- In this video we discuss betting and payouts of hardways. These bets are often discouraged but often played. Remember to subscribe and leave questions and/.
- You may have heard of the ‘hard way’ craps bet at one time or another if you played the game. It is sometimes known as betting on pairs or doubles. Basically you are betting on both dice to show the same numbers, such as: 22, 33, 44, and 55. These would be known as Hard 4, Hard 6, Hard 8 and Hard 10.
- Hard Four: 4 the Hard Way before 7 or Easy 4: 7:1: Hard six: 6 the Hard Way before 7 or Easy 6: 9:1: Hard Eight: 8 the Hard Way before 7 or Easy 8: 9:1: Hard Ten: 10 the Hard Way before 7 or Easy 10: 7:1: Any Seven: 7 on next roll: 4:1: Any Craps: 2, 3 or 12 on next roll: 7:1: Horn: 2 Craps: 2 on next roll: 30:1: Horn: 3 Craps: 3.
- Shows you how to use the Don’t bets to insure your 6 & 8 place bets.
IDS 12 Foot Deluxe Craps Dice Table with Diamond Rubber Blue 4.7 out of 5 stars 6 #9. AccuCraps Portable Craps Practice Table — Traditional Underlayment.
Craps dice
The following is a glossary of terms used in the dice game craps. Besides the terms listed here, there are many common and uncommon craps slang terms.[1][2][3]
A[edit]
ace deuceA roll of 3
B[edit]
Hard 6 Craps Machine
Big RedThe number 7 or a bet for any 7 to appearbonesA slang term for the dicebox numbersThe place numbers (4,5,6,8,9,10)boxcarsA roll of or bet on 12
C[edit]
center fieldNine, often called Center Field Ninechange onlywhen a player buys into a game specifically with cash, the ‘only’ means no bets are being placed at the time of the buy in. Can also be used when a player colours in. (Dealers will say this out loud so that a player can’t take a shot and say he wanted a bet on X.)Cheque changeBreaking down a chip into smaller denomination chips.colour upThe process of changing denominations of chips to larger denominationscold dicealso known as a cold table; an expression used when players are not hitting the established point and sevening outcome out1. The initial roll of the shooter2. To roll the dice when no point has been established[4]crap outTo roll a 2, 3, or 12 on the come out roll. A player betting on the Pass line or Come loses on crap out, but the roll does not lose when a point is established. Don’t Pass and Don’t Come wins if a 2 or 3 craps is rolled on come out, but ties (pushes) if a 12 is rolled on come out. The shooter may continue rolling after crapping out.crapsthe numbers 2, 3, and/or 12
D[edit]
double pitchIn dice control, when the dice stay on axis which rarely occurs (less than 5% of the rolls), but one turns two faces more than the other. If players set the dice with the same face, such as a hard ways or 3V set, the roll may likely result in a seven.downTo remove or reduce a bet, players often say ‘take it down’
E[edit]
easy wayRolling an even number with any combination other than doubles. Applies to 4, 6, 8, and 10 only.even moneyAny bet that pays out at 1:1.
F[edit]
fever fiveA roll of 5, also called five feverfree oddsSimply known as odds, is the odds which can be taken or laid behind the Pass/Come or Don’t Pass/Don’t Come. These are paid at true odds.fleaA player who bets at or near table minimum, normally for extended periods of time.
