Theoretical Probability Of Winning Craps
Fractional Odds. These types of odds are written as 10/1, 5/2, etc. And with them you can easily calculate how much you stand to win: if you bet the second number, you win the first number.
. Four or 10: Three ways to win and six to lose, so probability of winning is 3/(3+6). Bet $5 to win $9 and have a total of $14. Expected value of $5 is therefore (3/9)x($14)=$4.67. Five or nine: Four ways to win and six to lose so probability of winning is 4/(4+6). Bet $5 to win $7 and have a total of $12. The house advantage - the all-important percentage that explains how casinos make money - is also called the house edge, the theoretical win percentage, and expected win percentage. In double-zero roulette, this figure is 5.3%. In the long run the house will retain 5.3% of the money wagered.
People enjoy playing craps for multiple reasons, including the interactive experience and camaraderie.
Craps lets you physically determine the game’s outcome by rolling the dice. Contrast this to baccarat or blackjack, where you don’t even get to touch the cards that are dealt.
Another fun thing about craps is that many players like betting with the shooter through pass line and come bets. This is where the camaraderie comes in, because players cheer together when the shooter wins.
Strangely enough, the craps’ low house edge is one of the most undervalued reasons why people play. And perhaps this is why so many players make mistakes at the table and ruin their chances of winning.
Craps is always more fun when you combine winning with the camaraderie and interactivity. That said, I’m going to cover the biggest mistakes that players must avoid so they can win more often.
Mistake #1: Making Craps Bets without Knowing the Odds
In addition to the good points I covered in the introduction, another reason why people love this game is due to the betting variety. Craps offers dozens of wagers, including some exotic prop bets.
But this advantage is also a huge downside when players start making bets without knowing the odds. This might not be such a big deal in other casino games, but it’s a huge mistake in craps.
That’s because certain craps prop bets have house edges ranging in the double digits. This hurts worse when you realize that there are much better wages available.
Check out all of the craps bets below:
- Don’t pass line / don’t come bet = 1.36% house edge
- Pass line / come bet = 1.41%
- Place 6 / Place 8 = 1.52%
- Lay 4 / Lay 10 = 2.44%
- Lay 5 / Lay 9 = 3.23%
- Place 5 / Place 9 = 4.0%
- Lay 6 / Lay 8 = 4.0%
- Buy 4 / Buy 10 = 4.76%
- Buy 5 / Buy 9 = 4.76%
- Buy 6 / Buy 8 = 4.76%
- Field = 5.56%
- Place 4 / Place 10 = 6.67%
- Hard 6 / Hard 8 = 9.09%
- Big 6 / Big 8 = 9.09%
- Yo (11) = 11.11%
- 3 = 11.11%
- 2 or 12 (Hi-Lo) = 11.11%
- Craps (2, 3, or 12) = 11.11%
- Hard 4 / Hard 10 = 11.11%
- Horn = 12.5%
- Whirl World = 13.33%
- 2 = 13.89%
- 12 = 13.89%
- Any 7 = 16.67%
You can see that there are fewer than 10 bets actually worth making on the entire board. And it only makes sense to stick with the best wagers, including pass line, don’t pass line, come, and don’t come.
These bets are easy to find, because they’re written in big letters on the table. Let’s take a look at how each of these wagers work.
Pass Line
- Wins on the come out roll (first roll of a new round) when 7 or 11 are tossed
- Loses on the come out when 2, 3, or 12 are rolled
- Point number is established when 4, 5, 6, 8, 9, or 10 are tossed
- You need a shooter to roll the point number before 7 to win
- Pays 1:1
- 251:244 true odds
Don’t Pass Line
- Wins on the come out roll when 2 or 3 are tossed
- Loses on the come out when 7 or 11 are rolled
- Pushes when 12 is rolled
- Point number is established when 4, 5, 6, 8, 9, or 10 are rolled
- You need a shooter to roll 7 before the point number to win
- Pays 1:1
- 976:949 true odds
Come
- Players must wait for the point number before making a come bet
- The come out roll becomes the shooter’s next roll after you make this wager
- Wins on the come out roll when 7 or 11 are tossed
- Loses on the come out when 2, 3, or 12 are rolled
- You need a shooter to roll the point number before 7 to win
- Pays 1:1
- 251:244 true odds
Don’t Come
- Players must wait for the point number before making a come bet
- come out roll is the shooter’s next roll after you make this wager
- Wins on the come out roll when 2 or 3 are tossed
- Loses on the come out when 7 or 11 are rolled
- Pushes when 12 is rolled
- Point number is established when 4, 5, 6, 8, 9, or 10 are rolled
- You need a shooter to roll 7 before the point number to win
- Pays 1:1
- 976:949 true odds
Stigma Against Don’t Bettors
Based on the house edges, it makes sense to put your money on don’t pass line and don’t come. After all, these wagers have a house advantage that’s 0.05% lower than pass line and come.
But while these “don’t” bets give you a slightly stronger chance to win, they also come with a stigma in land-based casinos.
As mentioned before, many players bet with the shooter. This creates a feeling that the pass line and come bettors are backing the shooter, rather than the casino.
