Craps Side Bets
Craps Side Bets
- Most of the best bets at craps involve multiple rolls. Those with house edges under 2% are pass or come (1.41%), don’t pass or don’t come (1.36%), and place bets.
- (3x $2 bet) If the 'yo 11 rolls, player wins $16 minus the $2 bet = 14 and 'still up to win again'(7x $2 bet) $5 C&E is $2.50 on each side. If craps win you have 2.50 x 8 = 20 - 5 = 15 or 3 times the bet. If eleven wins you have 2.50 x 16 = 40 minus the $5 bet = 35 or 7 x the bet (7x5=35) $25 C & E You can do $12.50 x 16 then subtract 25.
Sep 08, 2020 Simply place your wager under the dotted line of either the 6 or the 8 on the far side of the craps table and hope that Lady Luck is on your side. Be careful not to fall victim to the “big 6” and “big 8” bets, which are exactly the same, but only pay 1:1.
In addition to all of the standard bets at the craps table, there are a number of side bets offered by casinos. While these can spice up the game, giving you a break from the regular betting options when things get a little monotonous and can earn you a few dollars on the side, some of them are purely sucker bets that have been added to give the house an even greater edge in these craps games and should be avoided.
Analyzing side bets at the table is often difficult, so it's best to know what they're all about before you play. Here we'll look at and analyze several of the most common craps side bets to help you do just that before your next online craps game.
It is important to keep in mind that side bets on all casino games generally carry high house edges so if you are looking to purely win the games you play they should be avoided. If however you are more of a casual gambler and just want to have some fun, with a little luck they can just pay off. So always keep your money on the less risky craps bets and place a side bet now and again for fun.
All Bet
The 'All Bet' craps bet is a rather long shot wager, but that said, it does offer a big payout when it comes in. Winning this bet is determined on the shooter throwing every other number before he/she throws a seven. The payout on this wager is a massive 174:1 and the house edge is a rather large 8% because the odds of the shooter accomplishing this are highly unlikely. That said the 8% house advantage is still low as far as side bets go, so some players may believe the risk is worth it for the large payout potential.
Fire Bet
The Fire Bet is probably one of the most popular side bets in Craps. This bet generally requires a $1 wager and pays out if the shooter hits a number of different points before failing to make the point and rolling a seven instead. It is important to remember that the points of the different numbers add to the total but can only be counted once. So for example, if the shooter rolls a point of five then does so again later, that will only count as a single point in the Fire Bet.
The Fire Bet wins when a shooter hits four or more points, which is typically a very rare occurrence, which of course makes the payouts on this side bet rather high at 25:1 if the shooter gets four points, 250:1 if he/she makes five and a whopping 1000:1 for making all six. Be sure however to check the payouts on these bets as paytables do vary from one casino to the next.
The house advantage on this wager generally works out to bet between 20 and 25 percent depending on the paytable, making it a rather bad wager in the long term. That said if you would play the lottery for a $1, then you could opt for this bet at better odds to add excitement to your game.
Midway Bet
This side bet originated in casinos in Atlantic City and typically carries a house edge of around 5.5% making it one of the better side bet options in craps. It pays out when a shooter throws a six, seven or eight on the roll after the bet is placed. A win generally pays even money, unless a hard six consisting of a pair of threes or a hard eight made up of a pair of fours is thrown, which then result in a 2:1 payout.
Point 7
The Point 7 bet is one of the simplest and most common side bets in craps. This bet carries an 11% house advantage is made on the shooter rolling a point on his/her come out roll and subsequently rolling a seven on the next one. If this happens you'll earn a payout of 7:1.
7 Point 7
If you make the 7 Point 7 side bet you'll be counting on the shooter rolling a 7 early in the game. If he/she rolls a 7 on the come out roll you'll be paid out at 2:1, a seven on the first roll after establishing point payout out at 3:1 and in all other instances this wager loses.