G[edit]
gardenSlang for the field betGeorgeA good tipper
H[edit]
hard wayRolling a 4, 6, 8, 10 with a pair of the same numberhi-loa single roll bet for 2 or 12hi-lo-yoa single roll bet for 2, 11, or 12highA bet on or roll of 12, also see boxcarshopA single roll bet for a specific combination of dice to come out. Pays 15:1 for easy ways and 30:1 for hard wayshornA divided bet on the 2, 3, 11, 12horn highA horn bet with addition units going to a specific number. For example ‘horn high ace deuce’ would generally mean a 5 unit bet with 2 units going on the 3.hot dicealso known as a hot table; an expression used when players are hitting the established points or rolling for long durations without seven outs
I[edit]
inside numbersbetting on the 5, 6, 8, 9
L[edit]
layTo bet on a seven to come before a specific point number. Lays are paid at true odds with commission taken.lay oddsTo give odds behind a Don’t Pass or Don’t Come. Betting against the shooterLittle JoePoint 4lowa single roll bet for a 2
M[edit]
mechanicA shooter who allegedly implements dice control
N[edit]
naturalRolling a 7 or 11 on the come out rollNinaRolling or betting on a 9
O[edit]
Off1. The come out roll; when no point has been established2. To have a bet on the table but not in play. The bet can not be won from or lost when it is Off.On1. When a point has been established2. A bet that is in play (working).outside numbersbetting on the 4, 5, 9, 10
P[edit]
parleyTo parley a bet is to take all the winnings from the previous bet (or up to maximum allowed for bet if winnings exceed maximum) and add it to the next bet.pressTo double a bet, players generally say ‘press it’ when doubling a bet, players can also press an additional one or more units and can increase the bet less than the original bet by saying ‘press X units’pusha tie
S[edit]
same betTo keep the previous winning bet as is. If a player says same bet it does not mean to double the bet, that is referred to as ‘pressing it’seven outA roll of 7 when the point is On. All bets on Pass, Pass Odds, Come, Come Odds, Place bets, Buy bets, hard ways and any single roll bets not for a seven loses. All bets on Don’t Pass, Don’t Pass Odds, Don’t Come, Don’t Come Odds, Lay bets and any single roll bets for a seven wins.snake eyesA roll of 2strokerA player who makes bets overly complicated and/or gives dealers unnecessary additional work
T[edit]
take oddsTo bet odds behind a Pass or Come. Betting with the shooter[5]take downSee downtrue oddsThe real odds for payout where house edge is 0%
W[edit]
workingA bet which is in play and can be won or lost.whirlA five-unit bet that is a combination of a horn and any-seven bet, with the idea that if a seven is rolled the bet is a push, because the money won on the seven is lost on the horn portions of the bet. The combine odds are 26:5 on the 2, 12, 11:5 on the 3, 11, and a push on the 7.worldSee whirlwrong way bettorWhen a person is betting against the shooter on the Don’t Pass Line.
Y[edit]
yoA roll or bet on 11 (6–5, 5–6), short for Yo-leven
References[edit]
- ^’Craps Lingo’. readybetgo.com. Retrieved 2016–03–03.
- ^’Craps Etiquette and Lingo Casino Gambling Game Rules and Strategy Guide’. VegasTripping.com. Retrieved 2016–03–03.
- ^Jack Botermans (2008). The Book of Games: Strategy, Tactics & History. Sterling. pp. 545–. ISBN978–1–4027–4221–7.
- ^Craps A Smart Shooters Guide. Cardoza Publishing. pp. 24–. ISBN978–1–58042–576–6.
- ^R. D. Ellison (2001). Gamble to Win: Craps. Lyle Stuart, Kensington Publishing Corporation. pp. 42–. ISBN978–0–8184–0621–8.
Retrieved from ‘https://en.wikipedia.org/w/index.php?title=Glossary_of_craps_terms&oldid=1004584483'
Introduction
Introduction
Welcome to the craps appendix. This is where I derive the player’s edge for all the major bets in craps. Outside of this appendix I usually speak about the house edge, which is just the product of the player’s edge and -1. To avoid multiplying by -1 for every bet I shall speak of everything in term’s of the player’s edge, which you can expect to be negative since the house ultimately has the edge on all bets except the free odds. Please stay a while and work through some of the bets yourself. Not only will this give you a deeper understanding of the odds but hopefully motivate you to refresh or improve your math skills.
Before going on you must have an understanding of the probability of throwing each total in one roll. This is explained in depth in my dice probability basics page. If you didn’t know or can’t figure out that the probability rolling a 6 is 5/36 then a visit to that page is a prerequisite for this page.
The general formula for the expected return of a bet is:
∑ (probability of event i) × (return of event i) over all possible outcomes.
The player’s edge is the expected return divided by the initial bet. For example when betting against the line on a sporting event you have to bet $11 to win $10. Assuming a 50% chance of winning the expected return would be 0.5×(10) + 0.5×(-11) = -0.5 . The player’s edge would be -0.5/11 = -1/22 ≈ -4.545%.
An exception to the house edge rule is when a tie is possible. In general ties are ignored in house edge calculations. To adjust for this, when a tie is possible, divide the expected return by the average bet resolved. The ‘average bet resolved’ is the product of the initial wager and the probability that the bet was resolved. In craps the only bets with a tie are the don’t pass and the don’t come.
