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Last Updated: January 6, 2017
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Craps Side Bets
Some casinos offer a "Fire Bet" that pays if the shooter makes at least 3 or 4 different points. The following table shows two different pay tables I have heard of. Pay Tables A and C were converted from a "for one" to a "to one" basis. The probabilities are exact.
Fire Bet — Pay Table A
Fire Bet — Pay Table B
Fire Bet — Pay Table C
The Fire Bet makes for a challenging math problem. For those of you up to it, here are my probabilities of making 0 to 6 points, with as many significant digits as Excel can handle.
Fire Bet Probabilities
I often get asked how to calculate the above probabilities. Most people do a random simulation, which is fine. However, it makes for a challenging math problem to get the exact probabilities. Here is a brief overview how I did it:
- There are 26=64 possible states according to whether or not the shooter made each of the 6 possible points.
- For each state there are 7 probabilities, one for each number of points he will eventually make before sevening out, 0 to 6.
- Start with the states close to the end, in which the shooter already made 5 points. For example, if the shooter needs a 4 only, then three things can happen: (1) He establishes and makes the 4, (2) He establishes and makes a point he already made, (3) He sevens out. The probability of (1) is (3/24)*(1/3) = 1/24 = 0.041667. The probability of (2) is (4/24)*(2/5) + (5/24)*(5/11) + (5/24)*(5/11) + (4/24)*(2/5) + (3/24)*(1/3) = 0.364394. The probability of (3) is 1- 0.041667 - 0.364394 = 0.593939. Eventually event (1) or (3) will happen. The probability that (1) will happen before (3) is 0.041667/(0.041667+0.593939) = 0.065554.
- Recursively work your way back to the starting point. This will either be time-consuming, redundant, and boring, or you can do it in a spreadsheet in an automated manner.
You can also use matrix algebra. Forgive me if I don't explain how.For more help, I offer three resources:
- Fire Bet math is discussed at my companion site Wizard of Vegas
- See my own spreadsheet, which I posted at GoogleDocs for anyone to download.
- The Doctrine of Chances: Probabilistic Aspects of Gambling by Stwart N. Ethier has a discussion of Fire Bet math.
In my Ten Commandments of Gambling I advise that you avoid gimmicks, and Crapless Craps is an illustrated example. In this game the player can not lose a pass bet on the come out roll. If any number other than a 7 is rolled on the come out roll, then it becomes the point. What you are giving up is the sure winner of 11 on the come out roll. To the mathematically challenged, it may seem a good deal, that you are only giving up 1 sure winner for 3 sure losers. The catch is that the probability of hitting a point of 2 or 12 is only 1/7, and the probability of hitting a point of 3 or 11 is only 1/4. So, the player is not gaining much on the 2, 3, and 12 since they will likely lose anyway, but is giving up a sure winner on the 11 for only a 1/4 chance of winning. Overall the house edge on the pass bet in crapless craps is 373/6930 = 5.382%.
Crapless craps does offer free odds of 6-1 on the 2 and 12, and 3-1 on the 3 and 11. The following table shows the combined house edge by combining the pass line and the odds:
Combined house edge on pass and buying odds in Crapless Craps
You can also make place bets on the 2, 3, 11, and 12. The 2 and 12 pay 11-2 with a house edge of 7.143%. The 3 and 11 pay 11-4 with a house edge of 6.250%. There is no don't pass bet in this game.
You can also make buy bets. On points of 4, 5, 6, 8, 9, and 10 the odds are the same as regular craps. The following table shows the odds on the 2, 3, 11, and 12. One reader claims they only charge the commission on wins in Mississippi but I'll list it both ways.
Buy Bets in Crapless Craps
|Bet||Pays||Prob. Win||House Edge|
|Place 2, 12||11 to 2||14.2857%||7.1429%|
|Place 3,11||11 to 4||25.0000%||6.2500%|
|Buy 2, 12 (commission only on wins)||119 to 20||14.2857%||0.7143%|
|Buy 3,11 (commission only on wins)||59 to 20||25.0000%||1.2500%|
|Buy 2, 12 (commission always)||119 to 21||14.2857%||4.7619%|
|Buy 3,11 (commission always)||59 to 21||25.0000%||4.7619%|
As far as I know, in Las Vegas Crapless Craps is offered at the Stratosphere, Las Vegas Club, The Plaza and Sunset Station.