It does however join the previously mentioned Midway bet in the lower house edge category at just 5.5%, yet it doesn't give you the opportunity to win big like the other side bets. Still if you're in for some added excitement that pays out small amounts on a more regular basis, this is the wager you'll want to make.
Sharp Shooter
The sharp shooter side bet wagers on the shooter going on a roll. This bet pays out if the shooter can achieve the point three or more times in a row but the largest payouts are earned if the shooter rolls a number of points. Payouts are as follows: Three Points will give you 5:1 payouts, if the shooter gets Four Points you'll be paid out at 9:1 and so the payouts increase until the shooter makes nine points (199:1) or the maximum possible 10 points in a row which would earn you a massive 299:1 payout.
Again the house edge is very high on this wager at around 22%. Still if you love risks and aren't too serious about winning, then it can be a great option and provide loads of entertainment for a relatively small wager.
- Appendices
- Craps Analysis
- Miscellaneous
Introduction
The Fire Bet is a popular side bet in craps that pays based on the number of unique points established and won by the shooter. I am aware of three pay tables, as follows. The house edge of each is in the bottom row of the table. Pay Table 1 is the most common. Pays are indicated on a 'to one' basis. A negative one indicates a loss.
Fire Bet Pay Tables
| Points Made | Pay Table A | Pay Table B | Pay Table C |
|---|---|---|---|
| 6 | 999 | 2000 | 299 |
| 5 | 249 | 200 | 149 |
| 4 | 24 | 10 | 29 |
| 3 | -1 | -1 | 6 |
| 2 | -1 | -1 | -1 |
| 1 | -1 | -1 | -1 |
| 0 | -1 | -1 | -1 |
| House edge | 20.76% | 24.86% | 20.73% |
Following is my analysis of Pay Table A. The lower right cell shows a house edge of 20.76%.
Fire Bet — Pay Table A
| Points Made | Pays | Probability | Return |
|---|---|---|---|
| 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 |
Following is my analysis of Pay Table B. The lower right cell shows a house edge of 24.86%.
Fire Bet — Pay Table B
| Points Made | Pays | Probability | Return |
|---|---|---|---|
| 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 |
Following is my analysis of Pay Table C. The lower right cell shows a house edge of 20.73%.
Fire Bet — Pay Table C
| Points Made | Pays | Probability | Return |
|---|---|---|---|
| 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 following table shows the probabilities of making 0 to 6 points, with as many significant digits as Excel can handle.
Fire Bet Probabilities
| Points Made | Probability |
|---|---|
| 0 | 0.593939393939394 |
| 1 | 0.260750492003903 |
| 2 | 0.101275355549231 |
| 3 | 0.0334342121788456 |
| 4 | 0.00879817844040312 |
| 5 | 0.00163993313895325 |
| 6 | 0.000162434749269826 |
Best Bets In Craps And Why
I often get asked how to calculate the above probabilities. It makes for a challenging math problem. Below, I list there ways to solve for the odds of making any number of points from 0 to 6.
Random Simulation
A random simulation is the easiest way to analyze the Fire Bet. With the speed of modern computers, it is also extremely accurate. Only the most mathematical purists (like me) will strive for an exact solution. The following table shows results of a simulation of almost 40 billion Fire bets resolved against pay table A. The lower right cell shows a house edge of 20.7531%. The actual house edge is 20.7628%, so the simulation was accurate to 0.01% of return.
Fire Bet Simulation
Craps Betting Strategy
| Points Made | Pays | Wins | Probability | Return |
|---|---|---|---|---|
| 6 | 999 | 6,452,452 | 0.000162 | 0.162257 |
| 5 | 249 | 65,165,019 | 0.001640 | 0.408438 |
| 4 | 24 | 349,553,690 | 0.008799 | 0.211173 |
| 3 | -1 | 1,328,267,592 | 0.033435 | -0.033435 |
| 2 | -1 | 4,023,371,732 | 0.101275 | -0.101275 |
| 1 | -1 | 10,358,742,102 | 0.260747 | -0.260747 |
| 0 | -1 | 23,595,605,529 | 0.593941 | -0.593941 |
| Total | 39,727,158,116 | 1.000000 | -0.207531 |
Markov Chain
A way to calculate the odds of the Fire Bet exactly is with a Markov Chain. This means to calculate the probability of completing any future number of points given any of the 64 possible states of points already completed. The math is fairly easy towards the end, needing only one more point to complete all six. Then work your way back to the beginning state of the first roll.
