# Understanding the Game of Craps: Odds and House Edge

Casino players who decide to try their luck on the craps table should know how probable certain outcomes of the game are, as well as the house edge they would be up against. There are dozens of bets in this game and some offer significantly better odds than others.

Compared to other traditional table games such as roulette or blackjack, craps comes with a mathematical advantage that varies dramatically, depending on the number or group of numbers players decide to bet on. The majority of games have a house edge that is more or less fixed while in craps, this fundamental part of the game fluctuates from 1.41% to nearly 20%. This is why players should carefully choose what to bet on if they want to improve their overall chances of winning in this game.

## The House Edge in Casino Games

Before craps players start placing real-money bets on this game, they should have a good understanding of what house edge is. It is a fundamental part of all casino games, bingo, lotteries, and, practically, all forms of gambling. This is the guaranteed advantage of the house over its patrons – with it, casinos manage to always generate profits even with the huge jackpots they regularly pay off. So, what exactly is the house edge and why is so important when playing craps?

House Edge

### House Edge

The house edge is the mathematical advantage commercial gambling venues have over their patrons as they play over time. The term is used to describe how lucrative or unprofitable a game is, whether that is craps, blackjack, poker, roulette, baccarat, or a slot game. This advantage guarantees returns for the casino over time and, therefore, an assured loss for the players.

There are various definitions of house advantage but simply put, it is the casino profit, which is expressed as a percentage of players’ total wager. If a game comes with a casino advantage of 5%, it suggests that the casino keeps 5% of players’ bets on average – or \$5 of your \$100 bet, for instance. The house edge is not a result of luck and instead, games are designed to provide casinos with a guaranteed income – the advantage is simply the difference between the true odds and the odds casinos are willing to pay.

However, the house edge is a theoretical concept based on probability theory and the so-called Law of Large Numbers, which produces stable long-term results for the averages of random events such as gambling games. It should be noted that it applies only when a large number of gaming rounds are considered – hundreds of thousands and even millions.

This means that casino players may end up with huge profits after playing 10 rounds of roulette or craps. After playing thousands of rounds, however, they will most probably lose a percentage of their total bet that is very close to the theoretical house edge.

The RTP or return to player is another term that describes the same idea but rather than focusing on the player’s losses, it is used to express the percentage of the bet that players are likely to keep over time. In other words, the RTP that is often displayed for some casino games is, in fact, the exact opposite of the house edge.

Games with a house edge of 5%, for instance, have an RTP of 95%. Players who bet \$100 on such a game are expected to end their gaming session with \$95. Once again, the return to player or expected return, as it is also referred to, is theoretical in nature and applies for a nearly unlimited number of gaming rounds.

Slot machines, for example, rarely offer good RTPs – the house edge in them usually ranges from 2% to 10%, depending on the particular game. Most blackjack variations, on the other hand, offer RTPs of over 99% – certain games have a house edge as low as 0.45%. When it comes to craps, the house edge is not fixed and it varies greatly, depending on the bet – it is 1.41% for the most basic wager, the Pass Line bet.

## Relationship between Odds and Probability

### 1The Odds

To find the house edge of a certain bet in craps, players should know its odds – how likely it is to win or lose. Since craps is completely random and based on chance, the odds have a major, direct effect on the house edge. As mentioned above, the casino advantage is basically the difference between the true odds of a certain outcome and the payout offered, also called casino odds.

### 2The Probability

The payouts for the different bets may vary across casinos but the true odds of a bet are fixed and very similar to the probability for that bet to win. In a separate article, dedicated to the dice probabilities in craps, we have explained the similarity between odds and probability but in short, these two terms are used to express the same thing – the likelihood of an event occurring.

The probability for rolling a 7, for instance, is 6/36 since there are 6 possible combinations of the dice that can form a total of 7. All possible combinations, at the same time, are 36 because each of the two dice has six sides. This means that a roll of 7 is expected to happen around 16.67% of the time.

### 3How to Convert the Probability Into Odds

To convert the probability into odds, we just need to consider the possible combinations (6) for rolling a 7 and compare them with the rest of dice combinations (30) and flip the numbers. We will have 6 to 30, also expressed as 6:30, which is mathematically equal to 5:1.

## How to Calculate the House Edge in Craps

There are various ways for calculating the house edge in a casino game – usually, it is the ratio of the expected player loss to the initial wager. One of the simplest formulas that can be used for craps, however, uses the general formula for the expected return. It combines the winning probability of an event multiplied by its return and the probability of losing multiplied by the lost initial bet:

Expected Return = {(ways to win*return) + (ways to lose*loss)}

So, what is the house edge for the Any 7 bet? This is a single-roll bet that is settled within a single roll of the dice – it wins if the dice land on any 7 (6 combinations) and it loses if the dice show any other total (30 combinations). Therefore, the equation for the expected return for this bet will look like this:

{(6/36)*4} + {(30/36)*(-1)}

Where 4 refers to the payout for Any 7 bet (4:1) and 30/36 shows that there are 30 combinations of the dice, which would lose. The negative number -1 is the bet we risk to lose. The calculation proceeds with 0.6666 – 0.8333 = – 0.1667. To receive the player’s edge, we divide the expected return by our initial wager and we come up with the same result as our initial wager is 1. Expressed as a percentage, the house edge is then 16.67%.

