Craps House Edge and Odds
Craps is one of the most popular dice games in the world, with a rich history that can be traced back to the Roman Empire. The dynamic pace of play and the wide range of betting options are what have caused craps to become an absolute staple in both online casinos and land-based gambling establishments.
Since craps relies heavily on chance and there is no way to affect the outcome of the dice toss, many inexperienced players wrongly assume craps is an easy game to play. This is not necessarily true as the sheer number of betting options will suffice to overwhelm any craps novice. While there is no way for players to predict the outcome of the dice with certainty, they can still turn up a good profit as long as they take the time to learn the bet types and the possible dice combinations. Understanding the house edge, the true odds, and the payouts certainly can work to the advantage of craps players.
Understanding the House Edge
Gambling establishments do not generate profits because the personnel manages to outplay the customers. The casinos’ profits result from the built-in advantage they have over their players. This built-in advantage is referred to as the “house edge” and is the key thing inexperienced players need to understand prior to joining the craps table.
All casino games are tilted in favor of the house as it utilizes the law of averages to gain its edge over the players. The house edge is typically expressed as a percentage and represents the average profit the casino collects from each wager the players make. Please note the house generates a profit on every single bet, regardless of whether it is a winning or a losing one.
As was mentioned earlier, there is a great number of bets you can place in craps. But what is more important, the house edge tends to fluctuate between the different bet types. On some craps bets, the house edge drops to zero while on others, the house’s advantage skyrockets to a two-digit figure. That is why, smart players choose bets with lower house edge which helps them to exploit the game and end their betting session on profit.
Let us demonstrate how the house edge works with an example. Bets on the Pass Line have a low edge of 1.41%. This means that for each $100 players wager on the Pass Line, the casino will collect an average of $1.41. Whether players win or lose is irrelevant – either way, they will lose $1.41 on average per every $100 they wager on the Pass Line. There are players who prefer to place Proposition bets because the latter have more substantial payouts. However, this is not always a good idea since the house edge for Proposition bets ranges between 5.56% and 16.67%.
Pass/Don’t Pass Line bets and Come/Don’t Come bets are considered a smarter option, especially for inexperienced players. The tilt in favor of the casino is smaller with such bets and the probability of the shooter rolling a winning dice combination for these bets is much greater. Because of this, such bets have lower payout ratio and pay even money.
Players, who wager on the Pass Line are allowed to lay or take odds on their bets. Once the shooter rolls his point, players can collect money on their Pass Line bets but will also be paid at true odds. This causes the house edge to drop to 0% and is the only instance in which the casino does not have an advantage over craps players. How winning bets are paid also influences the house edge. When paying out winning multiple-roll bets, the casino typically rounds the sum down to the nearest number.
Dice Combinations in Craps
In order to calculate the house edge on craps bets, players are required to acquaint themselves with the dice combinations and the probability of each number being rolled. As we know, craps is played with two dice and each die is a cube with six equal-sized sides. There are 11 possible outcomes of a two-die toss, namely 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The number of possible combinations is calculated by multiplying the number of the sides of the two dice. Thus, we get 6 x 6 = 36, from which it follows there are 36 combinations that all will total one of the eleven outcomes we have listed above. You can check the dice combinations and the totals they add up to below.
|Dice Combinations in Craps|
|Outcome||Possible Combinations with Two Dice||Ways to Rolls the Outcome|
|2||1 – 1||1|
|4||1-3, 3-1, 2-2||3|
|5||1-4, 4-1, 3-2, 2-3||4|
|6||1-5, 5-1, 2-4, 4-2, 3-3||5|
|7||1-6, 6-1, 2-5, 5-2, 3-4, 4-3||6|
|8||2-6, 6-2, 3-5, 5-3, 4-4||5|
|9||3-6, 6-3, 4-5, 5-4||4|
It certainly is not difficult to notice there are more combinations for some of the outcomes. There are more ways for the shooter to roll out 7 than any other number as becomes evident by the diamond shape of the middle column. Since there are 6 combinations of the dice that total 7, the chances of this particular number being rolled are the greatest. This is yet another thing players need to consider carefully when deciding which types of bets to place at the craps table.
How to Calculate the House Edge in Craps
As craps is a negative expectation game, it is mathematically impossible for players to gain advantage over the house. The only exception is when players are taking or laying odds on their bets. However, understanding the probability of specific numbers being rolled and the house edge on different bet types is essential as it would enable players to make better-informed decisions when placing their bets.
The two dice used in the game of craps allow for a total of 11 outcomes with totals from 2 to 12. There are 36 different ways in which the shooter can roll these 11 outcomes. From this, it follows that the total of 3 can be rolled in two different ways meaning that the probability of this number being thrown is 2 to 36. Similarly, there are six different combinations that add up to seven, so the chances of throwing this number are 6 in 36. The probability of rolling any of the other numbers can be calculated in the same fashion.
