Editing Craps (section)

== Bet odds and summary ==
{{Unreferenced section|date=April 2018}}
:Note: Individual casinos may pay some of these bets at different payout ratios than those listed below. Some bets are listed more than once below&nbsp;– the most common payout in North American casinos is listed first, followed by other known variants.

:Note: "True Odds" do not vary.
{{sticky header}}
{|class="wikitable sortable sticky-header" style="font-size:90%;text-align:center;"
|+ Summary of wagers, true odds, and typical payouts<ref name=Scarne74/>{{rp|110–126}}
! Bet !! Type
! True Odds !! Odds Paid !! House Edge
! Single or Multi Roll
! Win !! Lose 
! class="unsortable" | Notes
|-
!Pass / Come
| [[#Line bets|Line]]
|251:244||1:1||1.41%
|Multi
|style="text-align:left;" | Come out roll: 7, 11.<hr/>Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10)
|style="text-align:left;" | Come out roll: 2, 3, 12.<hr/>Once the point is established: 7
|style="text-align:left;" | Considered a "contract bet": once the point is established, the bet is locked until it wins or loses. See [[#Optimal betting|Optimal betting]]. Come uses only the come-out roll criteria (7, 11 to win "come") for a single roll after the point is established.<ref name=Scarne74/>{{rp|78;113}}
|-
!Don't&nbsp;Pass / Don't&nbsp;Come<br/>(Bar-12 or Bar-2)
| [[#Line bets|Line]]
|976:949||1:1||1.36%
|Multi
|style="text-align:left;" | Come out roll: 2 (or 12, depending on Bar), 3<hr/>Tie: 12 (or 2, depending on Bar)<hr/>Once the point is established: 7
|style="text-align:left;" | Come out roll: 7, 11.<hr/>Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10)
|style="text-align:left;" | Controlled by the player: can be decreased at any time, but see [[#Optimal betting|Optimal betting]]. In some casinos, Bar-3 (1–2) is applied in lieu of either Bar-12 or Bar-2; this increases the house edge to 4.39%.<ref name=Scarne74/>{{rp|112}} Don't come uses only the come-out roll criteria (2, 3, 12 to win or tie "don't come", depending on Bar) for a single roll after the point is established.<ref name=Scarne74/>{{rp|78–79;113}}
|-
!Pass&nbsp;Odds / Come&nbsp;Odds
| [[#Line bets|Line]]
|Same as paid||2:1 on 4,10;<hr/>3:2 on 5,9;<hr/>6:5 on 6,8||0%
|Multi
|style="text-align:left;" | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10)
|style="text-align:left;" | Once the point is established: 7
|style="text-align:left;" | Controlled by the player: can be increased or decreased at any time
|-
!Don't&nbsp;Pass&nbsp;Odds / Don't&nbsp;Come&nbsp;Odds
| [[#Line bets|Line]]
|Same as paid||1:2 against 4,10;<hr/>2:3 against 5,9;<hr/>5:6 against 6,8||0%
|Multi
|style="text-align:left;" | Once the point is established: 7
|style="text-align:left;" | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10)
|style="text-align:left;" | Controlled by the player: can be increased or decreased at any time
|-
| colspan=9 style="font-size:10%;background:#ddd;" | &nbsp;