Low Dice, High Dice
The Hard Rock in Las Vegas and Texas Treasure casino cruises offer a pair of side bets based on the total of the dice in one throw. The "Low Dice" bet pays 1 to 1 on totals of 3 to 6 and 5 to 1 on a total of 2. The "High Dice" pays 1 to 1 on totals of 8 to 11 and 5 to 1 on a total of 12. The following return table on the Low Dice bet shows the house edge is 5.56%. The High Dice bet is the opposite so has the same house edge.
|3 to 6||14||0.388889||1||0.388889|
|7 to 12||21||0.583333||-1||-0.583333|
In some jurisdictions, namely California, dice alone may not determine the outcome of a bet. In the game of "Card Craps" 24-card decks are used each consisting of ranks ace to six in all four suits. Two cards are drawn to simulate the roll of the dice. If the suits are different the "roll" stands. If the suits are the same, then the roll is ignored for all craps bets. The odds on all craps bets are the same as if dice were used.
However, there is an extra bet called the "No Call." This bet pays 3 to 1 if the two cards are suited, otherwise it loses. The house edge depends on the number of 24-card decks used as shown below.
Card Craps - No Call Bet
The Showboat in Atlantic City I'm told has a Midway bet in the normal location of the Big 6 and Big 8 on a total of 6 to 8 in the next roll. A hard 6 or 8 pay 2 to 1, and all other totals of 6 to 8 pay 1 to 1. The following table shows the house edge is 5.56%.
Small and Tall
The Small bet wins if the shooter rolls every total from 2 to 6 before a 7. The Tall bet requires the shooter to roll every total from 8 to 12 before a 7. Both have a probability of winning of 0.026354, or about 1 in 38. There are two known payoffs, as follows:
- If wins pay 34 to 1 (or 35 for 1), then the house edge is 7.76%.
- If wins pay 30 to 1 (or 31 for 1), then the house edge is 18.30%.
The All bet wins if the shooter rolls every total except a 7 before a 7. It is always offered along with the Small and Tall bets explained above. The probability of winning of 0.005258, or about 1 in 190. There are two known payoffs, as follows:
- If wins pay 175 to 1 (or 176 for 1), then the house edge is 7.47%.
- If wins pay 150 to 1 (or 151 for 1), then the house edge is 20.61%.
Four Rolls no Seven
I hear that Sam's Town in both Las Vegas and Shreveport offer this bet. The bet wins if the shooter can go four throws without rolling a seven. A win pays 1 to 1. The odds are as follows.
Four Rolls no Seven
Golden Dice Challenge
The "Golden Dice Challenge" is a craps side bet found at the MGM Grand in Detroit. The bet pays according to the number of pass line wins the player has before a seven-out. For purposes of the side bet, a win may be made either by rolling a 7 or 11 on the come out roll, or making a point. Rolling a 2, 3, or 12 on the come out roll does not affect the bet. There is a maximum win of $5,000.
The following return table shows the pays, probabilities, and return from each event, based on a $1 bet.
Golden Dice Challenge Return Table for $1 Bet
|20 or more||5000 to 1||0.000008||0.037819|
|17 to 19||2000 to 1||0.000037||0.07358|
|15 to 16||1000 to 1||0.0001||0.099877|
|13 to 14||100 to 1||0.000325||0.032478|
|11 to 12||50 to 1||0.001056||0.052806|
|9 to 10||25 to 1||0.003434||0.085858|
|7 to 8||10 to 1||0.011168||0.111678|
|5 to 6||5 to 1||0.036316||0.181578|
|0 to 4||Loss||0.947557||-0.947557|
Assuming the maximum win is $5000 the following is the house edge for various bet amounts.
