## Friday, November 8, 2013

### Ephron’s Magic Dice

Ephron’s Magic Dice

Consider dice with these numbers on their sides:

Red:             4        4        4        4        4        4
Blue:            1        1        5        5        5        5
Green:          2        2        2        6        6        6
Yellow:        3        3        3        3        7        7

When you roll these dice, red loses to blue 2/3rds of the time, blue loses to green 2/3rds of the time, green loses to yellow 2/3rds of the time, and yellow loses to red 2/3rds of the time. Red and green are of equal strength: 50-50. Finally yellow defeats blue 5/9ths of the time.
These dice are ‘nontransitive’; no one die is best. When two players chose dice to roll, the second one to choose has a 2:1 advantage. Whatever color die your opponent picks, pick the next one in this cycle:
Blue    <    Green    <    Yellow    <    Red    <    Blue
A short mnemonic is useful in the haste of a game. With this color code:
blue = winter;  green = spring;  yellow = summer;  red = fall;
then the mnemonic is “next season”.

Here are some games based on magic dice: Double-Cross, Double-Roll, Double-Bet, White Magic, Black Magic and Black Double-Cross.

In Double-Cross, one player has the red and green dice, the other player has yellow and blue. They roll one die each, simultaneously. Thus each player can undercut the other. This games combines a loop with even-odd, and adds the element of chance.
In Double-Roll, the four dice start in front of the players, who choose them one at a time before rolling. The second player to choose must win twice as often, to counter-bias the dice. In Double-Bet, the second player must bet twice as much.
In the game White Magic, the players choose dice one at a time, and the winner of each roll must choose first on the next round. Thus White Magic’s winners tend to lose and its losers tend to win; it evens out differences.
Whereas in Black Magic, the loser of each roll must choose first next round, and thus tend to keep losing. Black Magic accentuates differences in luck.
Combinations of these games yield hybrids such as Black Double-Cross, where one player has red-green dice, the other has yellow-blue, and the loser of each roll must choose a die first next time.
I’ve had some sets of these dice made. Care for a few rounds?