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No one can control the outcome of a craps dice roll (assuming legal dice are used). No one! And that includes all the dice-control hustlers on the Internet trying to convince you that their “proven” methods can give you a leg up on the casino (refer to our other lesson on dice control for all you need to know about that scam). The only weapon you have against the casino is the big hunk of fat between your ears. Yes, I’m talking about your brain. (And, yes, two-thirds of your brain is fat, or specialized fatty acids). Your knowledge of the game makes all the difference in how much you win or lose, and particularly whether you lose slowly or swiftly.

The single most effective (and simplest) thing you can do to minimize your craps losses is to stop making sucker bets, which are those with the highest house advantages. For example, there are about 10 bets with house advantages less than 2%, and about 10 bets with house advantages of more than 10%. The best thing you can do is stop making those stupid bets that have those ridiculously high house edges.

Let’s review what we learned in our other lesson about “house advantage” by summarizing the well-known example of a coin flip.

Every time you flip a coin, you have a 50/50 chance that either heads or tails will appear. That means you have an even chance of either result showing. In the gambling world, that means if you were to bet on each coin flip, you’d expect to get even money where the odds are expressed as 1:1 (“one to one”). That means if, if you win, you expect to get the same amount that you bet. For example, if you bet $5 and win, then you expect to be paid $5. As you learned in our other lessons, the casino is a business and wants to make a profit. To achieve its goal, it doesn’t give us “true” odds based on the statistical likelihood of expected outcomes (except for the Odds bet, which is discussed in our lessons about the Pass Line and Don’t Pass). Instead, the casino gives us what are called “casino odds,” which are less than (or not as good as) true odds. Basically, the casino doesn’t pay their fair share to us when they lose. If true odds were used instead of casino odds, everything would even out over a long period of time and both the casino and player would break even. However, using casino odds, the casino makes a profit over a long period of time because it never (except for the Odds bet) pays its fair share on its losses. For example, let’s go back to the coin flip.

Suppose you flip against the casino and you bet $1 on each flip. When you lose a flip, you pay the casino $1. But when you win a flip, the casino pays you, say, only 90 cents. Suppose you flip 100 times. Assuming a perfect distribution, suppose you win 50 times and lose 50 times (which is what you would expect). For your 50 losing flips, your total loss is $50 (i.e., $1 x 50 losing flips = $50). But for you 50 winning flips, your total win is only $45 (i.e., $0.90 x 50 winning flips = $45). So, even though you won and lost exactly the same number of flips, you end up a loser because the casino doesn’t pay its fair share when you win.

A major part of playing craps as a strong, solid rock is making bets that have the lowest casino odds, or lowest house advantages. Other strategies, which we discuss in other lessons, contribute to your ability to play rock solid, but simply knowing which bets to avoid is critically important. For example, let’s compare two bets, the Big 8 and the Pass Line. The Big 8’s house advantage is a “big” 9% (maybe that’s why the casino calls it the “Big 8”) compared the Pass Line’s house edge of only 1.4%. You ask, “What exactly does house advantage mean?” In the context of knowing how much we’re going to lose by making each of these bets, the Big 8’s house advantage of 9% means we expect an average loss of 90 cents for each $10 that we bet (or $9 for every $100 that we bet). A house advantage of 1.4% means we expect an average loss of 14 cents for each $10 that we bet (or $1.40 for every $100 that we bet). So, when we talk about a craps bet being “good” or “bad,” we base it on how much we expect to lose. In terms of the Big 8 versus the Pass Line, now that you know their house advantages and how much you can expect to lose, which one is “good” and which is “bad?” Yes, of course, the Big 8 is a bad bet compared to the Pass Line. Would you rather make bets where you lose 90 cents for every $10 you bet, or would you prefer making bets where you lose only 14 cents for every $10 you bet? It’s clear that if you make bets with high house edges, you’ll lose your money much more quickly than if you make bets with significantly lower house edges.

Let’s briefly review how the house advantage is calculated because it’s important. You think, “Good grief, do I have to do a bunch of math to figure all this stuff out?” Relax. Let’s just do one example so you have the basic understanding. After the example, we provide an easy-to-read table that contains house advantages for all craps bets.

Let’s consider the basic Flat Pass Line bet (no Odds), which almost every craps player makes. As we know from our other lesson about the Pass Line, it pays even money when we win but there are more ways to lose than win so the house is taking advantage of us by giving us only 1:1 casino odds instead of true odds. Let’s do the easy math and calculate the house advantage.