Golden Dice Challenge House Edge by Amout Bet
7 Point 7
7 Point 7 is a craps side bet, which debuted at the Orleans casino in Las Vegas, in late 2008. I have also seen it at the Hard Rock in Macau under the name "Double Trip Seven." The bet wins if the player gets a seven on the come out roll, or the dreaded "point 7," where the player sevens out on his second roll. The following table shows a house edge of 5.56%.
7 Point 7 Return Table
|7 on come out roll||2||0.166667||0.333333|
The "Sharp Shooter" is a side bet in craps spotted at the Hooters casino in Las Vegas in March, 2009. I hear it was removed in 2014.
The bet is made when a new shooter takes the dice, and pays according to how many times he makes a point. The following table shows what each number of points made pays and the probability. Pays have been converted to a "to one" basis, to be consistent with the rest of this page. The lower right cell shows a house edge of 21.87%.
Sharp Shooter — Return Table
|10 or more||299||0.000122||0.03644|
|2 or less||-1||0.933047||-0.933047|
Double Trip Seven
I noticed this bet at the City of Dreams in Macau in August 2009. It is the same thing as the7 Point 7 bet aleady described.
I saw this side bet at the 2009 Global Gaming Expo, and in June 2010 at the Las Vegas Hilton. It is licensed by Casino Gaming LLC. It is a side wager made on the come out roll. If the player rolls a point, and then a seven on the second roll, the bet pays 7 to 1. All other outcomes lose. The following table shows the house edge is 11.11%.
Replay is a craps side bet I spotted at the Boulder Station on September 16, 2010. It pays if the shooter makes the same point at least 3 times before sevening out. The following table shows what each event pays, the probability, and contribution to the return. The table is based on a random simulation of over 2 billion shooters. Only the highest win is paid. The lower right cell shows a house edge of 24.79%.
|4 or 10 four or more times||1000||0.000037||0.036892|
|5 or 9 four or more times||500||0.000207||0.103497|
|4 or 10 three times||120||0.000524||0.062847|
|6 or 8 four or more times||100||0.000698||0.069815|
|5 or 9 three times||95||0.001799||0.170927|
|6 or 8 three times||70||0.004294||0.300609|
Twice as Nice
Twice as Nice is a side bet that has been seen at an unknown casino in Biloxi. It wins if the shooter throws any specific pair, including a total of 2 and 12, twice before a seven. For example, rolling a hard 10 twice before a 7. Wins pay 6 to 1. The following table shows a house edge of 29.40%.
Twice as Nice
A win of 7 to 1 would have a house edge of 19.31%, and 8 to 1 would be 9.22%.
Pete and Repeat
Pete and Repeat has also been seen at the same mystery casino in Biloxi. It wins if any total is rolled twice before a 7. Wins pay even money. The following table shows a house edge of 5.79%.
Pete and Repeat
Place the Hard Ways
Place the Hard Ways is a proposition wager that was seen at the Orleans in Las Vegas in late 2011. It works like the other Place bets, except the point must be made the hard way. It differs from the Hard Way bets in that making the point the easy way does not cause a loss. There are four bets available, on the hard 4, 6, 8, and 10.
The following table shows the house edge is 14.3% per bet resolved.
Place the Hard Ways
In April 2012 I heard this side bet was being offered at the Harrington Raceway casino in Harrington, Delaware. It pays if the shooter makes at least four unique doubles before he sevens out. Come out rolls do not count. The following table shows all the possible outcomes, what they pay (on a "to one" basis), the probability, and return. The lower right cell shows a house edge of 14.71%.
|0 to 3||-1||0.969696||-0.969696|
Broad Bar 12
In April 2012 I heard this side bet was being offered at the Harrington Raceway casino in Harrington, Delaware. It acts like a place bet, winning on any double except 6-6, and losing on seven. The following return table shows the a house edge of 1.52%, per bet resolved.
