A LITTLE KNOWN GAME

Albert FRANK & Marc HEREMANS

Under the generic names of « yams », « yam » or « yatsee » fall hundreds of games sharing common features. We present here a little known version of yams. According to international chess master Marc Dutreeuw, this game is probably as difficult and interesting as chess. We largely share this opinion and wish to give an overview of the game.

1. Description of the game.

- Number of players: 2 to 5.

- Materials: 5 dice, and in front of each player the following grid:

	down	free	up	in 1	in 2
1
2
3
4
5
6
Total
Bonus
Full
Suite
+
-
Yams
Result

2. How of the game unfolds

To start with, every player throws a die. The player who obtains the smallest point begins. Then, the players play in turn, clockwise. At each turn the player has to fill in one of the 55 squares - 1, 2, 3, 4, 5, 6, full, suite, +, -, yams » from one of the columns.

- The 6 numeric values correspond to sums: if a player has three ‘5’ (and two points other than 5 – for example 5,5,5,3,1), he can write 15 in the ‘5’ cell.

- ‘Full’ means that 3 dice have the same value ‘x’, and the two other the same value ‘y’ (example: 4, 4, 4, 2, 2) – or, alternatively, 5 dice with the same point – its value is 20.

- ‘Suite’ means either « 1, 2, 3, 4, 5 » or « 2, 3, 4, 5, 6 ». Its value is 30.

- « + » and « – » represent the sum of the value of the five dice. Note the constraint « + » > « - » (in cases where « + » is not strictly superior to « - », both cells have to be crossed out and the points therein are not taken into consideration for the final count.

- ‘Yams’ represents 5 dice with the same value and is worth 40.

- ‘Bonus’: if the sum of the values of the 6 first lines (the numeric values) reaches 63 (an average of 3 dice of every numeric value), the bonus is 30 (otherwise the bonus is 0).

For the final count, the values attributed to every column vary: 4 for the ‘up’ column, 2 for ‘free’, 3 for all of the other. THESE VALUES ONLY will be taken into consideration to determine the result of the game, and not the total obtained for the column, like in other forms of yams that we know. Therefore, for the ‘down’ column, the player with the highest total in this column will receive 3, the others 0.

In a game with two players A and B, if A wins the columns ‘down’, ‘up’ and ‘in 1’, and B wins the two remaining columns, the score will be: A: 3+4+3=10; B: 2+3 =5, and A will have won the game by 10-5 = 5 points.

The fact of winning more than a given number of columns gives a bonus to the player (see below).

If two players are level for a given column, they draw lots to determine the winner (a lesser evil, otherwise the totals would be distorted).

The column ‘in 1’ is filled after a single roll of the dice. The column ‘in 2’ if filled after exactly two rolls of the dice. The columns ‘free’, ‘down’, ‘up’ and are filled after 1, 2 or 3 rolls of the dice, depending on the player’s choice. The column ‘down’ must be filled downwards i.e., first the « 1 », then the « 2 », etc. The same goes for the ‘up’ column: first the ‘yams’ (which is almost always crossed out), then the « - », etc.

The player begins by rolling the 5 dice. He then may either:

- Write something (or cross out a cell) in the ‘in 1’ or ‘free’columns, or in the cells he has reached in the ‘down’ or ‘up’ columns.

- Re-roll all or some of the 5 dice. In this case, after the second roll, he may choose between

- writing something in the ‘in 2’ or ‘free’ column, or in the ‘down’ or ‘up’ columns;

- re-roll all or some of the 5 dice (including dice that had been discarded after the first roll). In that case, he has to write something in one of the first three columns.

2. A more in-depth description of the game for two players

Game strategies strongly vary depending on the number of players. For the two players version, the bonus according to the number of columns is 2.5 for a player who wins 4 columns and 5 if he wins all 5 columns. Therefore, if a player wins all 5, his score will be 15+5 = 20  If a player wins all the columns with the exception of the ‘up’ column, his score is 3+2+3+3+2.5-4 = 9.5.

3. Strategic considerations and example

We first have to stress that, in spite of the presence of dice, this game cannot be considered as random, provided a sufficient number of games are played. In Antwerp, professional players have been competing regularly for more than 20 years. Like in chess, there are categories rating the strength of a player. Let’s also mention that in Orléans, around 15 players, contaminated by Albert, compete regularly. Two of them have attained a very high level of play.

This game is essentially a game of « zugzwang » (a German chess term which means reaching a position in which the opponent no longer has a good move) and of management (optimization of decisions with risk). The probabilities of occurrence of a given throw and improvements are easy to calculate but the standard deviations are high.

The existence of bonuses causes good players to rely more on mathematical expectation than probability. Even at a high level, different players do not always make the same decision in a given situation.

At the start of the game, 35 cells are available (3x11 + 2). Again, in the ‘down’ column, only the cell corresponding to the ‘1’ can be filled after the first turn (likewise, only the cell corresponding to the yams in the ‘up’ column). Every time a cell is filled in a column other than ‘down’ or ‘up’, this number decreases by 1.

Common example of a game start:

Turn 1:

Player A: 1,1,3,4,6. He keeps both ‘1’. He obtains 1,1,1,4,6. He keeps the three ‘1’. He obtains 1,1,1,5,6. He writes 3 in the ‘down’ column.

Player B: 2, 4,5,6,6. He keeps both ‘6’. He obtains 2,2,4,6,6. He keeps both ‘6’. He obtains 3,4,4,6,6. He crosses the ‘yams’ in the ‘up’ column.

Turn 2 :

Player A : 2,2,4,4,6. He keeps both ‘2’ (for the ‘down’ column). He obtains 2,2,2,3,3 This is a first example of diverging views, even amongst the best players : some will write ‘20’ in ‘full’, others will go on keeping the ‘2’ for the ‘down’ column.

A last analogy with chess: a majority of those who learn the game give it up, claiming either that they are never lucky at dice, or that their opponent is decidedly too much in luck !