Craps Rolling Odds
Basic craps Statistics. One question I get asked a lot is 'what is the probability of a shooter lasting x rolls in craps?' The following table answers that question for up to 50 rolls. The first column is the roll number. The second column is the probability of a seven-out on exactly that roll. The odds of actually rolling a 7 are 6 in 36 or 5:1. The house pays out 4:1 on a winning bet, which brings up an outrageous house edge of 16.67%. This is the absolute worst bet you can make in craps. The table below shows how the casino odds (or payoff odds) compare to the Place bet’s true odds. If you need to review our other article about basic craps math, now is a good time to do it. For example, if you don’t understand why the numbers are paired, ten you should go back and review the basic craps math. You can read about this in our odds and probabilities page if you would like to understand the concept behind this. For additional odds information, please view our craps probability odds page for information about true odds of rolling the dice and also visit our Vegas free odds page for information about odds payouts and house edge.
This is what The Wizard has written on this: 'Turning the come odds off on a come out roll increases the combined house edge from 0.326% to 0.377% in a 5-times odds game, not counting returned odds bets as bets made. So if you want to maximize your return on resolved bets then keep those come odds turned on.'
The Odds: Numbers
Since craps is a game of chance, you need to understand why you have a greater or lesser chance of rolling different numbers. Because you're rolling two dice, your chances of rolling a specific number in craps are determined by the number of die combinations that can add up to that number. For example, 2 can only be rolled with two 1s, but 4 can be rolled with either a 1 and a 3 or two 2s. That means you have twice the chance of rolling a 3 as you do a 2. Because the 7 has the greatest number of combinations (six), it is the number that has the potential to come up most often, which is why 7 is the magic number in craps.
There are 36 possible number combinations in craps. Here is a chart showing the possible combinations for each number using two die.
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From the chart, you can see that the most likely number you'll roll is a 7, followed by the 6 and the 8, then 5 and 9, then 4 and 10, then 3 and 11, and finally (and least likely) the 2 and the 12. This means you'll roll a 7 once out of every six rolls, a 6 or an 8 once out of every 7 to 8 rolls, and so on.
Odds for Each Number
By looking at the possible combinations, the 'true odds' for each number can be established. Knowing the odds in craps is good so you have a feel for the likelihood of one number being rolled before another one (e.g., is the 4 going to be rolled before the 7?).
House Edge
Now, true odds are not what the casino pays you unless you're also betting 'free odds' on top of your main bet. Free odds, which is an additional wager you place with your original line bet, pay true odds so the casino's edge is reduced. (We'll talk more about free odds in Strategies the Winners Use.)
To better explain how the casino edge works, let's take the example of flipping a coin. You have a 50/50 chance of the coin landing on heads, and a 50/50 chance of it landing on tails. If that were a bet on which you were being paid true odds, you would be paid even money. The casino, however, has to have an edge in order to make a profit on the game. So, the payoff for any given bet is less than what true mathematical odds would dictate. For example, on a bet that had true odds of 1:1, you would think that if you bet $1 and win, you would be paid $1 in winnings. But in a casino, depending on the bet, you might only be paid $.96. The difference between the true odds and what they pay you is how they make money -- it's called casino odds.
Another way to better understand casino odds versus true odds is to look at the definition of the casino (or house) edge. WizardOfOdds.com defines it as, 'The ratio of the average loss to the initial bet,' going on to explain that it's based on the original wager rather than the average wager so that players can have an idea of how much they are going to lose when they place a bet. For example, by knowing that the casino has a 1.41 percent edge in craps, you can know that you'll be losing 14.1 cents for every $10 bet.
For charts of odds for all types of bets, visit the Wizard of Odds.com.
On the next page, we'll talk about types of craps bets, their odds and what the casino pays for each.
Chart on the possibility of each number being rolled.