Broad Bar 12 — Not Counting Pushes
|Double, except 6-6||1.166667||5||0.454545||0.530303|
On December 27, 2013, a member of my Wizard of Vegas forum posted about seeing this side bet at the Dover Downs casino in Delaware. It pays based on how many "completed points" the shooter gets before rolling a seven. The shooter completes a point when he rolls it in all possible ways. For example, to complete a point of eight the shooter would need to roll a 2+6, 3+5, and 4+4. Following are the complete rules.
- The bet may be made only on a come out roll.
- The bet will be resolved when the shooter rolls a seven.
- The bet pays according to how many "completed points" the shooter achieves.
- To complete a point, the shooter must roll the given total all possible ways. The following list shows all the ways to roll each total.
- 4: 1+3, 2+2
- 5: 1+4, 2+3
- 6: 1+5, 2+4, 3+3
- 8: 2+6, 3+5, 4+4
- 9: 3+6, 4+5
- 10: 4+6, 5+5
- The player must complete at least two points to win. The following table shows how much each number of completed points pays.
Hot Roller Pay Table
|6||200 to 1|
|5||50 to 1|
|4||20 to 1|
|3||10 to 1|
|2||5 to 1|
|0 or 1||Loss|
The following table shows the probability and contribution to the return for all possible outcomes. The lower right cell shows a house edge of 7.50%. There are certainly much worse things you could bet on in craps.
Hot Roller Return Table
|0 or 1||-1||0.912360||-0.912360|
My methodology was a random simulation of 28 billion resolved bets.
Repeater is a set of craps side bets I noticed at the Suncoast casino in Las Vegas on April 6, 2015. The idea is that the player must roll a given number a specified number of times before a seven. For bets on 2 to 6, the player must roll that total the same number of times as the total itself. For example, for the bet on the number five to win, the shooter must roll 5 fives before a seven. For totals of 8 to 12, the player must roll the total 14 less whatever the total is. For example, on a total of 11, the player must roll an eleven 14-11=3 times before a seven.The following is what each specific bet pays:
- 2: 40 for 1
- 3: 50 for 1
- 4: 65 for 1
- 5: 80 for 1
- 6: 90 for 1
- 8: 90 for 1
- 9: 80 for 1
- 10: 65 for 1
- 11: 50 for 1
- 12: 40 for 1
The following table shows the probability of winning and house edge of each bet.
Repeater — Suncoast Rules
It should be noted that the player can achieve the same thing by parlaying place/buy bets. Here is the same chart for the better of place and buy bets. This assumes a buy bet on the 4 with commission on a win only (effective odds of 59 for 20), place bet on the 5 paying 7 to 5, and place bet on the 6 paying 7 to 6.
Place/Buy Parlay Strategy
Note how the house edge is lower on the 4 and 6 making place/buy bets, but greater on the 5.
According to the patent application for the Repeater Bets there are some other variants, as follows:
- Variant 1: Come out rolls don't count. In this version, the player can only lose on a "seven out" but any numbers rolled on a come out roll don't help either. The patent application doesn't specifically say that other numbers on a come out roll don't help, but it is implied by saying that the casino may choose to let the player turn the repeater bets on and off on a come out roll. Why would any player turn them off if the player could only advance on a come out roll and not lose?
- Variant 2: The player may also bet on a 8, 9, 10, 11, or 12. The win and number of rolls required are the same as the mirror image number below seven. For example, a player must roll 6 eights on the eight bet, which pays 90 for 1.
- Variant 3: The player may also bet on a 8, 9, 10, 11, or 12. However, unlike variant 2, the player must still achieve the given number that many times to win. For example, for a bet on eight, the shooter must roll 8 eights before a seven to win. The odds under this variant are shown below.
Repeater — "Variant 3" rules
Under 7, Over 7
The over and under 7 are a pair of side bets I noticed at the New York, New York on January 6, 2017. You can find them where the Big 6 and 8 bets used to be. Both bets pay even money bets and win if the next roll is over/under a 7. So, a total of 7 causes both to lose. The probability of winning is 15/36=41.67% and the house edge is 16.67% (ouch!).
- 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.
- Las Vegas craps survey — The max odds bet allowed at each casino.
Written by: Michael Shackleford