Editing Chuck-a-luck (section)

==Rules==
Chuck-a-luck is played with three standard six-sided, numbered [[dice]] that are kept in a device shaped somewhat like an [[hourglass]] which resembles a wire-frame bird cage and pivots about its centre. The dealer rotates the cage end over end, with the dice landing on the bottom.<ref name=Scarne74>{{cite book |url=https://archive.org/details/scarneondice0000scar/ |title=Scarne on Dice |first=John |last=Scarne |author-link=John Scarne |date=1974 |publisher=Stackpole Books |location=Harrisburg, Pennsylvania |isbn=978-0-8117-1516-4 |url-access=registration}}</ref>{{rp|335}}

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. In the simplest variant, bettors place stakes on a board with six numbered spaces, labelled 1 through 6, inclusive. They receive a 1:1 payout if the number bet on appears once, a 2:1 payout if the number appears twice, and a 3:1 payout if the number is rolled all 3 times.<ref>{{Cite web|url=https://www.britannica.com/topic/chuck-a-luck|title=Chuck-a-luck|website=Encyclopedia Britannica|access-date=2020-05-21}}</ref> In this respect, the basic game is identical to [[Crown and Anchor]], but with numbered dice instead of symbols.<ref name=Scarne74/>{{rp|338}}

Additional wagers that are commonly seen, and their associated odds, are set out in the table below.<!-- Note that "dice" is plural, the  singular being "die"; do not "correct" this, as you would actually be introducing a grammatical error -->

{| class="wikitable" style="font-size:100%;text-align:center;"
!Type
!Wager
!Typical payout
! Actual odds{{efn|Probability of the outcome occurring}}
! House edge{{efn|Difference between payout and actual odds}}
|-
!rowspan=3 | Single Die Bet
|rowspan=3 style="text-align:left;" | A specific number will appear
|1 die matches:<br/>1 to 1
| {{frac|75|216}}<br/>({{#expr:100*75/216 round 2}}%)
| rowspan=3 | {{#expr:100*(1-2*75/216-3*15/216-11*1/216) round 2}}%<br/>(10:1){{efn|Assuming a 10 to 1 payout on triple}}<hr/>{{#expr:100*(1-2*75/216-3*15/216-4*1/216) round 2}}%<br/>(3:1){{efn|Assuming a 3 to 1 payout on triple}}
|-
|2 dice match:<br/>2 to 1
|{{frac|15|216}}<br/>({{#expr:100*15/216 round 2}}%)
|-
| 3 dice match:<br/>10 to 1{{efn|Sometimes this is adjusted to 3 to 1}}
| {{frac|1|216}}<br/>({{#expr:100*1/216 round 2}}%)
|-
!Any Triple{{efn|name=sometimes|This wager is not always offered}}
| style="text-align:left;" | Any of the triples (all three dice show the same number) will appear
|30 to 1
| {{frac|6|216}}<br/>({{#expr:100*6/216 round 2}}%)
| {{#expr:100*(1-31*6/216) round 2}}%
|-
!Big{{efn|name=sometimes}}{{efn|name=SicBo|House advantage derives from the possibility of a triple. Refer to the related games of [[Sic bo]] and Grand Hazard.}}
| style="text-align:left;" | The total score will be 11 (sometimes 12) or higher with the exception of a triple
|1 to 1
| {{frac|105|216}}<br/>({{#expr:100*105/216 round 2}}%)
| {{#expr:100*(1-2*105/216) round 2}}%<br/>(≥11)
|-
!Small{{efn|name=sometimes}}{{efn|name=SicBo}}
| style="text-align:left;" | The total score will be 10 (sometimes 9) or lower with the exception of a triple
|1 to 1
| {{frac|105|216}}<br/>({{#expr:100*105/216 round 2}}%)
| {{#expr:100*(1-2*105/216) round 2}}%<br/>(≤10)
|-
!Field{{efn|name=sometimes}}
| style="text-align:left;" | The total score will be outside the range of 8 to 12 (inclusive)
|1 to 1
| {{frac|91|216}}<br/>({{#expr:100*91/216 round 2}}%)
| {{#expr:100*(1-2*91/216) round 2}}%<br/>(<8 & >12)
|}

;Notes
{{notelist}}

===House advantage or edge===
Chuck-a-luck is a [[gambling|game of chance]]. On average, 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 certain wagers. According to [[John Scarne]], "habitual gamblers stay away from Chuck-a-Luck because they know how little chance they have against such a high [house edge]. They call Chuck-a-Luck 'the champ chump's game.{{'"}}<ref name=Scarne74/>{{rp|101}}

For the single die bet, there are 216 (6 × 6 × 6) possible outcomes for a throw of three dice. For a specific number:

* there are 75 possible outcomes where only one die will match the number;<!-- Note that "dice" is plural, the  singular being "die"; do not "correct" this, as you would actually be introducing a grammatical error -->
* there are 15 possible outcomes where two dice will match; and
* there is one possible outcome where all three dice will match; and so
* there are 125 possible outcomes where no die will match the number.

At payouts 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 more disadvantageous payouts 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%

If the payouts are adjusted to 1 to 1, 3 to 1 and 5 to 1 respectively, the expected loss as a percentage is:

1 - ((75/216) × 2 + (15/216) × 4 + (1/216) × 6) = 0%

Commercially organised gambling games almost always have a house advantage which acts as a fee for the privilege of being allowed to play the game,<ref name=Scarne74/>{{rp|55}} so the last scenario would represent a payout system used for a home game, where players take turns being the role of banker/casino.