This first state is represented as the first row in the table, not counting the column headings. It shows the probabilities shown above for completing any number of points from 0 to 6.
Fire Bet Markov Chain
| Points Already Made | Probability 0 Points | Probability 1 Points | Probability 2 Points | Probability 3 Points | Probability 4 Points | Probability 5 Points | Probability 6 Points |
|---|---|---|---|---|---|---|---|
| None | 0.593939 | 0.260750 | 0.101275 | 0.033434 | 0.008798 | 0.001640 | 0.000162 |
| 10 | 0.000000 | 0.619763 | 0.256759 | 0.091331 | 0.026183 | 0.005375 | 0.000589 |
| 9 | 0.000000 | 0.636364 | 0.252138 | 0.084540 | 0.022402 | 0.004153 | 0.000404 |
| 9,10 | 0.000000 | 0.000000 | 0.666100 | 0.244772 | 0.072316 | 0.015152 | 0.001660 |
| 8 | 0.000000 | 0.656067 | 0.244255 | 0.076831 | 0.019163 | 0.003370 | 0.000314 |
| 8,10 | 0.000000 | 0.000000 | 0.687719 | 0.234612 | 0.063990 | 0.012405 | 0.001274 |
| 8,9 | 0.000000 | 0.000000 | 0.708220 | 0.225365 | 0.055933 | 0.009618 | 0.000864 |
| 8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 6 | 0.000000 | 0.656067 | 0.244255 | 0.076831 | 0.019163 | 0.003370 | 0.000314 |
| 6,10 | 0.000000 | 0.000000 | 0.687719 | 0.234612 | 0.063990 | 0.012405 | 0.001274 |
| 6,9 | 0.000000 | 0.000000 | 0.708220 | 0.225365 | 0.055933 | 0.009618 | 0.000864 |
| 6,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 6,8 | 0.000000 | 0.000000 | 0.732710 | 0.210728 | 0.048135 | 0.007762 | 0.000665 |
| 6,8,10 | 0.000000 | 0.000000 | 0.000000 | 0.772414 | 0.190903 | 0.033563 | 0.003120 |
| 6,8,9 | 0.000000 | 0.000000 | 0.000000 | 0.798371 | 0.173323 | 0.026215 | 0.002091 |
| 6,8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.845739 | 0.142050 | 0.012211 |
| 5 | 0.000000 | 0.636364 | 0.252138 | 0.084540 | 0.022402 | 0.004153 | 0.000404 |
| 5,10 | 0.000000 | 0.000000 | 0.666100 | 0.244772 | 0.072316 | 0.015152 | 0.001660 |
| 5,9 | 0.000000 | 0.000000 | 0.685315 | 0.237358 | 0.064328 | 0.011875 | 0.001124 |
| 5,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.719927 | 0.224997 | 0.049645 | 0.005432 |
| 5,8 | 0.000000 | 0.000000 | 0.708220 | 0.225365 | 0.055933 | 0.009618 | 0.000864 |
| 5,8,10 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 5,8,9 | 0.000000 | 0.000000 | 0.000000 | 0.769382 | 0.195368 | 0.032496 | 0.002754 |
| 5,8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.813278 | 0.170376 | 0.016346 |
| 5,6 | 0.000000 | 0.000000 | 0.708220 | 0.225365 | 0.055933 | 0.009618 | 0.000864 |
| 5,6,10 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 5,6,9 | 0.000000 | 0.000000 | 0.000000 | 0.769382 | 0.195368 | 0.032496 | 0.002754 |
| 5,6,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.813278 | 0.170376 | 0.016346 |
| 5,6,8 | 0.000000 | 0.000000 | 0.000000 | 0.798371 | 0.173323 | 0.026215 | 0.002091 |
| 5,6,8,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.845739 | 0.142050 | 0.012211 |
| 5,6,8,9 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.876957 | 0.114977 | 0.008066 |
| 5,6,8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.934446 | 0.065554 |
| 4 | 0.000000 | 0.619763 | 0.256759 | 0.091331 | 0.026183 | 0.005375 | 0.000589 |
