicle sticks or tongue depressors, then p = q = 1/2 , for which the score probabilities for one throw of the sticks are the ones you state at as item 3 under strategy.

One: 1/4

Two: 3/8

Three: 1/4

Four: 1/16

Note however, that these sum to 15/16, because the probability of zero is 1/16. To correct these, divide each one by 15/16 so that they sum to 1.

In general, the probabilites of the possible scores (after trying again as many times as it takes) are

One: 4 * p * q^3 / (1 – q^4); Two: 6 * p^2 * q^2 / (1 – q^4); Three: 4 * p^3 * q / (1 – q^4); Four: p^4 / (1 – q^4)

In the case where p = q = 1/2, these are simply 4,15, 6/15, 4/15, 1/15, respectively.

Suppose, however, that the sticks are cylinders cut in half , so that the probability of rolling onto the flat side is not small. As an example, let p = 7/10 so that q = 3/10. Then the probabilities are one: 108/1417, two: 378/1417, three: 588/1417, four: 343/1417.

Thus, the asymmetry of the sticks in a particular Aseb game set could be significant to the game play.

This issue of the asymmetry of the sticks arises in all the games in which the sticks are round on one side and flat on the other!

Eli says

Cool. Thank you.

Elena Kudinova says

Wow! And what is really cool is that, as follows from this article, https://hapax.github.io/mathematics/physics/statistics/dice/ the probability distribution will depend on the speed of rolling!!!