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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.
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 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 |
External Links
Mini Dice information, from the Genting casino in Malaysia.