|-
!Yo (11)
| [[#Single-roll bets|Prop]]
|17:1||15:1||11.11%
|Single
|11
|Any other number
|style="text-align:left;" | 
|-
!3
| [[#Single-roll bets|Prop]]
|17:1||15:1||11.11%
|Single
|3
|Any other number
|style="text-align:left;" | 
|-
!2
| [[#Single-roll bets|Prop]]
|35:1||30:1||13.89%
|Single
|2
|Any other number
|style="text-align:left;" | 
|-
!12
| [[#Single-roll bets|Prop]]
|35:1||30:1||13.89%
|Single
|12
|Any other number
|style="text-align:left;" | 
|-
!Hi-Lo (2 or 12)
| [[#Single-roll bets|Prop]]
|17:1||15:1||11.11%
|Single
|2 or 12
|Any other number
|style="text-align:left;" | 
|-
!Craps (2, 3, or 12)
| [[#Single-roll bets|Prop]]
|8:1||7:1||11.11%
|Single
|2, 3, 12
|Any other number
|style="text-align:left;" | 
|-
!C&nbsp;&amp;&nbsp;E (the combined bet)
| [[#Single-roll bets|Prop]]
|5:1||3:1 on 2,3,12;<hr/>7:1 on 11||11.11%
|Single
|2, 3, 11, 12
|Any other number
|style="text-align:left;" | 
|-
!Any&nbsp;7
| [[#Single-roll bets|Prop]]
|5:1||4:1||16.67%
|Single
|7
|Any other number
|
|-
!Field
| [[#Single-roll bets|Prop]]
|5:4||1:1 on 3,4,9,10,11;<hr/>2:1 on 2,12||5.56% (2.78% if 12 pays 3:1, 0% if 2 and 12 pay 3:1)
|Single
|2,3,4,9,10,11,12
|Any other number
|style="text-align:left;" | Most common payout schedule. Some casinos pay 2:1 for 2 and 3:1 for 12, reducing house edge to 2.78%. A few pay both 2 and 12 at 3:1, eliminating the house edge.
|-
!Horn (the combined bet)
| [[#Single-roll bets|Prop]]
|5:1||27:4 on 2,12;<hr/>3:1 on 3,11||12.5%
|Single
|2,3,11,12
|Any other number
|style="text-align:left;" | 
|-
!Whirl/World (the combined bet)
| [[#Single-roll bets|Prop]]
|2:1||26:5 on 2,12;<hr/>11:5 on 3,11;<hr/>0:1 (push) on 7||13.33%
|Single
|2,3,7,11,12
|Any other number
|style="text-align:left;" | 
|-
| colspan=9 style="font-size:10%;background:#ddd;" | &nbsp;
|-
!Hard&nbsp;4 / Hard&nbsp;10
| [[#Hard way|Hard way]]
|8:1||7:1||11.11%
|Multi
|4 as a pair (2-2)<hr/>10 as a pair (5-5)
|7<hr/>4 as a non-pair (1–3)<hr/>10 as a non-pair (4–6)
|style="text-align:left;" | In the UK and Australia, the payout is 7.5:1 lowering the house edge to 5.56%.<ref name=":5">{{cite web |url=https://wizardofodds.com/games/craps/basics/ |title=Craps - Wizard of Odds |website=wizardofodds.com |access-date=2019-05-24}}</ref>
|-
!Hard&nbsp;6 / Hard&nbsp;8
| [[#Hard way|Hard way]]
|10:1||9:1||9.09%
|Multi
|6 as a pair (3-3)<hr/>8 as a pair (4-4)
|7<hr/>6 as a non-pair (1–5,2-4)<hr/>8 as a non-pair (2–6,3-5)
|style="text-align:left;" | In the UK and Australia, the payout is 9.5:1 lowering the house edge to 4.55%.<ref name=":5" />
|-
!Big&nbsp;6 / Big&nbsp;8
| [[#Big 6 and Big 8|Big 6/8]]
|6:5||1:1||9.09%
|Multi
|6/8
|7
|style="text-align:left;" | Same true odds, better payout if the player places the 6/8
|-
| colspan=9 style="font-size:10%;background:#ddd;" | &nbsp;
|-
!Place&nbsp;4 / Place&nbsp;10
| [[#Place|Place]]
|2:1||9:5||6.67%
|Multi
|4/10
|7
|style="text-align:left;" | Same true odds, better payout if the player buys the 4/10
|-
!Place&nbsp;5 / Place&nbsp;9
| [[#Place|Place]]
|3:2||7:5||4%
|Multi
|5/9
|7
|style="text-align:left;" | 
|-
!Place&nbsp;6 / Place&nbsp;8
| [[#Place|Place]]
|6:5||7:6||1.52%
|Multi
|6/8
|7
|style="text-align:left;" | 
|-
| colspan=9 style="font-size:10%;background:#ddd;" | &nbsp;