When playing online Craps, it is important to understand the probability of each dice combination being rolled. Once you know what the probability is, you can work out what the house edge is on particular bets. The odds paid to you, the probability of your bet being successful and the house edge are all important factors in how lucrative Craps will be for you.
Why Use a Craps Probability Chart?
The more information that you have at our disposal, the better decisions you can make. A more informed and smarter Craps player has a much better chance of winning on a regular basis. Whether you are a seasoned online craps professional or a casual players, a craps probability chart is crucial to understanding the probability of each dice roll result. With this knowledge, you can make smarter bets at the craps table.
For example, you can see on our craps probability chart that the most common number to come up after a dice roll is a seven. This is the reason that most craps professionals will recommend the pass line as the smartest bet you can make when formulating a solid craps strategy. On the other hand, you can easily see that, according to our craps probability chart, the most uncommon dice roll results are two (or snake eyes in many circles) and 12. Taking this into account, making a bet on two or 12 would likely not be the best bet that you could make.
How to Use a Craps Probability Chart
Obviously, there is nothing to stop you from printing out our craps probability chart and posting it by your computer any time that you are playing craps online. However, by reading our extensive section on the rules and etiquette of craps in offline casinos, you will also find that there are no rules preventing you from printing out the craps probability chart (or copying it on paper with a pencil) and bringing it with you to your favorite offline craps casino.
Every time you are considering a bet, you can consult the craps probability chart to see if the odds match up to the amount of your bet. However, a craps probability chart is simply a tool and cannot alone formulate your entire craps strategy. Some situations require a great deal more information than a craps probability chart before determining whether or not the bet is wise. For more information, you can consult our craps strategy section if you are unsure how to discover the total odds of a bet being successful. For now, memorizing the craps probability chart is your first step towards becoming a craps professional.
The game of craps is a wonderful opportunity to enjoy an energetic casino experience. The high enthusiasm for the game is mixed with the lure of “tempting fate” with the chance of betting on dice rolls. Players and onlookers rejoice together when the shooter hits the point and satisfies several bets, or lament together when the “dice” are against them.
In addition to this, part of what craps offers interested gamblers is a simple way to work the odds of the casino to a player’s favor. Winning at craps is entirely about learning the true probabilities of certain dice rolls occurring and making sure a player has money on the rolls with the best probability. The surest way to win in craps is to maximize bets with good odds and avoid bets with very poor odds.
Dice Probability
The essential starting ground for craps odds and probabilities is with the dice roll itself. Since bets are made based on the potential outcome of the dice, knowing how often, or how infrequently a number combination will occur is the foundation for betting odds in craps.
A pair of standard six-sided dice offers thirty-six possible number combinations that can occur with each roll. First, players need to understand that craps, and dice probabilities are literally roll by roll. Mathematically, what makes craps a game of chance is that every time the shooter picks up the dice, the exact same overall odds apply. There are not cumulative effects roll by roll, so the gambler’s fallacy of “what hasn’t occurred in a while is more likely to occur soon” cannot apply to craps, though many players bet like it will.
In reality, the dice odds stack in a pyramid that symmetrically pairs combinations of numbers, which have the same odds of occurring. The most frequently rolled number is a seven, which a player can mathematically expect to see once in every six rolls. This high probability is due to the fact that seven has the highest possible number of dice combinations to form it between the two dice.
The craps dice odds and probabilities list as follows:
- 2 and 12 have only one way they can be formed on two dice, thus carrying odds of 35 to 1 (a one in thirty-six chance of being rolled).
- 3 and 11 have two possible formations, so the odds of these appearing are 17 to 1.
- 4 and 10 each have three potential combinations, improving the odds of showing either of these to 11 to 1.
- 5 and 9 have four possible formations each, thus holding odds of 8 to 1.
- 6 and 8 are the second most frequently rolled combinations, with five possible ways to see a six or eight on the dice. The odds of either are 6.2 to 1.
- 7 has six possible formations, the most possible and gives it 5 to 1 odds of showing.