I hate dealing with fractions because they make it more difficult to understand, so let’s play with the numbers so we can deal with whole numbers (no fractions). Let’s first determine how many rolls we need to achieve winners and losers using whole numbers. The Flat Pass Line bet wins on the come-out with a 7 or 11, and loses on the come-out with a 2, 3, or 12. If a point is established, the Pass Line bet wins if the shooter makes the point, and loses if a 7 shows. To get results that are whole numbers, we determine that it takes 55 rounds of 36 rolls, or 1,980 rolls (55 x 36 = 1,980). The following table shows the results of 1,980 rolls for a perfect distribution.

**Flat**** Pass**** Line Winners and Losers after 1,980 Rolls**

Number Rolled | # of Times Rolled (Out of 1,980 rolls) | # of Winning Rolls | # of Losing Rolls |
---|---|---|---|

7 | 330 | 330 | 0 |

11 | 110 | 110 | 0 |

2,3,12 | 220 | 0 | 220 |

4 | 165 | 55 | 110 |

5 | 220 | 88 | 132 |

6 | 275 | 125 | 150 |

8 | 275 | 125 | 150 |

9 | 220 | 88 | 132 |

10 | 165 | 55 | 110 |

Total | 1980 | 976 | 1004 |

For a basic understanding, let’s look at how we derive the numbers in the above table. You might think, “I don’t care about the numbers or how they’re derived, so why bother?” The point is to get you in the mindset where you’re thinking about the math. Craps is all about math. You don’t need a PhD in mathematics, but you should understand how the odds and house advantages for various bets compare and at least understand the basic concept for how they’re derived. You may not be a mathematician, but let’s go through this to get you thinking like a “crapsmatician.” The more you treat craps like a math exercise, the more likely you are to walk away a winner.

Row #1 (the number 7): This row is for a 7 showing on the come-out roll. There are six ways out of 36 possible dice combinations to make a 7. Therefore, 6 / 36 = 0.1666. 0.1666 x 1980 = 330. Therefore, a winning 7 on the come-out appears 330 times out of 1,980 rolls.

Row #2 (the number 11): This row is for an 11 showing on the come-out roll. There are two ways to make an 11. Therefore, 2 / 36 = 0.0555 x 1980 = 110. Therefore, a winning 11 on the come-out appears 110 times out of 1,980 rolls.

Row #3 (the numbers 2, 3, and 12): This row is for a craps showing on the come-out roll. There are four ways to make a 2, 3, or 12. Therefore, 4 / 36 = 0.1111 x 1980 = 220. Therefore, a losing craps on the come-out appears 220 times out of 1,980 rolls.

Row #4 (the number 4): This row is for winning and losing a Pass Line bet when the point is 4. There are three ways to make a 4. Therefore, 3 / 36 = 0.0833 x 1980 = 165. When the point is 4, the true odds indicate there’s a 2:1 chance the shooter will 7-out. In other words, for every three rolls when the point is 4, the shooter will 7-out twice and hit the point once. Therefore, 165 / 3 = 55. Considering the 2:1 true odds when the point is 4, the shooter wins by hitting the point 55 times (i.e., 1 x 55 = 55), and loses with a 7-out 110 times (i.e., 2 x 55 = 110). 55 + 110 = 165. (Isn’t it so cool how the math works in the game of craps?!?!)

Row #5 (the number 5): This row is for winning and losing a Pass Line bet when the point is 5. There are four ways to make a 5. Therefore, 4 / 36 = 0.1111 x 1980 = 220. When the point is 5, the true odds indicate there’s a 3:2 chance the shooter will 7-out. In other words, for every five rolls when the point is 5, the shooter will 7-out three times and hit the point twice. Therefore, 220 / 5 = 44. Considering the 3:2 true odds when the point is 5, the shooter wins by hitting the point 88 times (2 x 44 = 88), and loses with a 7-out 132 times (i.e., 3 x 44 = 132). 88 + 132 = 220.

Row #6 (the number 6): This row is for winning and losing a Pass Line bet when the point is 6. There are five ways to make a 6. Therefore, 5 / 36 = 0.1388 x 1980 = 275. When the point is 6, the true odds indicate there’s a 6:5 chance the shooter will 7-out. In other words, for every eleven rolls when the point is 6, the shooter will 7-out six times and hit the point five times. Therefore, 275 / 11 = 25. Considering the 6:5 true odds, when the point is 6, the shooter wins by hitting the point 125 times (5 x 25 = 125), and loses with a 7-out 150 times (i.e., 6 x 25 = 150). 125 + 150 = 275.