Many of the bets in craps win if one particular event happens before another. These bets can take several rolls or more to resolve. If a wager wins with probability p, loses with probability q, and stays active with probability 1-p-q then the probability of winning eventually is:
∑ p×(1-p-q)i (for i=0 to infinity) =
p × (1/(1-(1-p-q))) = p × (1/(p+q)) = p/(p+q).
Throughout this page you will see a lot of expressions of the form p/(p+q). To save space I do not derive the expression each time since it is worked out above.
Pass/Come
The probability of winning on the come out roll is pr(7)+pr(11) = 6/36 + 2/36 = 8/36.
The probability of establishing a point and then winning is pr(4)×pr(4 before 7) + pr(5)×pr(5 before 7) + pr(6)×pr(6 before 7) + pr(8)×pr(8 before 7) + pr(9)×pr(9 before 7) + pr(10)×pr(10 before 7) =
(3/36)×(3/9) + (4/36)×(4/10) + (5/36)×(5/11) + (5/36)×(5/11) + (4/36)×(4/10) + (3/36)×(3/9) =
(2/36) × (9/9 + 16/10 + 25/11) =
(2/36) × (990/990 + 1584/990 + 2250/990) =
(2/36) × (4824/990) = 9648/35640
The overall probability of winning is 8/36 + 9648/35640 = 17568/35640 = 244/495
The probability of losing is obviously 1-(244/495) = 251/495
The player’s edge is thus (244/495)×(+1) + (251/495)×(-1) = -7/495 ≈ -1.414%.
Don’t Pass/Don’t Come
The probability of winning on the come out roll is pr(2)+pr(3) = 1/36 + 2/36 = 3/36.
The probability of pushing on the come out roll is pr(12) = 1/36.
The probability of establishing a point and then winning is pr(4)×pr(7 before 4) + pr(5)×pr(7 before 5) + pr(6)×pr(7 before 6) + pr(8)×pr(7 before 8) + pr(9)×pr(7 before 9) + pr(10)×pr(7 before 10) =
(3/36)×(6/9) + (4/36)×(6/10) + (5/36)×(6/11) + (5/36)×(6/11) + (4/36)×(6/10) + (3/36)×(6/9) =
(2/36) × (18/9 + 24/10 + 30/11) =
(2/36) × (1980/990 + 2376/990 + 2700/990) =
(2/36) × (7056/990) = 14112/35640
The total probability of winning is 3/36 + 14112/35640 = 17082/35640 = 2847/5940
The probability of losing is 1-(2847/5940 + 1/36) = 1-(3012/5940) = 2928/5940
The expected return is 2847/5940×(+1) + 2928/5940×(-1) = -81/5940 = -3/220 ≈ 1.364%
Most other sources on craps will claim that the house edge on the don’t pass bet is 1.403%. The source of the discrepancy lies is whether or not to count ties. I prefer to count ties as money bet and others do not. I’m not saying that one side is right or wrong, just that I prefer counting them. If you don’t count ties as money bet then you should divide by figure above by the probability that the bet will be resolved in a win or loss (35/36). So 1.364%/(35/36) ≈ -1.403%. This is the house edge assuming that the player never rolls a 12 on the come out roll.
Place Bets to Win
Place bet on 6 or 8: [(5/11)×7 + (6/11)×(-6)]/6 = (-1/11)/6 = -1/66 ≈ -1.515%
Place bet on 5 or 9: [(4/10)×7 + (6/10)×(-5)]/5 = (-2/10)/5 = -1/25 = -4.000%
Place bet on 4 or 10: [(3/9)×9 + (6/9)×(-5)]/5 = (-3/9)/5 = -1/15 ≈ -6.667%
Place Bets to Lose
Place bet to lose on 6 or 8: [(6/11)×4 + (5/11)×(-5)]/5 = (-1/11)/5 = -1/55 ≈ -1.818%
Place bet to lose on 5 or 9: [(6/10)×5 + (4/10)×(-8)]/8 = (-2/10)/8 = -1/40 = -2.500%
Place bet to lose on 4 or 10: [(6/9)×5 + (3/9)×(-11)]/11 = (-3/9)/11 = -1/33 ≈ -3.030%
Note: These bets are not allowed in land casinos. They can only be found in some Internet casinos.