| 4,10 | 0.000000 | 0.000000 | 0.647934 | 0.250930 | 0.079930 | 0.018752 | 0.002454 |
| 4,9 | 0.000000 | 0.000000 | 0.666100 | 0.244772 | 0.072316 | 0.015152 | 0.001660 |
| 4,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.698752 | 0.234682 | 0.058434 | 0.008131 |
| 4,8 | 0.000000 | 0.000000 | 0.687719 | 0.234612 | 0.063990 | 0.012405 | 0.001274 |
| 4,8,10 | 0.000000 | 0.000000 | 0.000000 | 0.722581 | 0.221643 | 0.049624 | 0.006153 |
| 4,8,9 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 4,8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.786359 | 0.188851 | 0.024790 |
| 4,6 | 0.000000 | 0.000000 | 0.687719 | 0.234612 | 0.063990 | 0.012405 | 0.001274 |
| 4,6,10 | 0.000000 | 0.000000 | 0.000000 | 0.722581 | 0.221643 | 0.049624 | 0.006153 |
| 4,6,9 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 4,6,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.786359 | 0.188851 | 0.024790 |
| 4,6,8 | 0.000000 | 0.000000 | 0.000000 | 0.772414 | 0.190903 | 0.033563 | 0.003120 |
| 4,6,8,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.816667 | 0.164832 | 0.018502 |
| 4,6,8,9 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.845739 | 0.142050 | 0.012211 |
| 4,6,8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.899083 | 0.100917 |
| 4,5 | 0.000000 | 0.000000 | 0.666100 | 0.244772 | 0.072316 | 0.015152 | 0.001660 |
| 4,5,10 | 0.000000 | 0.000000 | 0.000000 | 0.698752 | 0.234682 | 0.058434 | 0.008131 |
| 4,5,9 | 0.000000 | 0.000000 | 0.000000 | 0.719927 | 0.224997 | 0.049645 | 0.005432 |
| 4,5,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.758221 | 0.208531 | 0.033248 |
| 4,5,8 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 4,5,8,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.786359 | 0.188851 | 0.024790 |
| 4,5,8,9 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.813278 | 0.170376 | 0.016346 |
| 4,5,8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.862486 | 0.137514 |
| 4,5,6 | 0.000000 | 0.000000 | 0.000000 | 0.745247 | 0.209635 | 0.041004 | 0.004114 |
| 4,5,6,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.786359 | 0.188851 | 0.024790 |
| 4,5,6,9 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.813278 | 0.170376 | 0.016346 |
| 4,5,6,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.862486 | 0.137514 |
| 4,5,6,8 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.845739 | 0.142050 | 0.012211 |
| 4,5,6,8,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.899083 | 0.100917 |
| 4,5,6,8,9 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.934446 | 0.065554 |
| 4,5,6,8,9,10 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 |
If you plan to try to recreate my work, here is some advice on going from one state to another. 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.
Calculus
The first step in this method is to calculate the probability of all 7 possible pertinent outcomes of a pass line bet after a point is established. We can ignore the 12 combinations, or 1/3 chance, of the player winning or losing immediately on the come out roll, because those events are not significant to the Fire Bet. So the first roll is based on 24 possible combinations, as opposed to 36.