Rows 7, 8, and 9 (for the numbers 8, 9, and 10): These rows are identical to their paired numbers (i.e., from our other lesson on basic craps math, we know that the 8 pairs with 6, and the 9 pairs with 5, and the 10 pairs with 4).

Therefore, from the table above, for an even-money Flat Pass Line bet after 1,980 rolls in a perfect distribution, the player wins 976 times while the house wins 1,004 times (976 + 1,004 = 1,980). However, the Flat Pass Line is an even‑money bet and for a true even-money bet, we expect to win and lose an equal number of times (i.e., 990 wins and 990 losses since 990 + 990 = 1,980). Since the house has 28 more ways to win than the player (i.e., from the table above, 1004 – 976 = 28), we calculate the house advantage as 28 / 1980 = 0.01414, which is 1.4% expressed as a percentage. Therefore, the even-money Flat Pass Line bet has a 1.4% house advantage over the player because the house pays only even money casino odds instead of true odds.

The house advantage is calculated similarly for all other bets. Results are summarized in the table below, sorted from lowest-to-highest house advantage. “Good” means the bet is safe or a bet that you want to make because of the relatively low house advantage. “Maybe” means think twice about making the bet. “Bad” means you shouldn’t make the bet because of the relatively high house advantage. “Terrible” and “Just plain stupid” are for drunks and idiots. In the table below, all house advantages are rounded to two decimal places, and the acronym “HA” stands for “House Advantage.”

NOTE: Although the Hard 4 and Hard 10 are labeled as “terrible” because their house advantages are greater than 10%, these are okay bets to make as tips for the dealers. Refer to our other lesson about tipping the dealers and the benefits you can gain from it. I routinely make a $1 Hard 4 or Hard 10 bet as a tip for the crew every 15 or 20 minutes. The $4 per hour investment in tipping the dealers usually pays for itself as described in our other lesson.

**House Advantages for Craps Bets**

Bet | True Odds | Casino Odds | House Advantage (%) | Good / Bad |
---|---|---|---|---|