|-
!Buy&nbsp;4 / Buy&nbsp;10
| [[#Buy|Buy]]
|2:1||2:1 -5% of intended bet||4.76% (1.67% if commission taken only on win)
|Multi
|4/10
|7
|style="text-align:left;" | Certain casinos such as [[Santa Ana Star Casino]] offer "Free buy" reducing house edge to 0%
|-
!Buy&nbsp;5 / Buy&nbsp;9
| [[#Buy|Buy]]
|3:2||3:2 -5% of intended bet||4.76% (1.96% if commission taken only on win)
|Multi
|5/9
|7
|style="text-align:left;" | Same true odds, better payout if the player places the 5/9
|-
!Buy&nbsp;6 / Buy&nbsp;8
| [[#Buy|Buy]]
|6:5||6:5 -5% of intended bet||4.76% (2.22% if commission taken only on win)
|Multi
|6/8
|7
|style="text-align:left;" | Same true odds, better payout if the player places the 6/8

|-
| colspan=9 style="font-size:10%;background:#ddd;" | &nbsp;

|-
!Lay&nbsp;4 / Lay&nbsp;10
| [[#Lay|Lay]]
|1:2||1:2 -5% of intended win||2.44% (1.67% if commission taken only on win)
|Multi
|7
|4/10
|style="text-align:left;" | 
|-
!Lay&nbsp;5 / Lay&nbsp;9
| [[#Lay|Lay]]
|2:3||2:3 -5% of intended win||3.23% (2% if commission taken only on win)
|Multi
|7
|5/9
|style="text-align:left;" | 
|-
!Lay&nbsp;6 / Lay&nbsp;8
| [[#Lay|Lay]]
|5:6||5:6 -5% intended win||4.00% (2.27% if commission taken only on win)
|Multi
|7
|6/8
|style="text-align:left;" | 
|}

The probability of dice combinations determine the odds of the payout. There are a total of 36 (6 × 6) possible  combinations when rolling two dice. The following chart shows the dice combinations needed to roll each number.  The two and twelve are the hardest to roll since only one combination of dice is possible. The game of craps is built around the dice roll of seven, since it is the most easily rolled dice combination.

[[File:Roll2dice.svg|thumb|right|upright=1.8|Combinations of two dice, illustrated]]
{|class="wikitable" style="text-align:center;"
|+Combinations of two dice, with probability of occurrence<ref name=Scarne74/>{{rp|86;88}}
! Dice roll (sum) !! Possible dice combinations !! colspan=2 | Probability
|-
|2||1–1 ||{{frac|1|36}} || ({{#expr:100/36 round 2}}%)
|-
|3||1–2, 2–1 ||{{frac|2|36}}={{frac|1|18}} || ({{#expr:100/18 round 2}}%)
|-
|4||1–3, 2–2, 3–1 ||{{frac|3|36}}={{frac|1|12}} || ({{#expr:100/12 round 2}}%)
|-
|5||1–4, 2–3, 3–2, 4–1 ||{{frac|4|36}}={{frac|1|9}} || ({{#expr:100/9 round 2}}%)
|-
|6||1–5, 2–4, 3–3, 4–2, 5–1 ||{{frac|5|36}} || ({{#expr:500/36 round 2}}%)
|- style="background:white; color:red;"
|'''7'''||'''1–6, 2–5, 3–4, 4–3, 5–2, 6–1'''  ||{{frac|6|36}}={{frac|1|6}} || ({{#expr:100/6 round 2}}%)
|-
|8||2–6, 3–5, 4–4, 5–3, 6–2 ||{{frac|5|36}} || ({{#expr:500/36 round 2}}%)
|-
|9||3–6, 4–5, 5–4, 6–3 ||{{frac|4|36}}={{frac|1|9}} || ({{#expr:100/9 round 2}}%)
|-
|10||4–6, 5–5, 6–4 ||{{frac|3|36}}={{frac|1|12}} || ({{#expr:100/12 round 2}}%)
|-
|11||5–6, 6–5 ||{{frac|2|36}}={{frac|1|18}} || ({{#expr:100/18 round 2}}%)
|-
|12||6–6 ||{{frac|1|36}} || ({{#expr:100/36 round 2}}%)
|}

