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Last Updated: May 16, 2012

# Chuck a Luck

## Introduction

Chuck a luck is simple dice game, in which the player has various wagering options on the outcome of the roll of three dice. In Las Vegas it can be found in the New York New York and the Pairs. In Malaysia and Singapore the game is known as "Mini Dice." For those familiar with sic bo, chuck a luck is like a simplified version.

The chuck a luck table consists of a shaker, inside of which are three dice, and a table with various betting options. Like the big six wheel the players stand up to play. The table placement often suggests it is meant to entice people to make a spur of the moment bet or two as opposed to playing for an extended period of time.

Following are the bets available in Chuck a Luck.

## Single Number

The player may bet on any single number from one to six. It pays according to the number of dice that land on the chosen number. One instance pays 1 to 1, and two pays 2 to 1. I've seen three instances pay everything from 3-1 to 12-1. The following table shows the odds if three instances pay 12 to 1. The lower right cell shows a house edge of 3.70%.

### Single Number Bet — Liberal Pay Table

Matching
Dice
Pays Combinations Probability Return
3 12 1 0.004630 0.055556
2 2 15 0.069444 0.138889
1 1 75 0.347222 0.347222
0 -1 125 0.578704 -0.578704
Total 216 1.000000 -0.037037

The next table shows the house edge of the single number bet according to what three instances of the chosen number pays.

Three of a
Kind Pays
House Edge
12 3.70%
11 4.17%
10 4.63%
9 5.09%
8 5.56%
7 6.02%
6 6.48%
5 6.94%
4 7.41%
3 7.87%

## Field Bet

The field bet is a simple wager that pays even money if the total of the three dice is within a winning range. I have seen two different versions, which I address below.

The liberal version wins if the total of the three dice is 5 to 8 or 13 to 16. The lower right cell of the table below shows a house edge of 3.70%.

### Field Bet — Liberal Version

Event Pays Combinations Probability Return
Win 1 104 0.481481 0.481481
Lose -1 112 0.518519 -0.518519
Total 216 1.000000 -0.037037

The stingy version pays if the total is 3 to 7 or 13 to 18. The lower right cell of the table below shows a house edge of 15.74%.

### Field Bet — Stingy Version

Event Pays Combinations Probability Return
Win 1 91 0.421296 0.421296
Lose -1 125 0.578704 -0.578704
Total 216 1.000000 -0.157407

## Under 10/Over 11

The Under 10 and Over 11 are a pair of bets on the total of the three dice. The names of the bets pretty much describe them. The odds are the same. The table below shows a house edge of 25%.

### Under 10/Over 11

Event Pays Combinations Probability Return
Win 1 81 0.375000 0.375000
Lose -1 135 0.625000 -0.625000
Total 216 1.000000 -0.250000

## Probabilities

The following table shows the number of combinations and probability for all possible sums of the total of three dice.

### Three Dice Probabilities

Total Combinations Probability
3 1 0.004630
4 3 0.013889
5 6 0.027778
6 10 0.046296
7 15 0.069444
8 21 0.097222
9 25 0.115741
10 27 0.125000
11 27 0.125000
12 25 0.115741
13 21 0.097222
14 15 0.069444
15 10 0.046296
16 6 0.027778
17 3 0.013889
18 1 0.004630
Total 216 1.000000

information, from the Genting casino in Malaysia.

Written by: Michael Shackleford

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