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# Craps Side Bets

## Fire Bet

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

0 -1 0.593939 -0.593939
1 -1 0.260750 -0.26075
2 -1 0.101275 -0.101275
3 -1 0.033434 -0.033434
4 24 0.008798 0.211156
5 249 0.001640 0.408343
6 999 0.000162 0.162272
Total 1 -0.207628

### Fire Bet — Pay Table B

0 -1 0.593939 -0.593939
1 -1 0.260750 -0.26075
2 -1 0.101275 -0.101275
3 -1 0.033434 -0.033434
4 10 0.008798 0.087982
5 200 0.001640 0.327987
6 2000 0.000162 0.324869
Total 1 -0.248562

### Fire Bet — Pay Table C

0 -1 0.593939 -0.593939
1 -1 0.260750 -0.26075
2 -1 0.101275 -0.101275
3 6 0.033434 0.200605
4 29 0.008798 0.255147
5 149 0.001640 0.244350
6 299 0.000162 0.048568
Total 1 -0.207295

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

0 0.593939393939394
1 0.260750492003903
2 0.101275355549231
3 0.0334342121788456
4 0.00879817844040312
5 0.00163993313895325
6 0.000162434749269826

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:

1. There are 26=64 possible states according to whether or not the shooter made each of the 6 possible points.
2. For each state there are 7 probabilities, one for each number of points he will eventually make before sevening out, 0 to 6.
3. 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.
4. 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
• by Stwart N. Ethier has a discussion of Fire Bet math.

## Crapless Craps

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

Odds House Edge
1X 2.936%
2X 2.018%
3X 1.538%
5X 1.042%

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

This pair of bets are 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.

### Low Bet

Total Combinations Probability Pays Return
2 1 0.027778 5 0.138889
3 to 6 14 0.388889 1 0.388889
7 to 12 21 0.583333 -1 -0.583333
Total 36 1 -0.055556

## Card Craps

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

Decks Probability House Edge
1 0.217391 13.0435%
2 0.234043 6.383%
3 0.239437 4.2254%
4 0.242105 3.1579%
5 0.243697 2.521%
6 0.244755 2.0979%
7 0.245509 1.7964%
8 0.246073 1.5707%
9 0.246512 1.3953%
10 0.246862 1.2552%
11 0.247148 1.1407%
12 0.247387 1.0453%
13 0.247588 0.9646%
14 0.247761 0.8955%
15 0.247911 0.8357%
16 0.248042 0.7833%

## Midway 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%.

### Midway Bet

Total Combinations Probability Pays Return
Hard 6,8 2 0.055556 2 0.111111
Soft 6,8 8 0.222222 1 0.222222
7 6 0.166667 1 0.166667
All other 20 0.555556 -1 -0.555556
Total 36 1 -0.055556

## 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%.

## All

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

Event Pays Probability Return
Win 1 0.482253 0.482253
Loss -1 0.517747 -0.517747
Total 1 -0.035494

## 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

Event Pays Probability Return
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
Total 1 -0.271883

Assuming the maximum win is \$5000 the following is the house edge for various bet amounts.

Bet House Edge
\$100 49.22%
\$50 46.87%
\$25 45.43%
\$10 41.10%
\$5 33.89%
\$4 32.78%
\$3 30.94%
\$2 29.08%
\$1 27.19%

## 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

Event Pays Probability Return
7 on come out roll 2 0.166667 0.333333
Point 7 3 0.111111 0.333333
Loser -1 0.722222 -0.722222
Total 1 -0.055556

## Sharp Shooter

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

Event Pays Probability Return
10 or more 299 0.000122 0.03644
9 199 0.000178 0.035474
8 99 0.000439 0.043461
7 49 0.001081 0.052975
6 29 0.002662 0.077212
5 19 0.006557 0.12458
4 9 0.016148 0.145328
3 5 0.039766 0.198831
2 or less -1 0.933047 -0.933047
Total 1 -0.218744

## 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.

## Point Seven

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%.

### Point Seven

Event Pays Probability Return
Win 7 0.111111 0.777778
Loss -1 0.888889 -0.888889
Total 1 -0.111111

## Replay

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%.