Viewed another way:

{| class="wikitable" style="text-align:center;"
|+Sum of two six-sided dice<ref name=Scarne74/>{{rp|86}}
! {{diagonal split header|Die B|&nbsp; Die A}}
! style="width:4ex;"|1 {{die|1}}
! style="width:4ex;"|2 {{die|2}}
! style="width:4ex;"|3 {{die|3}}
! style="width:4ex;"|4 {{die|4}}
! style="width:4ex;"|5 {{die|5}}
! style="width:4ex;"|6 {{die|6}}
|-
! 1 {{die|1}}
| 2||3||4||5||6||style="background:white; color:red;"|'''7'''
|-
! 2 {{die|2}}
| 3||4||5||6||style="background:white; color:red;"|'''7'''||8
|-
! 3 {{die|3}}
| 4||5||6||style="background:white; color:red;"|'''7'''||8||9
|-
! 4 {{die|4}}
| 5||6||style="background:white; color:red;"|'''7'''||8||9||10
|-
! 5 {{die|5}}
| 6||style="background:white; color:red;"|'''7'''||8||9||10||11
|-
! 6 {{die|6}}
| style="background:white; color:red;"|'''7'''||8||9||10||11||12
|}

The [[expected value]] of all bets is usually negative, such that the average player will always lose money. This is because the house always sets the paid odds to below the actual odds. The only exception is the "odds" bet that the player is allowed to make after a point is established on a pass/come Don't Pass/Don't Come bet (the odds portion of the bet has a long-term expected value of 0). However, this "free odds" bet cannot be made independently, so the expected value of the entire bet, including odds, is still negative.  Since there is no correlation between die rolls, there is normally no possible long-term winning strategy in craps.

There are occasional promotional variants that provide either no house edge or even a player edge. One example is a field bet that pays 3:1 on 12 and 2:1 on either 3 or 11. Overall, given the 5:4 true odds of this bet, and the weighted average paid odds of approximately 7:5, the player has a 5% advantage on this bet. This is sometimes seen at casinos running limited-time incentives, in jurisdictions or gaming houses that require the game to be fair, or in layouts for use in informal settings using play money. No casino currently runs a craps table with a bet that yields a player edge full-time.<ref name=Scarne74/>{{rp|108}}

Maximizing the size of the odds bet in relation to the line bet will reduce, but never eliminate the house edge, and will increase [[variance]].  Most casinos have a limit on how large the odds bet can be in relation to the line bet, with single, double, and five times odds common.  Some casinos offer 3–4–5 odds, referring to the maximum multiple of the line bet a player can place in odds for the points of 4 and 10, 5 and 9, and 6 and 8, respectively.  During promotional periods, a casino may even offer 100× odds bets, which reduces the house edge to almost nothing, but dramatically increases variance, as the player will be betting in large betting units.

Since several of the multiple roll bets pay off in ratios of fractions on the dollar, it is important that the player bets in multiples that will allow a correct payoff in complete dollars. Normally, payoffs will be rounded down to the nearest dollar, resulting in a higher house advantage. These bets include all place bets, taking odds, and buying on numbers 6, 8, 5, and 9, as well as laying all numbers.