These odds are calculated by taking the number of possible formations out of thirty-six, reducing it to it’s lowest denominator and placing it in odds terms. For example, the four has three ways of being formed on the dice, thus a 3 in 36 chance of occurring or, reduced a one in twelve chance of being rolled. In odds terms one in twelve becomes 11 to 1. Understanding and remembering the dice odds is the basis for effective betting in craps.
The chance factor comes in with the fact that even though these odds are mathematically true over dozens and hundreds of rolls, and can be trusted to show in these ratios over a larger sample, they won’t “perfectly” occur with human shooters. Thus a shooter who gains six rolls can sometimes roll all six without showing a seven. This is what brings the element of risk and excitement to craps betting.
Making Good Odds Bets
There are three groupings of bets that have the best odds and the lowest house edge that a craps player can come by. These are the bread and butter of a craps player’s existence, and the wisest and winningest craps players use these bets like clockwork to maximize their odds of taking home cash, not just laying it down on the table. These are the most commonly used bets, as well.
On the right bettor side are the pass bet and the come bet. Pass bets are made during the come out roll; come bets are made after the shooter has established the point. Both of these are sweeping bets that the shooter will roll seven or eleven or a point number before rolling craps, 2, 3 and 12, the low frequency numbers. Pass bets and come bets parallel each other. Both of these bets have true odds of 251 to 244. The house edge, or casino advantage on these bets is one of the lowest at 1.41 %, which means bettors placing pass or come bets have a very good chance of winning this bet.
The wrong bettor partners to the pass and come bets are the don’t pass and don’t come bets. These bets go against the shooter (and thus are sometimes disliked by players), betting that the shooter will hit craps before hitting his point or seven. The house edge on these wrong bets actually drops further to 1.36%, and the odds of these bets showing are 976 to 949.
Free Odds Bets
The free odds bets that go with these are even better from an odds standpoint. The best bets to make in craps, free odds bets multiply a pass or come bet (or a don’t pass or don’t come bet). The advantage of these is the house edge gets lowered to almost zero, meaning players have a good chance of winning these bets at their actual mathematical odds. The odds bets have to be made in conjunction with the main pass/come and don’t pass/don’t come bets. On the right bettor side for pass and come odds bets, making this bet is called “taking the odds.” On the wrong bettor side, odds bets with don’t pass and don’t come bets are called “laying the odds.”
The pass odds and come odds bets have actual odds 2 to 1 on four and ten, 3 to 2 on five and nine, and 6 to 5 on six or eight. The payout ratios for these odds bets match the odds ratios for each number. On the don’t pass/don’t come odds side, the true odds are 1 to 2 against four and ten, 2 to 3 against five and nine, and 5 to 6 against six and eight. Again, the payout ratio when one of these bets wins is the same as the odds of occurrence.
Place Bet Odds
The third category of bets that use the dice probabilities to a great advantage are the place bets on the box numbers at the top of the craps table. Essentially, a place bet makes the same assertion as the free odds bet, that the shooter will roll one of these numbers before a seven or craps. The advantage to place bets is they can be made independently and don’t require a pass line bet first. However, the disadvantage is they payout at poorer odds than the free odds bets.
Four of the six possible place bets have a low house edge, making them still some of the better bets to make as far as player advantage. Place bets on six and eight have the third lowest house edge at 1.52%, making them very profitable bets. The odds of winning on place six and place eight bets are 6 to 5 or 45.45%. Payouts are at 7 to 6 odds. For even dollar payouts, player should bet in increments of $6 on these place bets, preventing rounding down by the casino on paying winnings.
Place bets on five and nine are also still lower house edges than most bets on the table at 4%. Players have a 40% chance of winning or 3 to 2 odds, and they payout at 7 to 5 odds. Place these bets in multiples of $5 for even dollar payouts without rounding.
