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Chuck a Luck

Introduction

Chuck a Luck is a straightforward dice game where players can place various bets based on the results of rolling three dice. In Las Vegas, this game is located in venues like New York-New York and the Paris. In countries like Malaysia and Singapore, it's referred to as 'Mini Dice.' For those acquainted with sic bo the game, chuck a luck can be considered a more accessible format.

In a game of chuck a luck, players interact with a table containing a shaker holding three dice and a layout displaying multiple betting options. Similar to the big six wheel, the setup encourages quick bets rather than prolonged gaming sessions.

Here are the betting options in Chuck a Luck.

Single Number

Players can wager on any individual number from one to six, with the payouts determined by how many dice show that chosen number. For instance, if one die shows the number, the payout is 1 to 1; if two dice show it, the payout increases to 2 to 1. It’s not uncommon for a payout of three instances to vary between 3-1 and 12-1. The accompanying table outlines the odds in a scenario where three instances yield a 12 to 1 payout. The house edge is noted as 3.70%.

Single Number Bet — Generous Payout Structure

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 table below illustrates the house edge for single number bets based on the payout for three matching instances of the selected number.

Single Number Bet House Edge

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 basic wager that returns even money if the cumulative total of the three dice falls within a favorable range. I've come across two distinct variations of this bet, which I'll explain below.

The liberal variant is a winning bet if the total of the three dice is between 5 and 8 or between 13 and 16. The house edge is indicated in the lower right corner of the table below at 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 more restrictive version pays out if the total ranges from 3 to 7 or from 13 to 18. The house edge for this variant, shown in the lower right corner of the corresponding table, is 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 bets focus on the cumulative total of the three dice, with their names reflecting their nature. Both bets share the same odds, and the table below indicates 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 subsequent table delineates the different combinations and the probabilities for every potential total attainable with 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

External Links

Mini Dice Data sourced from the Genting casino in Malaysia.