Chuck-a-luck

More of a carnival game than anything else (no gaming commission in the world will allow it), Chuck-a-luck is a simple gambling game. There is a cage containing three dice. Players have the option of betting on the numbers 1 through 6. Should one of your numbers come up once, you get paid even money. Should one of your numbers come up twice you get paid 2-1. Should your number come up three times, you get paid 3-1.

Even an elementary examination will find that the game's expected value (barring loaded dice, which are common), is far worse than that of any other table game. The game is sometimes used as a fundraiser for charity, but the odds of coming away with more money than originally put in are quite small.

Rules

Chuck-a-luck is played with three standard dice that are kept in a device shaped somewhat like an hourglass that resembles a wire-frame bird cage and that pivots about its centre. The dealer rotates the cage end over end, with the dice landing on the bottom.

Wagers are placed based on possible combinations that can appear on the three dice. The possible wagers are usually fewer than the wagers that are possible in sic bo and, in that sense, chuck-a-luck can be considered to be a simpler game.

The wagers, and their associated odds, that are typically available are set out in the table below.

House Advantage or Edge

Chuck-a-luck is an unequal game of chance. That is, on average, even if the dice are not loaded, the players are expected to lose more than they win. The casino's advantage (house advantage or house edge) is greater than most other casino games and can be much greater.

For example, there are 216 (6 x 6 x 6) possible outcomes for a single throw of three dice. For a specific number:

• there are 75 possible outcomes, where one die only will match the number;
• there are 15 possible outcomes, where two dice only will match; and
• there is one possible outcome, where all three dice will match.

At odds of 1 to 1, 2 to 1 and 10 to 1 respectively for each of these types of outcome, the expected loss as a percentage of the stake wagered is:

1 - [(75/216) * 2 + (15/216) * 3 + (1/216) * 11] = 4.6%

At worse odds of 1 to 1, 2 to 1 and 3 to 1, the expected loss as a percentage of the stake wagered is:

1 - [(75/216) * 2 + (15/216) * 3 + (1/216) * 4] = 7.9%

Variants

• A version of the Big Six wheel is loosely based on chuck-a-luck, with various combinations of three dice appearing in 54 slots on a spinning wheel. Because of the distribution of the combinations, the house advantage or edge for this wheel is greater than for chuck-a-luck.
• Chuck-a-luck is essentially identical to the traditional Vietnamese game Bau cua ca cop.
• The games C 3; Chuck A Luck and C 9; Chuck A Luck use the numbers 1-3 and 1-9 (respectively) as the computer does not know how many faces a die has.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.