Buy
Buy bet on 6 or 8: [(5/11)×23 + (6/11)×(-21)]/21 = (-11/11)/21 = -1/21 ≈ -4.762%
Buy bet on 5 or 9: [(4/10)×29 + (6/10)×(-21)]/21 = (-10/10)/21 = -1/21 = -4.762%
Buy bet on 4 or 10: [(3/9)×39 + (6/9)×(-21)]/21 = (-9/9)/21 = -1/21 ≈ -4.762%
Lay
Lay bet to lose on 6 or 8: [(6/11)×19 + (5/11)×(-25)]/25 = (-11/11)/25 = -1/25 ≈ -4.000%
Lay bet to lose on 5 or 9: [(6/10)×19 + (4/10)×(-31)]/31 = (-10/10)/31 = -1/31 = -3.226%
Lay bet to lose on 4 or 10: [(6/9)×19 + (3/9)×(-41)]/41 = (-9/9)/41 = -1/41 ≈ -2.439%
Big 6/Big 8
[(5/11)×1 + (6/11)×(-1)]/1 = -1/11 ≈ 9.091%
Hard 4/Hard 10
Note: The hard 4 and hard 10 pay 7 to 1, or 8for 1. In craps the odds on the cloth are listed on a for 1 basis, including the graphic above.
The probability of a hard 4 on any given roll is 1/36.
The probability of a 7 on any given roll is 6/36.
The probability of a soft 4 on any given roll is 2/36 (1+3 and 3+1).
The probability of winning on any given roll is 1/36.
The probability of losing on any given roll is 6/36 + 2/36 = 8/36.
The probability of winning the bet is p/(p+q) (see above) = (1/36)/(9/36) = 1/9
The expected return is (1/9)×7 + (8/9)×(-1) = -1/9 ≈ 11.111%.
The player’s edge is also -1/9 since the bet is 1 unit.
The odds are the same for a hard 10.
Hard 6/Hard 8
Note: The hard 4 and hard 10 pay 9 to 1, or 10for 1. In craps the odds on the cloth are listed on a for 1 basis, including the graphic above. William hill monopoly live.
The probability of a hard 6 on any given roll is 1/36.
The probability of a 7 on any given roll is 6/36.
The probability of a soft 6 on any given roll is 4/36 (1+5, 2+3, 3+2, and 5+1).
The probability of winning on any given roll is 1/36.
The probability of losing on any given roll is 6/36 + 4/36 = 10/36.
The probability of winning the bet is p/(p+q) (see above) = (1/36)/(11/36) = 1/11
The expected return is (1/11)×9 + (10/11)×(-1) = -1/11 ≈ 9.091%.
The player’s edge is also -1/11 since the bet is 1 unit.
The odds are the same for a hard 8.
Craps 2/Craps 12
[(1/36)×30 + (35/36)×(-1)]/1 = -5/36 ≈ -13.889%
Craps 3/Craps 11
[(2/36)×15 + (34/36)×(-1)]/1 = -4/36 ≈ -11.111%
Any Craps
[(4/36)×7 + (32/36)×(-1)]/1 = -4/36 ≈ -11.111%
Hard 6 Craps Table
Any 7
[(6/36)×4 + (30/36)×(-1)]/1 = -6/36 ≈ -16.667%
Horn
The probability of rolling either a 2 or 12 is 1/36 + 1/36 = 2/36.
The probability of rolling either a 3 or 11 is 2/36 + 2/36 = 4/36.
The probability of roling anything else is 1–2/36–4/36 = 30/36.
Remember that the horn bet is like all four craps bets in one. Even if one wins the other three still lose. The house edge is:
[(2/36)×27 + (4/36)×12 + (30/36)×(-4)]/4 = (-18/36)/4 = 12.500%
Field
When the 12 pays 2:1 the expected return is:
2×(pr(2)+pr(12)) + 1×(pr(3)+pr(4)+pr(5)+pr(10)+pr(11)) + -1×(pr(6)+pr(7)+pr(8)+pr(9)) =
2×(1/36 + 1/36) + 1×(2/36 + 3/36+ 4/36 + 3/36 + 2/36) + -1×(5/36 + 6/36 + 5/36+ 4/36) =
2×(2/36) + 1×(14/36) + -1×(20/36) = -2/36 = -1/18 ≈ 5.556%.
