by Douglas Zare
1 February 2014
Backgammon stands out from other games of skill and chance because of the doubling cube. In fact, the doubling cube could be added to many other activities, even spectator sports. However, many casual players don't know how the doubling cube is used. While it is good to learn the rules of checker play first, many experienced casual players have never learned to use the doubling cube. One said, "I think after you play the game, you roll the doubling cube to see how many points you win." Well, that's creative. The doubling cube does resemble a large die. What can you learn from rolling it? In this column we will see two applications of the idea of rolling the doubling cube.
A game of dice
Suppose you get to choose between rolling the doubling cube (labeled 2, 4, 8, 16, 32, 64) and an ordinary die (labeled 1, 2, 3, 4, 5, 6). I'll roll the other. The game will be to roll the larger number. Given the choice, you would pick the doubling cube, of course. Because the nth number on the doubling cube is larger than the nth number on the regular die, it is clearly better to choose to roll the cube even though it is possible to lose by rolling a 2 or 4 against a 5, for example, or we could tie.
To make it more fair, let's say that when you roll the ordinary die, the numbers are multiplied by 5. So, a roll showing 3 pips would be 15. This has the side benefit of eliminating ties. Which die should you choose? Now the game is much closer, and perhaps it isn't obvious which has an advantage.
|The rest of this article (12.59 K) is premium content. Please subscribe below.|
Article text Copyright © 1999-2018 Douglas Zare and GammonVillage Inc.