Don’t bettors are often referred to as the “dark side,” because they’re wagering on the shooter to lose and aligning with the casino.
While being a don’t bettor won’t get you beat up in the parking lot, you also don’t get to share in the joy of cheering a hot shooter. Therefore, you need to decide how much gaining the extra 0.05% advantage on the house edge is worth.
Of course, you should always make don’t bets in online craps. You might as well take the best available house edge in this case, because you’re playing by yourself.
Mistake #2: Failing to Take Advantage of Craps Odds
Craps is truly unique in that it offers a bet with no house edge. Unfortunately, many craps players fail to take advantage of this wager because they don’t even know about it.
Odds is a bet that you can place behind either a pass line or don’t pass line wager. This bet pays at true odds, which is why it doesn’t have a house advantage.
The goal is to bet the highest odds you can, because this lowers the overall house edge when combining your pass line or don’t pass line bet. The table below shows how the house advantage decreases with higher odds:
| Odds | Pass Line & Come | Don’t Pass Line & Don’t Come |
| 0x | 1.41% house edge | 1.36% house edge |
| 1x | 0.848% | 0.682% |
| 2x | 0.606% | 0.455% |
| Full Double Odds | 0.572% | 0.431% |
| 3x | 0.471% | 0.341% |
| 3x-4x-5x | 0.374% | 0.273% |
| 5x | 0.326% | 0.227% |
| 10x | 0.184% | 0.124% |
| 20x | 0.099% | 0.065% |
| 100x | 0.021% | 0.014% |
You can make odds bets in both land based and online casinos. But land-based establishments usually offer higher odds.
The Cromwell in Las Vegas has the industry’s best craps odds at 100x. Vegas’ Main Street Station offers the second highest odds at 20x
What’s great is that you only have to make a $5 minimum bet in both casinos. You can then back your bet with the highest odds, which puts you at nearly an even proposition with the casino.
Betsoft and Playtech offer the highest online craps odds at 3x.
Obviously, this is nowhere near the top Vegas casinos. But both Betsoft and Playtech allow you to play for as little as $1 per bet.
As for making odds bets, you must wait until a point has been established before backing a pass line or don’t pass line bet with odds. Be sure to notify the dealer when making these wagers in a land-based casino, because odds doesn’t have a specific box on the table.
You “take odds” when wagering behind pass line and “lay odds” when betting behind don’t pass line. Here are the payouts based on the point numbers you lay or take:
Taking Odds
- Shooter must roll point before 7 for you to win
- 2:1 payout on point numbers of 4 and 10
- 3:2 on points of 5 and 9
- 6:5 on points of 6 and 8
Laying Odds
- Shooter must roll 7 before point for you to win
- 1:2 payout on points of 4 and 10
- 2:3 on points of 5 and 9
- 5:6 on points of 6 and 8
Mistake #3: Expecting to Win More through Hedging Bets
Some craps players are under the impression that they can win by hedging enough bets. The idea is to cover multiple numbers so that you have a strong chance to win at least one wager per round.
Here’s a common method of hedging bets:
- I make a $10 pass line bet.
- I make a $1 Any Craps wager.
- Any Craps pays 7:1 and wins when a 2, 3, or 12 is rolled.
- Pass line loses when a 2, 3, or 12 appear on the come out roll.
The logic is that if my pass line loses, I still win $7 from the Any Craps win.
This looks good on paper, because I only lose $3 instead of $10 thanks to the Any Craps hedge. Furthermore, I only lose $1 if any number other than 2, 3, or 12 are tossed.
But the primary problem with hedging bets is that you’re not doing anything to overcome the house edge. This is especially the case with Any Craps, which carries an 11.11% house advantage.
Hedging wagers is a fun way to get more action and create additional chances to win in each round. But don’t look at this as a way to boost your long-term odds of winning.
Mistake #4: Relying on Craps Betting Systems
Most craps betting systems amount to complicated ways of hedging bets. A perfect example of this is the Iron Cross.
The Iron Cross is popular because it covers seven different numbers and offers 2:1 payouts on some bets. Here’s a complete look at what this betting strategy entails:
- 5:4 true odds of winning
- 1:1 payouts on 3, 4, 9, 10, and 11
- 2:1 payouts on 2 and 12 (sometimes 3:1 on 12)
- Loses on any other number (5, 6, 7, 8)
- 5.56% house edge
- 2.78% house edge if 12 pays 3:1
Again, the major draw to the Iron Cross is that you’re covering seven numbers and giving yourself multiple ways to win. But the problem comes in when examining your actual odds of winning.
You can see this below:
- 1 combo forms a 2
- 2 combos form a 3
- 3 combos form a 4
- 4 combos form a 9
- 3 combos form a 10
- 2 combos form an 11
- 1 combo forms a 12
- 16 total combinations will help you win with the Iron Cross
Here are all the ways that you’ll lose:
- 4 combos form a 5
- combos form a 6
- 6 combos form a 7
- 5 combos form an 8
- 20 combinations result in a loss
Your true odds are 5:4 when taking the 20 losing combos and 16 winning combos into account. Even the 2:1 payouts on 2 and 12 aren’t much help, because they only cover 2 possible combinations.
