THE MONTENEGRIN DICE GAME.
(
Puzzle Games.)
It is said that the inhabitants of Montenegro have a little dice game
that is both ingenious and well worth investigation. The two players
first select two different pairs of odd numbers (always higher than 3)
and then alternately toss three dice. Whichever first throws the dice so
that they add up to one of his selected numbers wins. If they are both
successful in two successive throws it is a draw and they try again. For
example, one player may select 7 and 15 and the other 5 and 13. Then if
the first player throws so that the three dice add up 7 or 15 he wins,
unless the second man gets either 5 or 13 on his throw.
The puzzle is to discover which two pairs of numbers should be selected
in order to give both players an exactly even chance.
Answer:
The players should select the pairs 5 and 9, and 13 and 15, if the
chances of winning are to be quite equal. There are 216 different ways
in which the three dice may fall. They may add up 5 in 6 different ways
and 9 in 25 different ways, making 31 chances out of 216 for the player
who selects these numbers. Also the dice may add up 13 in 21 different
ways, and 15 in 10 different ways, thus giving the other player also 31
chances in 216.