Don’t Pass, Don’t Come (with single Odds) | 1.03:1 | 1:1 | 0.69 | Good |

Pass Line, Come (with single Odds) | 1.03:1 | 1:1 | 0.85 | Good |

Don’t Pass, Don’t Come | 1.03:1 | 1:1 | 1.40 | Good |

Pass Line, Come | 1.03:1 | 1:1 | 1.41 | Good |

Place 6 or 8 | 6:5 | 7:6 | 1.52 | Good |

Buy 4 or 10 (pay vig on win) | 2:1 | 2:1 | 1.64 | Good |

Lay 4 or 10 (pay vig on win) | 1:2 | 1:2 | 1.64 | Good |

Buy 5 or 9 (pay vig on win) | 3:2 | 3:2 | 1.96 | Good |

Lay 5 or 9 (pay vig on win) | 2:3 | 2:3 | 1.96 | Good |

Buy 6 or 8 (pay vig on win) | 6:5 | 6:5 | 2.22 | Maybe |

Lay 6 or 8 (pay vig on win) | 5:6 | 5:6 | 2.22 | Maybe |

Lay 4 or 10 (pay vig up front) | 1:2 | 1:2 | 2.44 | Maybe |

Field (triple for 12 or 2) | 20:19 | 1:1 2:1 for 2 3:1 for 12 | 2.78 | Maybe |

Lay 5 or 9 (pay vig up front) | 2:3 | 2:3 | 3.23 | Maybe |

Lay 6 or 8 (pay vig up front) | 5:6 | 5:6 | 4.00 | Maybe |

Place 5 or 9 | 3:2 | 7.5 | 4.00 | Maybe |

Buy 4 or 10 (pay vig up front) | 2:1 | 2:1 | 4.76 | Bad |

Buy 5 or 9 (pay vig up front) | 3:2 | 3:2 | 4.76 | Bad |

Buy 6 or 8 (pay vig up front) | 6:5 | 6:5 | 4.76 | Bad |

Field (double for 2 and 12) | 10:9 | 1:1 2:1 for 2 and 12 | 5.55 | Bad |

Place 4 or 10 | 2:1 | 9:5 | 6.67 | Bad |

Big 6 or Big 8 | 6:5 | 1:1 | 9.09 | Bad |

Hard 6 or Hard 8 | 10:1 | 9:1 | 9.09 | Bad |

Any Craps | 8:1 | 7:1 | 11.10 | Terrible |

3 or 11 | 17:1 | 15:1 | 11.10 | Terrible |

C & E | 15:3 | 13:3 | 11.10 | Terrible |

Hard 4 or Hard 10 | 8:1 | 7:1 | 11.10 | Terrible |

Hop two ways | 17:1 | 15:1 | 11.10 | Terrible |

Horn | 20:4 | 17:4 | 12.50 | Just plain stupid |

Whirl (World) | 10:5 | 8:5 | 13.33 | Just plain stupid |

2 or 12 | 35:1 | 30:1 | 13.89 | Just plain stupid |

Hop one way | 35:1 | 30:1 | 13.89 | Just plain stupid |

Any 7 | 5:1 | 4:1 | 16.67 | Incredibly stupid |

Over 7 or Under 7 | 21:15 | 1:1 | 16.67 | Incredibly stupid |

When reviewing the house advantages, always remember that their classification as bad or good assumes many rolls over a long period of time. Because we don’t stand at a craps table 24 hours per day, 7 days per week, 365 days per year where the distribution variance has time to shake itself out, the relatively short amount of time that we play may produce some really weird variances where a stupid bet can hit many more times than the norm. For example, suppose you’ve been playing the Pass Line and taking 2x Odds steady as a rock like you’re supposed to, but the last 30 minutes have been cold as ice and not one shooter has made a point. The table is thinning out with only four people left. No one is saying a word except the drunk across from you. He’s clapping and cheering to himself because every one of his Big 6 bets have hit. In this example, two things are noteworthy. First, one of the best bets on the craps table (i.e., Pass Line with Odds) hasn’t hit since the Stone Age. Second, a really bad bet (i.e., Big 6) has hit the last eight times in a row. In this case, the distribution variance has taken a wacky turn and temporarily gone crazy. So, as you stand there losing your “good” Pass Line bet time after time, you begin to wonder if all this “house advantage and good bet versus bad bet” stuff is a bunch of hooey.

Calm down. That drunk who continually plays the Big 6 certainly has paid, or will pay, a big price for his short-lived wins. Too bad his temporary winning streak occurred while you were at the table to see it. Rest assured, his winning streak will end and the variance will turn on him causing him to lose his shirt. It might not be tonight while you’re at the table witnessing his lucky streak, but it will eventually. The lesson here is, any bet that consistently hits at any specific moment can be considered the “best” bet at that particular moment. Don’t give in to temptation. Don’t play like the drunk. Stick to what you know is right. Play smart, be rock solid. Otherwise, you’ll soon be walking the Vegas Strip with your empty pockets turned inside out, looking for your wife to beg her for more money.

Let’s talk just a moment about the Pass Line with Odds bet, which along with the Don’t Pass with Odds is the best bet on the craps table in terms of house advantage.

Note in the table above that the Flat Pass Line bet has a 1.41% house advantage while the Pass Line with Single Odds has a much lower 0.85% house advantage (that’s less than 1%). I know what you’re thinking! I’m impressed that you observed this and wondered about it. It’s good that you’re thinking about the math! You think, “Suppose you and I are at the table together. If I make only Flat Pass Line bets with no Odds, and you make the same Flat Pass Line bets but with single Odds, how can the house advantage for your bets be lower than my bets? It doesn’t make sense because the Odds bet is supposed to have neither a house nor player advantage over time. Therefore, won’t we be losing the same amount of money over time?”

Technically, yes. You’re starting to think like a “crapsmatician.” That’s good! Over time and on average, both of us will lose 1.4 cents for each dollar we bet on the Flat Pass Line because of the built-in 1.41% house advantage. However, with my Single Odds bet in addition to my Flat bet, I’m betting more money without taking any additional risk. Remember, over time and on average, the Odds bet has neither a house nor player advantage (i.e., the Odds bet is the only bet on the craps table that’s based on true odds, not casino odds). Therefore, although I have more money in play than you, I’m taking the same amount of risk as you. That means, by taking Odds, I lose a smaller percentage of my bankroll than you.

The larger the Odds bet, the smaller the house advantage becomes. You can never eliminate the house advantage because of the Flat bet (i.e., you can’t make an Odds bet without first making a Flat bet), but you can chip away at it by increasing the Odds bet amount. Therefore, if you’re fortunate enough to have a big bankroll, you should always make the minimum Flat Pass Line bet allowed with the maximum Odds allowed. For example, suppose you’re at a $5 table that allows 100x Odds. If you have a big bankroll, you should bet $5 on the Pass Line and take $500 in Odds. Or, if you prefer, bet $5 on the Don’t Pass and lay $1,000 in Odds. But who has that kind of money? Certainly not me and probably not you. So, then what?