- Point of 4 made and won = (3/24) × (3/9) = 1/24 = apx. 4.17%
- Point of 5 made and won = (4/24) × (4/10) = 1/15 = apx. 6.67%
- Point of 6 made and won = (5/24) × (5/11) = 25/264 = apx. 9.47%
- Point of 8 made and won = (5/24) × (5/11) = 25/264 = apx. 9.47%
- Point of 9 made and won = (4/24) × (4/10) = 1/15 = apx. 6.67%
- Point of 10 made and won = (3/24) × (3/9) = 1/24 = apx. 4.17%
- Any point made and 7-out = 2×((3/24) × (6/9))+ 2× ((4/24) × (6/10)) + 2×((5/24) × (6/11)) = 98/165 = apx. 59.39%
Please note, the sum of these probabilities equals 1.
Next, instead of the Fire Bet being decided by the roll of two dice, one roll at a time, consider the time between events to occur randomly, with the time between events following an exponential distribution with a mean of one unit of time between events. If an event does occur, the particular event will follow the craps probabilities we just calculated.
For example, the probability of a point-4 win is 1/24. Thus, the time between point-4 wins will average 24 units. The probability of going x units of time without a point-10 win is exp(-x/24). To take the compliment, the probability of at least one point-10 win in x units of time is 1-exp(-x/24).
To adjudicate the Fire Bet, it doesn't matter how much time elapses between events -- just what the events are. So we can the integrate over all time for a winner to the bet as follows:
Let me explain what that integral means. It is the probability that after x units of time there has been at least one win of every point but not a 7. Since the probability of a point-4 and point-10 win is the same, we can square the probability of a point-4 win. Same as for 5 and 9, as well as 6 and 8. Finally we multiply the whole thing by 98/165, the probability of a seven-out, to close off the bet. If we didn't do that, the player might get paid for multiple overlapping wins.
Integrating this by hand would be very tedious and error prone. Fortunately, there are integral calculators. To use the one for this problem, click on the link and put the following into the text box at the top: (1-exp(-x/24))^2*(1-exp(-x/15))^2*(1-exp(-25x/264))^2*exp(-98x/165)/(165/98). Then click on options and set the lower bound to 0 and the upper bound to infinity. Then click go.
Before considering the bounds of integration, the answer is (98*(-(165*e^(-(98*x)/165))/98+(2640*e^(-(839*x)/1320))/839+(330*e^(-(109*x)/165))/109-(220*e^(-(149*x)/220))/149+(880*e^(-(303*x)/440))/303-(1760*e^(-(309*x)/440))/309-(11*e^(-(8*x)/11))/8-(1320*e^(-(241*x)/330))/241+(1320*e^(-(491*x)/660))/491-(5280*e^(-(997*x)/1320))/997+(528*e^(-(203*x)/264))/203+(2640*e^(-(1019*x)/1320))/1019-(60*e^(-(47*x)/60))/47+(2640*e^(-(263*x)/330))/263-(132*e^(-(107*x)/132))/107+(528*e^(-(217*x)/264))/217+(80*e^(-(33*x)/40))/33-(1760*e^(-(369*x)/440))/369+(40*e^(-(17*x)/20))/17-(88*e^(-(19*x)/22))/19-(15*e^(-(13*x)/15))/13-(480*e^(-(107*x)/120))/107+(528*e^(-(239*x)/264))/239-(12*e^(-(11*x)/12))/11+(15*e^(-(14*x)/15))/7+(48*e^(-(23*x)/24))/23-e^(-x)))/165.
Fortunately, that calculator does allow for bounds of integration and gives the solution as 3700403899126040038831518494284887738125 / 22780863797678919004236184338193605974839452, which is approximately equal to 0.0001624347492698264.
Of course, that is just the probability of making all six points, but the same logic could be used to find the probability of any number of points. I'll leave that as an exercise to the reader ;-).
External Links
- 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.
Acknowledgements
I would like to thank Wizard of Vegas forum member Ace2 for his tireless advice on solving for the probability of the Fire Bet using integration.