Once players understand how to calculate probability, they can proceed to calculate the house edge. It would be best to provide an example to make things as clear as possible. The Craps 2 bet wins whenever a total of 2 comes up on the next roll of the dice. In other words, there are 35 ways to lose and a single way to win with this type of bet. If it wins, the payout will be 30 to 1. Since there are only two outcomes for this type of bets, win or lose, its expected value can be calculated in the following way: (1/36)x30 – (35/36) = -5/36 = -13.89%.
Other wagers, like the Any Craps bet, allow for more winning combinations. The Any Craps bet pays out 7 to 1 whenever numbers 2, 3 or 12 are rolled. There is one combination for number 2, two combinations that add up to number 3, and one combination that adds up to 12. Thus, there are 4 ways to win out of 36 possible combinations, so the probability of collecting a payout with this bet can be expressed like this: 4/36 = 1/9. This means that out of every nine Any Craps bets, one will win and the other eight will lose. The expected return for this bet can be expressed as follows: (4/36)x7 – (32/36) = -4/36 = -1/9 = -11.11%.
As you can see, the house edge in craps tends to fluctuate greatly depending on the type of bet you place. With some bet types where the outcome is determined by multiple rolls of the dice, calculating the built-in house advantage is a mean feat. Players, who experience difficulties performing such complex calculations, can try to learn the house edge of craps bets by heart.
Understanding the True Odds
You may have noticed there is a discrepancy between the probability of winning with specific bets and the way the winnings are paid out. This discrepancy is exactly what gives the house its edge. The house succeeds in maintaining an advantage over players by paying less for winning bets than the true odds would dictate. For instance, bets on the Pass Line pay even money and have the lowest house edge of 1.41% only, which means players will lose $1.40 on average per every $100 they wager at the craps table. Basically, the only exception to this rule is when free odds are taken or laid on the bet – in this case, the house holds no advantage over players because winnings are paid at true odds.
You may wonder why players persist in betting on craps when the game is obviously tilted against them. The truth of the matter is smart players exploit a phenomenon, called distribution variance, which is precisely what causes the hot and cold streaks when the dice are rolled repeatedly, because perfect, even distribution is something that occurs rarely, if ever, in nature.
Also, it is important to remember that it takes prolonged periods of time for the odds to balance out so that the house can make a profit. Thousands of hundreds of dice rolls are required for the odds to follow their natural path and maintain equilibrium. However, many players remain at the craps table for short periods of time only. It is precisely during these fleeting moments of time that variance creeps in and allows craps players to turn up a profit. At least, if they bet smartly, manage their bankroll properly, and understand the probabilities of winning with different types of bets.
- The Probability of Point Numbers In Craps
|Point Number||Probability of getting 7||Probability of a point being established|
Gambling enthusiasts can resort to this table to find out how likely their Pass Odds and Don’t Pass Odds bets to become winning ones are. What they should not forget, however, is that the odds will be in their favor, on the condition that they go for the Don’t Pass Odds bet. Opting for the Pass Odds bet means that the odds will be against them.
Crapless Craps is a variant of the casino classic, which is worth considering, and what makes such games stand out is that the outcome of the rounds is determined during the come-out round. With such games, 2, 3, 11, and 12 will also play the role of craps numbers, along with 4, 5, 6, 8, 9, and 10. The most essential thing to consider with these games is that players will be paid at true odds when their odds bets are winning ones.
Still, opting for such craps variants might not be players’ best bet simply because the expected value of a $1 Pass Line bet will be approximately 0.946176, which renders it a significantly worse option than regular craps games. Besides, players should take into account that Don’t Pass bets are unavailable with such craps versions.
Independent Trials in Craps
One of the most essential things beginner-level players should pay close attention to is that, much like roulette, craps is also a game of independent trials. This means that chances of getting a specific dice combination do not chance with any individual throw of the dice. Thus, even if the straight seven has come out five times in a row or the number has not come out during the past few rolls of the dice, the probability of 7 coming out on the next round will invariably be 16.66%.
So, why the odds will invariably stay the same in craps? Craps is a game of independent events, which means that the outcome from the current round will not depend on the way the game has panned out in the previous rounds. This is so because the dice have no memory, and even if a combination has turned out multiple times in a row or has not come out for a while, the probability of rolling it on the next round will stay the same all the time. In this way, craps comes exceptionally close to roulette, which is also a game of independent events, and the previous spins will not have an impact on the current or future spins of the wheel.
If we assume that a player has flipped a fair coin 10,000 times, since there are just two possible outcomes, each one will turn out an equal number of times. Please bear in mind that if you flip the coin, and heads turn out, the odds of getting heads on the next round will remain 50 to 50. As soon as players go for another flip of the coin, they will reset the odds, meaning that both outcomes will be equally likely to appear.