If you don’t have that kind of bankroll (because your wife, like mine, won’t give you more than $100 for gambling every two or three hours), then you should search out the lowest table minimum and take at least double Odds (i.e., 2x Odds).

If you’re on the Vegas Strip, take 20 minutes to visit several casinos in the immediate area and play at the one that offers the lowest table minimum and highest Odds allowed. Better yet, email or call the casinos before you even get to Vegas so you know exactly where to go as soon as you dump your suitcase in the room. If you play at my favorite Vegas casino that still has $5 tables with 20x Odds, consider dropping $5 on the Pass Line with $10 in Odds. This approach allows you to minimize your Flat bet and maximize your Odds bet, while keeping your limited bankroll under control. Also, please check out some best rated rtg casino such as Sun Palace, Casino Max, or Slots Plus to play craps for money. We also have a bonus guide and some Craps FAQ.

You can now got the page that we list the craps bets or You can now head over to the table of contents to find more great content.

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## Comments 4

I was wondering about the math on combining house advantage to find out the overall house advantage of all your bets on the table. For example, what would the overall house advantage be on a $22 inside bet that would include the point if there was a 5, 6, 8 or 9 as the point, Or a pass line bet with single odds on an 8 with a placed 6, Or a single pass line bet with single odds and a placed 6 & 8 if the point is 4, 5, 9 or 10? Thank you for taking the time to explain this.

Brendan, both of your posts deal with the house advantage for multiple bets working at the same time. As noted in our lesson on hedge bets, you increase the house advantage with every bet that you have working at the same time. You calculate house advantage using the same approach no matter what bets you make or how many you have working at the same time. For whatever bet combinations you want to make, identify the winning rolls and the losing rolls over a perfect distribution, and then figure out how many losing rolls there are compared to winning rolls. The house always has more ways to win than you do. So, however many ways that is (i.e., the number of more ways the house wins than you), divide that number by the total number of rolls. As noted, the more bets you make at a time, the more you add to the house advantage. That’s why the smartest thing you can do is play only the Pass Line with Odds or Don’t Pass with Odds and nothing else (i.e., don’t make any other bets because if you do, then you increase the house advantage). But as noted in the lesson, that can get boring. When playing strictly the Pass Line with Odds (or Don’t Pass with Odds), the house advantage is very low, which means the game with go back and forth with you winning some and the house winning some, and over time the house will slowly chip away at your chip stack. To make it more interesting and lot more fun, you can make Place bets. Note that we start with only one or two Place bets on the 6 and/or 8, depending on the point (Placing the 6 and 8 have relatively low house advantages). We do not start immediately covering all the inside numbers because we don’t want to give the house too big of an advantage to start with. We’re patient and let the warm rolls cover all the numbers for us (i.e., our Place bets must hit before we cover more numbers). As we increase the quantity of Place bets that we have working at the same time, we’re also increasing the house advantage, but we don’t care because we’re taking profit in between adding to the quantity of our Place bets. Yes, it’s true, the house advantage has increased fairly substantially by the time we cover all the numbers, but we’re willing to accept that because we’ve taken profit as we covered the numbers (i.e., basically, we get the casino to pay for covering all the numbers by the fact that we take profit in between increasing the quantity of our Place bets, and we cover the cost of the added Place bets by using the winnings). For example, we don’t make a Place 5 or 9 until we win our Place 6 and/or 8—–the winnings from the Place 6 or 8 pays for our Place 5 or 9. When we have all the numbers covered, the increase in house advantage is acceptable because now we’re to the point where we press the Place bets and that’s when we start making big wins. So, at this point when we have all the numbers covered, we don’t care about the house advantage—we’re hoping the hot roll continues so we can press the Place bets to high dollar amounts. Anyway, rather than calculate the house advantage for you for all your numerous “what if” betting combinations, the concept for calculating it is as described above. For whatever bet combinations you choose, use the concept as described above. Remember, the idea behind the “system” in our lesson is in part to give us more fun and excitement at the tables. We accept the increased house advantage when we make more Place bets because the added action gives us that fun and excitement. Otherwise, if we weren’t interested in getting as much fun and excitement out of the game, we’d only play the Pass Line with Odds to keep the house advantage down to a minimum. But, again, that can become boring after an hour. The extra action from the Place bets is what helps us get the fun we look for. Hope that helps. Good luck at the tables, and have fun!

how does someone calculate the house edge if they are covering multiple numbers? (i.e. placed 6 & 8)

See answer below.