Considering the Iron Cross’ 5.56% house edge, you’re better off sticking with pass line or don’t pass line wagers backed with odds.
Mistake #5: Believing that Dice Control is the Craps Holy Grail
Certain casino games have advantage-play methods that give you an opportunity to win long-term profits. Examples include blackjack card counting, roulette dealer signatures, positive expectation video poker machines, and skill-based games like poker and sports betting.
Some contend that you can use an advantage play technique called dice control (a.k.a. controlled shooting) to get an edge at the game.
The premise behind dice control is that you hold the dice in a specific way (a.k.a. setting) and practice your tosses. The idea is to develop your skills through habitual practice until you can control your rolls.
In most cases, a controlled shooter is looking to avoid throwing 7s. This is why the V-shape grip, where the 3s form a V and cover all possible 7s, is one of the most popular settings techniques.
A dice control expert doesn’t have to produce the desired result very often to win long term. Instead, they only need to avoid throwing a 7 once in a while.
Here’s how this works out:
- The average player rolls a 7 on six out of 36 rolls.
- But let’s say that you only roll this number on 5.5 out of 36 rolls.
- This is all you need to gain a long-term advantage.
Dice control believers often rig up homemade craps tables so that they can practice their tosses. The hope is that with enough practice, they can control some of their rolls.
Noted gambling authors like Dominic “The Dominator” LoRiggio and Frank Scoblete have argued for years that dice control is a legitimate way to beat craps.
And they’ve earned a lot of money by pushing books and training courses on the subject of controlled shooting.
But this practice has never truly been proven to beat craps. In fact, few industry experts have stepped forward and vouched for dice control.
“There are too many variables,” said gaming consultant Bill Zender, who spoke with Vice on the matter. “If the dice turn just a fraction of an inch, they’re going to roll off that axis. I hate to say it, but I think it’s a big scam.”
As Zender alluded to, it’s likely impossible to control craps tosses with any certainty. After all, you have to toss the dice off a diamond-patterned back wall.
Mistake #6: Playing Craps Longer Just to Get Comps
Craps players can rack up a lot of comps in a short time span. But this is only possible when you’re making multiple bets on each turn and/or playing high stakes.
Theoretical Probability Of Winning Craps Games
The truth is that casinos don’t offer many rewards to the average craps player, because the game has such a low house edge. Many casinos only comp players on 0.1% of their total wagers.
Nevertheless, some players continue playing past their means just to chase more comps. The biggest thing to understand here is that the rewards you accumulate don’t overcome theoretical losses.
Here’s some math to explain this point:
- I make $25 pass line bets (1.41% house edge).
- The average number of rolls at my table is 119.
- My pass line bet lasts for an average of 7 rolls.
- This means I place 17 bets per hour, or $425 total.
- My comp value is $0.43 per hour (425 x 0.001 rate).
- My theoretical losses are $5.99 per hour (425 x 0.0141).
The comps that I receive in this situation are only equal to 7.2% of the theoretical losses. I doubt that any sane craps player would continue playing an extra hour for comps if they knew this.
Mistake #7: Not Getting Craps Comps in Land Based Casinos
While I definitely think that it’s a bad idea to chase craps rewards, this doesn’t mean you should completely ignore them. After all, it’s nice to pick up freebies on top of your play.
But some land-based craps players miss out on comps, because they don’t bet enough to attract the pit boss’ attention.
The pit boss needs to rate your play to determine how many comps you deserve. And they’re looking for table game players who either bet a lot of money or stay at the tables for a long time.
But they also rate player’s club members who take the proper steps to earn rewards. Here are the steps for how you can join the rewards program:
- Sign up for the casino’s rewards program, either in person or through their website.
- You’ll be issued a player’s club card.
- Take this card with you to the craps table.
- Tell the dealer that you wish to be rated.
- The dealer will hand your card to the pit boss and ask them to rate you.
- The pit boss will use your bet sizes and volume to determine how many comps you receive.
What’s nice is that you don’t have to worry about all the steps in online craps.
Most internet casinos automatically enroll you into their VIP programs as soon as you sign up and make a deposit. From here, all you need to do is start playing real money craps to earn comps.
Conclusion
Maybe you appreciate craps for the team-like atmosphere or the betting variety. But if you avoid the mistakes that I’ve covered here, you’ll also enjoy craps because it offers a great chance to win.
This is especially true if you stick with the main bets and back them with odds. Putting as little as 2x odds behind a pass line wager lowers the overall house edge to 0.61%.
Theoretical Probability Of Winning Craps Odds
Other mistakes that you want to avoid include hedging bets, overusing systems, and wasting time with controlled shooting.
Craps already gives you an excellent chance to win money. And you don’t have to use any of these strategies in a vain attempt to improve your odds.
Theoretical Probability Of Winning Craps Against
Finally, avoid playing craps longer than you’d like just to get rewards. But on the same token, get comps by signing up for the player’s club and making sure that you’re rated.