If we suppose that you have decided to stake $1 on tails, after all 10,000 flips take place, you will break even as when tails turn out 5,000 times, you will get $5,000. Since heads will also turn out 5,000 times, this will mean that you will lose $5,000. As we already explained, casinos do not pay players at true odds and instead base the offered payouts on casino odds in order to guarantee themselves a profit. This is possible as casino odds are slightly less than true odds. Thus, if we return to the example with the flip of a coin, and say that the house will not pay us $1 but $0.95 instead, the remaining $0.05 will be collected by the house. This is exactly how the house maintains the upper hand. An important detail to consider is that when we lose, the house will collect the full size of our wager, or, in this case, $1.
Now, let’s imagine that you have bet on all 10,000 flips of the coin, which will mean that you will need to risk $10,000 in total. Considering the odds, players will lose $5,000, and will win $4,800 because of the built-in casino advantage.
Now, let’s return to craps, where the dice that are used should produce completely random results, it will be impossible for players to predict which of the possible outcomes will show up as the probability of getting each combination will invariably be the same. Of course, this will not be the case if you are using biased dice. The same also applies craps games that are available over the Internet, and with such games, the randomness of the outcomes is guaranteed through a Random Number Generator.
Perhaps, at this point, you might be wondering if there is something you can do in order to minimize your losses and get the most out of your craps betting session. Since craps is a game of independent trials, and no strategy or dice throwing technique can help players improve their results, the only thing they can do is avoid the clearly bad bet types. Placing a Pass Line bet is an alternative players have if they want to enjoy more fruitful results because the edge of the house is only 1.41%. The best thing is that players can reduce it further if they place odds behind their bets.
The Payouts of Craps Bets
What causes confusion among inexperienced players is the overwhelming number of bets they can place at the craps table. Needless to say, as the probability of rolling out specific numbers varies, the payouts for different craps bets also differ. Since the chances of winning with bets on the Pass/Don’t Pass Line and Come/Don’t Come bets are the greatest, these wagers pay even money. The chances of winning with Proposition bets are smaller, so their payouts are more significant. You will be able to find the payouts and the house edge for all bets in craps in the table below.
|Craps Bets Payout and House Edge|
|Type of Bet||Payout||True Odds||House Edge|
|Pass Line/Come Bet||1 to1||251 to 244||1.41%|
|Don’t Pass/Don’t Come Bet||1 to 1||976 to 949||1.36%|
|Free Odds Bet on the Pass Line||2 to 1 (4 or 10), 3 to 2 (5 or 9), 6 to 5 (6 or 8)||Same as Payout||0.00%|
|Free Odds on Don’t Pass Bets||1 to 2 (4 or 10), 2 to 3 (5 or 9), 5 to 6 (6 or 8)||Same as Payout||0.00%|
|Free Odds on Come Bets||2 to 1 (4 or 10), 3 to 2 (5 or 9), 6 to 5 (6 or 8)||Same as Payout||0.00%|
|Free Odds on Don’t Come Bets||1 to 2 (4 or 10), 2 to 3 (5 or 9), 5 to 6 (6 or 8)||Same as Payout||0.00%|
|Place Bets on 4 and 10||9 to 5||2 to 1||6.67%|
|Place Bets on 5 and 9||7 to 5||3 to 2||4.00%|
|Place Bets on 6 and 8||7 to 6||6 to 5||1.52%|
|Place Bets to Lose 4 and 10||5 to 11||3.03%|
|Place Bets to Lose 5 and 9||5 to 8||2.50%|
|Place Bets to Lose 6 and 8||4 to 5||1.82%|
|Field Bets on 3, 4, 9, 10 and 11||1 to 1||5.56%|
|Field Bets on 2 and 12||2 to 1||5.56%|
|Hardway Bets on 6 or 8||9 to 1||10 to 1||9.09%|
|Hardway Bets on 4 or 10||7 to 1||8 to 1||11.11%|
|Big 6 or 8||1 to 1||9.09%|
|Lay Bets on 4 and 10 (5% Commission)||1 to 2||2.44%|
|Lay Bets on 5 and 9 (5% Commission)||2 to 3||3.23%|
|Lay Bets on 6 and 8 (5% Commission)||5 to 6||4.00%|
|Buy Bets on 4 and 10 (5% Commission)||2 to 1||4.76%|
|Buy Bets on 5 and 9 (5% Commission)||3 to 1||4.76%|
|Buy Bets 6 and 8 (5% Commission)||6 to 5||4.76%|
|Big Red/Seven Bets||4 to 1||5 to 1||16.67%|
|Any Craps Bets||7 to 1||8 to 1||11.11%|
|Proposition Bets on 2 and 12||30 to 1||35 to 1||13.89%|
|Proposition Bets on 3 and 11||15 to 1||17 to 1||11.11%|