Craps Odds

dice distributions

Craps offers some of the best odds in the casino. It also offers some of the worst. The best bet on the table doesn’t even appear on the layout, while the worst ones are some of the easiest to make. Every wager one the table is presented in such a way as to make it seem like the player could win big at any time. But unless you can influence the dice, the odds are always stacked against you in craps.

The Pass Line bet is the most common wager on the table. When you bet a Pass Line, the natural house edge is around 1.42%. If the Pass Line bet wins, it is paid even-money – a ten dollar bet wins ten dollars. The Free Odds bet is paid at true odds. For example, a winning $10 Free Odds bet on the point of four will be paid 2 to 1, or $20. The Free Odds bet has no house edge, but you cannot place it unless you have already made a bet that does have a house edge – either the Pass and Come, or the Don’t Pass and Don’t Come. When you back one of these bets with free odds, the overall effect is to reduce the house edge. The greater the proportion of your bet that is on free odds, the lower the edge will get. However, the casino always has an advantage over the player with this bet – albeit a small one.

A placard posted on the table will clearly state what proportion of your bet may be placed as a free odds bet. If the placard states that it is a $10 – 10X odds game, it means the minimum wager is $10, and you can take up to ten times your wager in Free Odds. Allowable odds may range from single to unlimited, up to the table’s maximum bet.

If you are playing a single odds game, you can place a free odds bet equal to your Pass Line wager. When playing the Don’ts, you can lay odds sufficient to win an amount equivalent to your Don’t Pass bet. The single odds game is commonly found on cruise ships and isolated vacation destinations like the Caribbean islands. They can get away with offering an inferior game because you are a captive player. It’s the only game available.

Most land based casinos offer double odds or higher. In Las Vegas, the 3, 4, 5X odds game is the most common. This game allows you to take 3X odds on the four and ten, 4X odds on the five and nine, and 5X odds on the six and eight. For example, in a $5 game with 3, 4, 5X odds game, the maximum free odds you could take on the four or ten would be $15 – three times your $5 flat bet. You could wager $20 on the five and nine, and $25 on the six and eight. Casinos do this as much for their own convenience as for the players. In a $5 game with 3, 4, 5X odds, the correct payoff on every wager with full odds is $35.

Some casinos offer 5X, 10X, 20X, or even 100X odds. Some of the most sought after games are low limit tables with 100X odds. With those odds, the house’s edge over the players is miniscule. But as mentioned earlier, regardless of how large of a free odds bet they allow, the casino always has the edge. Remember, casinos rake in vast profits on margins as little as .07 %. That is not seven percent. It is seven-one-hundredths of a percent.

The pay offs on the Free Odds bets are calculated based on the relationship between the number of ways a particular bet can win versus the number of ways it can lose. The best way to understand this is to look at this chart, which demonstrates how many combinations of the various numbers there are on a pair of fair dice.

As you can see from the chart at the top of this page, the seven is the most common number on the dice. Six of thirty-six possible combinations of the dice add up to seven. There are more ways to make a seven with two dice than any other number. That means that on any given roll, there is a better chance a seven will come up before any other number.

Take a look at the odds of rolling a four. There are three ways to roll a four, compared to six ways to roll a seven. Reduce those 6 – 3 odds to their lowest common denominator and you come up with true odds of 2 – 1. A winning $10 Pass Line or Come bet established on the four with 3X or $30 in free odds would be paid a total of $70. The player would receive $10 for his winning Pass Line bet, which is paid at even money, and $60 for his winning $30 free odds bet, which is paid at 2 – 1.

Free Odds on the five and nine are always paid at 3-2. This can lead to some confusion for the novice player. For example, if you played a $5 Pass Line bet and then took single odds for $5, the casino could not give you a proper payout. The free odds bet has to be an even number – divisible by two – in order for them to pay true odds of 3-2. In this example, in addition to paying the $5 flat bet on the line, the casino would pay 3-2 on $4 of the free odds wager, plus even money on the extra $1 for a total of $7 on the free odds bet. Since the casinos do not generally pay fractions of dollars, they short you on your payout. The correct single odds wager on a $5 Pass Line bet on the five or nine is $6. In addition to the $5 Pass Line payout, the correct $6 free odds wager is paid $9.