### Replay

Event Pays Probability Return
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
Loser -1 0.992441 -0.992441
Total 1.000000 -0.247853

## 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

Event Pays Probability Return
Win 6 0.100863 0.605178
Loss -1 0.899137 -0.899137
Total 1 -0.293959

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

Event Pays Probability Return
Win 1 0.471066 0.471066
Loss -1 0.528934 -0.528934
Total 1 -0.057868

## Double D

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%.

### Double D

Unique
Doubles
Pays Probability Return
6 250 0.001083 0.270633
5 50 0.006494 0.324683
4 10 0.022728 0.227282
0 to 3 -1 0.969696 -0.969696
Total 1.000000 -0.147097

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

Event Pays Combinations Probability Return
Double, except 6-6 1.166667 5 0.454545 0.530303
Seven -1 6 0.545455 -0.545455
Total 11 1.000000 -0.015152

## Hot Roller

On December 27, 2013, a member of my 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.

1. The bet may be made only on a come out roll.
2. The bet will be resolved when the shooter rolls a seven.
3. The bet pays according to how many "completed points" the shooter achieves.
4. 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
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

Completed
Points
Pays
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

Completed
Points
Pays Probability Return
6 200 0.000412 0.082441
5 50 0.002219 0.110968
4 20 0.007528 0.150567
3 10 0.021193 0.211934
2 5 0.056287 0.281435
0 or 1 -1 0.912360 -0.912360
Total 1.000000 -0.075013

My methodology was a random simulation of 28 billion resolved bets.

## Repeater

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

Bet Pays
(for 1)
Probability House
Edge
2 40 0.020408 0.183673
3 50 0.015625 0.218750
4 65 0.012346 0.197531
5 80 0.010240 0.180800
6 90 0.008820 0.206209
8 90 0.008820 0.206209
9 80 0.010240 0.180800
10 65 0.012346 0.197531
11 50 0.015625 0.218750
12 40 0.020408 0.183673

At Caesars Palace I noticed they added a "Dealer Envy" win to the same Suncoast pay table above. The following table shows the return to the player, the dealer, and the total.

### Repeater — Caesars Palace Dealer Envy Rules

Dice
Total
Number
Needed
Player
Win
Dealer
Envy
Player
Return
Dealer
Return
Total
Return
2 2 40 2 81.63% 4.08% 85.71%
3 3 50 3 78.13% 4.69% 82.81%
4 4 65 4 80.25% 4.94% 85.19%
5 5 80 5 81.92% 5.12% 87.04%
6 6 90 6 79.38% 5.29% 84.67%
8 6 90 6 79.38% 5.29% 84.67%
9 5 80 5 81.92% 5.12% 87.04%
10 4 65 4 80.25% 4.94% 85.19%
11 3 50 3 78.13% 4.69% 82.81%
12 2 40 2 81.63% 4.08% 85.71%

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.

Bet Pays
(for 1)
Probability House
Edge
4 75.73 0.012346 0.065018
5 79.63 0.010240 0.184627
6 103.46 0.008820 0.087534

Note how the house edge is lower on the 4 and 6 making place/buy bets, but greater on the 5.

According to the 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

Bet Pays
(for 1)
Probability House
Edge
2 40 0.020408163265 0.183673
3 50 0.015625000000 0.218750
4 65 0.012345679012 0.197531
5 80 0.010240000000 0.180800
6 90 0.008819905157 0.206209
8 400 0.001822294454 0.271082
9 2,500 0.000262144000 0.344640
10 25,000 0.000016935088 0.576623
11 100,000 0.000000238419 0.976158
12 50,000,000 0.000000000072 0.996388

## 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!).

## Hard Way Place Bets

.

On May 30, 2017 I noticed place bets on the hard ways on the craps tables at the Orleans casino in Las Vegas. These would win if the specified hard way, for example 5-5, where rolled before a total of seven. Each bet pays 5 to 1.

The following return table shows a house edge of 14.29%, ignoring rolls that neither win nor lose.

### Hard Way Place Bets

Bet Pays Combinations Probability Return
Win 5 1 0.142857 0.714286
Loss -1 6 0.857143 -0.857143
Total 7 1.000000 -0.142857

• — The max odds bet allowed at each casino.

Written by: Michael Shackleford

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