Line Bets
Single-Roll Bets
Multi-Roll Bets

### Line Bets

The Line bets are the most fundamental wagers in the game of craps and with them, players bet that the shooter will win or lose. They include the Pass and Don’t Pass bets, which are necessary for the round to begin, and the Come and Don’t Come wagers, which are practically the same. However, they are not mandatory and instead of being placed before the come-out roll, chips for them can be placed on the table only after the point number has been established.

In addition, players who have made any of these wagers can also take Odds on them by adding more chips on the table. To take 5x odds on their Pass Line, players simply put their chips (5 times the number of chips for the Pass bet) behind the Pass Line on the layout. However, these bets are rarely resolved in a single roll, which is why calculating the house edge for them requires several and more complex equations. The table below includes the house edge percentages – per bet made, as well as per bet resolved and per roll.

Type of Bet Payout True Odds House Edge (HE) HE (per bet resolved) HE (per roll)
Pass Line 01:01:00 255:04:00 1.41% 1.41% 0.42%
Don’t Pass 01:01:00 991:49:00 1.36% 1.40% 0.40%
Come 01:01:00 255:04:00 1.41% 1.41% 0.42%
Don’t Come 01:01:00 991:49:00 1.36% 1.40% 0.40%
Pass/Come Odds 2:1 on 4,10; 3:2 on 5, 9; 6:5 on 6, 8 2:1 on 4,10; 3:2 on 5, 9; 6:5 on 6, 8 0.00% 0.00% 0.00%
Don’t Pass/ Don’t Come Odds 1:2 – 4, 10 2:3 – 5, 9 5:6 – 6, 8 1:2 – 4, 10 2:3 – 5, 9 5:6 – 6, 8 0.00% 0.00% 0.00%

### Single-Roll Bets

Single-roll bets, also called proposition bets, are quite straightforward and unlike the Pass Line and Don’t Pass bets, they are resolved in a single roll of the dice. Generally, these wagers come with a much higher house edge since players bet on particular numbers or a small group of numbers.

Type of Bet Payout True Odds Dice Combinations House Edge
Snake Eyes (2) 30:01:00 35:01:00 01/01/19 13.89%
Ace-Deuce (3) 15:01:00 17:01:00 1-2, 2-1 11.11%
Any Craps (2, 3, 12) 07:01:00 08:01:00 1-1, 1-2, 2-1, 6-6 11.11%
Any 7 04:01:00 05:01:00 1-6, 6-1, 2-5, 5-2, 3-4, 4-3 16.67%
Hi-Lo (2, 12) 15:01:00 17:01:00 1-1, 6-6 11.11%
Yo (11) 15:01:00 17:01:00 5-6, 6-5 11.11%
Boxcars (12) 30:01:00 35:01:00 06/06/19 13.89%
C&E (2, 3, 12 + 11) 3:1 on 2,3,12; 7:1 on 11 05:01:00 1-1, 1-2, 2-1, 6-6, 5-6, 6-5 11.11%
Horn (2, 3, 11 or 12) 27:4 on 2,12; 3:1 on 3,11 05:01:00 1-1, 1-2, 2-1, 6-6, 5-6, 6-5 12.50%
World (2,3,7,11,12) 26:5 on 2,12; 11:5 on 3,11; 0:1 (push) on 7 02:01:00 1-1, 1-2, 2-1, 1-6, 6-1, 2-5, 5-2, 3-4, 4-3, 6-6, 5-6, 6-5 13.33%
Field (2,3,4,9,10,11,12) 1:1 on 3,4,9,10,11; 2:1 on 2,12 05:04:00 1-1, 1-2, 2-1, 6-6, 5-6, 6-5, 1-3, 3-1, 6-3, 3-6, 4-5, 5-4, 5-5, 6-4, 4-6 5.56% (2.78% if 12 pays 3:1)

### Multi-Roll Bets

Another group of wagers in craps includes those bets that usually cannot be resolved in a single roll of the dice. Called multi-roll bets, they often require several subsequent rolls and can be canceled if the shooter makes the point number before some of these bets. The rules, associated with when and how to make them, their payouts, and more may vary across casinos.

Note that the winnings generated from some of these bets are paid minus a 5% commission that is charged by the casino. Sometimes, the commission is taken only on the winnings, but in some cases, the 5% vig, as the commission is also called, applies to the bet.

Type of Bet Payout True Odds House Edge
Hard 4/10 07:01:00 08:01:00 11.11%
Hard 6/8 09:01:00 10:01:00 9.09%
Big 6/ Big 8 01:01:00 06:05:00 9.09%
Place 4/10 09:05:00 02:01:00 6.67%
Place 5/9 07:05:00 03:02:00 4.00%
Place 6/8 07:06:00 06:05:00 1.52%
Buy 4/10 2:1 – 5% of bet 02:01:00 4.76%
Buy 5/9 3:2 – 5% of bet 03:02:00 4.76%
Buy 6/8 6:5 – 5% of bet 06:05:00 4.76%
Lay 4/10 1:2 – 5% of win 01:02:00 2.44%
Lay 5/9 2:3 – 5% of win 02:03:00 3.23%
Lay 6/8 5:6 – 5% of win 05:06:00 4.00%
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