The simplest way to remember the correct free odds wager is to memorize the old axiom: “Odd numbers get even odds.” The five and nine are the only “odd” box numbers on the layout, and in order to receive a correct payout you must bet an even amount of money on those numbers.

Last of all, remember that the Come Bet performs exactly like the Pass Line Bet and the same odds apply to both bets. Likewise, the Don’t Come bet performs exactly like the Don’t Pass bet and the same odds apply to both bets. On Pass Line, Come Bets, Don’t Pass or Don’t Come, the house’s ultimate edge comes from the even money payoff on the winning flat bet – not the Free Odds bet. For that reason, most players prefer to risk the minimum amount possible on the Pass or Don’t Pass, and risk more of their bankroll on the free odds wagers.

There are many more bets available to the player on the traditional banker’s craps layout. In every case, the house gets its edge by paying the player less than true odds. To get a better understanding of this, let’s look at place betting first. Many players prefer to place bet numbers for many reasons. It gives them immediate action in the game. They get to choose what numbers they play as opposed to letting the Come Bet decide which numbers they wager on. Their number only has to roll once for them to get paid. In exchange for these privileges, these players are willing to give up an additional edge to the house.

The most popular numbers to Place Bet are the six and eight. One look at the odds chart and it is easy to see why. There are five ways each to roll the six and eight compared to six ways to roll the seven. As we mentioned earlier, the true odds on the six or eight are 6 – 5. But if you want to Place Bet those numbers the house requires a wager in six-dollar increments. In a $5 game the correct Place Bet wager on the six or eight is a minimum of $6. In a $10 game it is a minimum of $12. And instead of being paid at true 6 – 5 odds, the Place Bet is paid 7 – 6. This “reduced” pay off is where the house gets its edge – in this case, 1.51% on the 6 and 8.

The five and nine are Place Bet in increments of five dollars, and are paid at 7 – 5. That gives the house an edge of 4% over the player. The story on the four and ten is even worse. These numbers are paid at 9 – 5, which yields a house edge of a whopping 6.67%.

Prominently located in the center of the layout are the Proposition or Prop Bets. These are the bets the stickman hawks like a carnival barker with his endless chatter, “Get your hops, props, hardways, high-lows, yos, horn bets, worlds.” These are all high-vigorish bets that generally should be avoided. Let’s take a look at them.

The Any Seven bet, sometimes called the Big Red bet, is usually located at the top of the prop box. This is a one-roll wager that the seven will be the next number to roll. The winning bet pays 4 to 1, compared to correct odds of 5 to 1. That one unit difference gives the house a 16.67% edge.

Beneath the Any Seven bet are the Hardway Bets. These are individual wagers that the hard four (2-2), hard six (3-3), hard eight (4-4), or hard ten (5-5) will roll “hard” before they roll easy or before the seven rolls. The payoff is 9 – 1 on the 6 or 8 and 7 – 1 on the 4 or 10. The house edge is 9.09% and 11.11%, respectively.

The next section in the Prop Box consists of specific non-box numbers known as the horn numbers. They are the two, three, eleven and twelve. These numbers can be bet on individually, in pairs, or all at the same time. Each bet has it’s own moniker.

The Ace-Deuce bet is a one-roll wager on the three-craps. The payoff is 15 – 1, but the true odds are 17 – 1. The house edge is a whopping 11.1%.

The Eleven or “Yo” is a one-roll wager on the eleven. When bet alone, the wager is placed in the “E” circle adjacent to the prop box. For more details on that see the discussion of “C and E” bets, below. The payoff on the eleven is exactly the same as the Ace-Deuce, 15 – 1, and it carries the same 11.1% house edge.

The “Aces” bet is a one-roll wager on the two-craps. The payoff is 30 – 1, while the true odds are 35 – 1. The house edge on this wager is also 16.67%.

