Mathematical_Recreations-Kraitchik-2e

300 Mathematical Recreations
be used for three or four players, each playing for himself.
The winner is the one who first exhausts his hand, or the one
with the lowest total in his hand at the end of play. If four
persons play partners, two against two, each player draws
only six dominoes. If a player exhausts his hand, his side
wins. If no player exhausts his hand, the side with the lower
remaining total wins. In either case the winners score the
total of the points remaining in their opponents' hands.
When four play, each for himself, it is possible for two of
the players to be unable to play at all while a third exhausts
his hand. Let the players in their order of play be A, B,
C, D. Suppose A draws 0-0, 0-1, 0-2, 0-3, 1-4, 1-5, 1-6,
and D draws 0-4,0-5,0-6,1-1,1-2,1-3, and any other domino.
The remaining 14 are divided in any way between B
and C. If A and D play alternately in the following order,
it will be seen that Band C have no opportunity to play:
0-0,0-6,6-1,1-3,3-0,0-5,5-1,1-2,2-0,0-4,4-1,1-1,1-0.
A wins with a total of 120, the maximum possible win. By
a different permutation of the numbers 0, 1" . " 6 the same
result can be obtained, except that A's winnings will not be
as great.
In a partnership game the maximum score in one game is
105; in a game between two players, 69.
Matador is a variation in which the chain of dominoes is
formed by the requirement that the ends which abut must
add up to 7. Since no domino could be added to a 0, one is
permitted to place a matador (that is a domino totaling 7,
and sometimes the 0-0) crosswise against a 0, and play is
resumed with a ° against the other side of the matador.
Otherwise the rules are about the same, and the game may
be played by two, three, or four individual players, (V' by
partners.
M uggins is another variation, playable by two, three, or
four individual players. Play proceeds by the same rules as