When the 12 pays 3:1 the expected return is:
3×pr(2) + 2×pr(12)) + 1×(pr(3)+pr(4)+pr(5)+pr(10)+pr(11)) + -1×(pr(6)+pr(7)+pr(8)+pr(9)) =
3×(1/36) + 2×(1/36) + 1×(2/36 + 3/36+ 4/36 + 3/36 + 2/36) + -1×(5/36 + 6/36 + 5/36+ 4/36) =
3×(1/36) + 2×(1/36) + 1×(14/36) + -1×(20/36) = -1/36 ≈ 2.778%.
Buying Odds
4 and 10: [(3/9)×2 + (6/9)×(-1)]/1 = 0.000%
5 and 9: [(4/10)×3 + (6/10)×(-2)]/2 = 0.000%
6 and 8: [(5/11)×6 + (6/11)×(-5)]/5 = 0.000%
Laying Odds
4 and 10: [(6/9)×1 + (3/9)×(-2)]/1 = 0.000%
5 and 9: [(6/10)×2 + (4/10)×(-3)]/2 = 0.000%
6 and 8: [(6/11)×5 + (5/11)×(-6)]/5 = 0.000% $10 minimum deposit usa casino.
Combined Pass and Buying Odds
The player edge on the combined pass and buying odds is the average player gain divided by the average player bet. The gain on the pass line is always -7/495 and the gain on the odds is always 0. The expected bet depends on what multiple of odds you are allowed. Lets assume full double odds, or that the pass line bet is $2, the odds bet on a 4, 5, 9, and 10 is $4, and the odds on a 6 or 8 is $5.
The average gain is -2×(7/495) = -14/495.
The average bet is 2 + (3/36)×4 + (4/36)×4 + (5/36)×5 + (5/36)×5 + (4/36)×4 + (3/36)×4] =
2 + 106/36 = 178/36
The player edge is (-14/495)/(178/36) = -0.572%.
The general formula if you can take x times odds on the 6 and 8, y times on the 5 and 9, and z times on the 4 and 10 is (-7 / 495) / [ 1 + ((5x + 4y + 3z) / 18) ]
Hard 6 Craps Tips
Combined Don’t Pass and Laying Odds
The player edge on the combined don’t pass and laying odds is the average player gain divided by the average player bet. The gain on the don’t pass is always -3/220 and the gain on the odds is always 0. The expected bet depends on what multiple of odds you are allowed. Lets assume double odds and a don’t pass bet of $10. Then the player can lay odds of $40 for a win of $20 on the 4 and 10, $30 for a win of $20 on the 5 and 9, and $24 on the 6 and 8 for a win of $20. The average gain is -10×(3/220) = -30/220.
The average bet is 10 + 2×[(3/36)×40 + (4/36)×30 + (5/36)×24] = 30.
The player edge is (-30/220)/30 = -0.455%.
The general formula if you can buy x times odds then the house edge on the combined don’t pass and laying odds is (3/220)/(1+x).
Net Gain/Loss per Session
The chart below shows the net gain or loss you can expect over 100 trials, or come out rolls. For purposes of creating the chart the player would bet $1 on the pass line and take full double odds.
Here are some actual numbers that show the probability of falling into various intervals.
Session Win/Loss
IntervalProbabilityloss of over $1000.0422%loss of $76-$1000.6499%loss of $51-$754.6414%loss of $26-$5016.3560%loss of $1-$2530.0583%break even0.6743%win of $1-$2528.6368%win of $26-$5014.4257%win of $51-$753.9097%win of $76-$1000.5639%win of over $1000.0418%
The graph and table were created by simulating 1,000,000 sessions of 100 trials, or come out rolls, and tabulating the results of each session.
Internal Links
See Full List On Crapspit.org
- How the house edge for each bet is derived, in brief.
- The house edge of all the major bets on both a per-bet made and per-roll basis
- Dice Control Experiments. The results of two experiments on skillful dice throwing.
- Dice Control Advantage. The player advantage, assuming he can influence the dice.
- Craps variants. Alternative rules and bets such as the Fire Bet, Crapless Craps, and Card Craps.
- California craps. How craps is played in California using playing cards.
- Play Craps. Craps game using cards at the Viejas casino in San Diego.
- Number of Rolls Table. Probability of a shooter lasting 1 to 200 rolls before a seven-out.
- Ask the Wizard. See craps questions I’ve answered about:
- Simple Craps game. My simple Java craps game.
Written by: Michael Shackleford
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