Last of all is the twelve-craps, sometimes called “midnight.” Like the Aces bet, the twelve-craps pays 30 – 1 and carries a house edge of 16.7%.

When all four of these numbers are wagered at the same time it is called a Horn bet. A player makes a horn bet by tossing his chips to the stickman and calling out his bet. For example, “$4 horn.” This gives him $1 on each of the aces, ace-deuce, eleven and twelve.

The final variation of the Horn bet is the World bet. The World bet is simply a Horn plus an Any Seven bet. A $5 world bet gives the player $1 each on the aces, ace-deuce, eleven, twelve, and any seven. The World simply takes a bad bet, the Horn, and makes it worse by adding another dollar to a high vigorish wager.

On either side of the prop box you will see the C and E bets mentioned earlier. There are several of these betting circles on each side of the table, and each corresponds to a different player position at the table.

The “C” is an Any Craps bet. The Any Craps bet is a wager that the 2, 3, or 12 will roll on the next toss. If any other number rolls the Any Craps wager immediately loses. The winning wager pays 7 – 1, and is exposed to a house edge of 11.1%.

The “E” is the eleven or “Yo” bet. As mentioned earlier, it could be set up in the horn section of the prop box. However, most stickmen are trained to set the bet up in the appropriate “E” circle, which makes it easier to determine which player the bet belongs to in a crowded game. The odds are the same, no matter where the bet is set up. The house has an 11.1% advantage over the player.

The Field Bet is one of the most prominent on the table. It is a one-roll bet that the next number to roll will be a Field number. The Field numbers are 2, 3, 4, 9, 10, 11, and 12. At first appearance it looks like a good bet. You have seven out of eleven possible numbers working for you. However, the numbers that are not covered, the 5, 6, 7, and 8, give the house more ways to win than the player. There are 20 combinations of the dice that win for the house, versus 16 combinations that win for the player. Depending on whether the house pays “double” or “triple” on the twelve, the house edge varies from 5.56% to 2.28%.

Some layouts include a Big 6 and Big 8 wager in one corner. These are self-service bets a player can make on the six and eight. However, instead of being paid 6 – 5 true odds, or 7 – 6 place odds, the player is paid even money on this wager. That yields a house edge of 9.09%.

From time to time you will see a player make a Buy Bet. Buy Bets pay off at true odds instead of place odds. In order to get this privilege, the player pays the house a 5% commission. A quick look at the odds chart reveals that in most instances, the four and ten are the only numbers that are worth buying.

A $20 Buy Bet carries a $1 vigorish. Buying the 4 or 10 for $20 reduces the house edge from 6.67% to 4.76%. Green chip bettors are usually permitted to Buy the 4 or 10 for $25 and still pay just a $1 commission. That reduces the house edge to just 4%. Some casinos only collect the vigorish on a winning bet, which serves to reduce the edge even more. Finally, a few casinos will allow the player to Buy the 4 and 10 for $30 or more before charging the extra $1 commission. This practice, combined with collecting the vigorish only on winning bets, can reduce the house’s edge on these numbers to as little as 1.11%, making it one of the best bets on the table.

Lay Bets or exactly the opposite of Buy Bets. A Lay bettor is wagering that the seven will roll before the number he is laying against rolls. Lay bets are typically made in amounts to win $20 increments. Correctly sized Lay Bets are $41 No 4 or No 10, $31 No 5 or No 9, and $25 No 6 or No 8. One dollar of each of these wagers is the commission paid to the casino for the right to lay against the numbers. The house edge in Lay Bets against the 4 and 10 is 2.44%. The edge against the 5 and 9 is 3.23%. The edge against the 6 and 8 is 4%.

In summary, the theoretical best bets when playing the “right” side of the game are Pass Line with odds, Come Bet with odds, and Place Bet the 6 and 8. The best bets when playing the “wrong” side of the game are Don’t Pass with odds, Don’t Come with odds, and Laying against the 4 and/or 10.