Place bets on four and ten are still decent bets, but the house edge starts to climb–it’s 6.67%. The odds of winning a place four/place ten bet are 33.33% but if it does win, the payout rate is 9 to 5. These bets should also be made in $5 increments for even payout amounts.
Another advantage to place bets is that when a place bet wins, the dealer pays the player’s winnings but leaves the original bet on the table effectively starting another place bet. The player doesn’t have to add money to the bet to continue it. Players can ask the dealer to “turn off” the standing place bet or remove it if they wish.
Craps Roll Odds Table
A few online casinos offer the wrong side version of place bets called place bets to lose. Live casino Star City in Sydney, Australia also allows place bets to lose. These bets flip the bet to lose when the shooter hits the number first, but win if the shooter rolls a seven before the number. The odds of winning these place bets go from 54.55% to 66.67%, rather than under 50% for their right side counterparts. Place to lose on six and eight pay out at 4 to 5; on five and nine they pay out at 5 to 8; and on four and ten they pay out at 5 to 11.
Betting the Field Odds
The field box bets are right in front of the players and can be enticing bets. Their major disadvantage stands in that they are single roll bets, only valid for the next immediate dice roll. The house edge at 5.56% is smaller than many other craps bets, but still starting to be larger than is wise for a player to use often. The payout odd for field bets on three, four, nine, ten and eleven are 1 to 1, even money. For the more rarely rolled two and twelve, the payout odds are 2 to 1. The true odds of betting on the field are 5 to 4.
Odds on Proposition Bets
The proposition bets located in the center of the craps table actually hold the poorest odds for a player, and with high house edges hold great odds for the casino winning. Craps experts consistently advise staying away from these various “sucker bets” that catch novices or people who have not bothered to learn a few key points about playing craps.
Proposition bets are mostly single, next roll bets on specific numbers. The rates of the occurrence for the dice roll is the first basis for the enticingly high payouts, but the house edge factors in on the lesser likelihood that the single next roll will produce that number or combination of numbers.
The list of odds for the main proposition bets is as follows:
- Craps 2 or 12 has true odds of 35 to 1, that single dice combination. The payout odds are 30 to 1, with a huge house edge of 13.89%.
- Single number bets on 3 or Yo (11) carry true odds of 17 to 1, but the casino pays 15 to 1 odds on a winning bet. The house edge is 11.11%
- A Hi-Lo bet matches the odds of 3/11 bets with true odds of 17 to 1 and payout odds of 15 to 1. The house edge is also 11.11%.
- Any Craps bets (looking for 2, 3, or 12) have true odds of 8 to 1, payouts of 7 to 1 and that ever-large 11.11% house edge.
- C-E or Craps-Eleven bets have true odds of 5 to 1. The payouts vary at 3 to 1 for craps (2, 3, 12) and 7 to 1 on eleven. This also carries an 11.11% house edge.
- Any 7 bets have true odds of 5 to 1 with payout odds at 4 to 1. Any 7 has the largest house edge on the table at 16.67%.
- Horn bets carry a higher house edge of 12.5%. The true odds are 5 to 1. Payout odds are 27 to 4 on two or twelve and 3 to 1 on three or eleven.
World or whirl bets are a variation of the horn bet on 2, 3, 7, 11 and 12. The true odds are 2 to 1. The payout odds on two or twelve are 26 to 5 and on three or eleven are 11 to 5. The house edge is 13.33%.
Big 6 and Big 8
The corner proposition bets of Big 6 and Big 8 have been banned from Atlantic City casino craps tables because the odds make them such poor bets. With a large house edge of 9.09%, bets on Big 6 and Big 8 only payout even money, though the true odds of rolling a six or eight before a seven, like in Place 6/Place 8 bets is 6 to 5.
Hardways Bets
Hardways proposition bets can be ongoing bets, but these are also costly bets to make. The hard four and hard ten bets have an 11.11% house edge and pay 7 to 1 if they win, but only carry an 11.11% chance of winning. Hard six and hard eight bets payout at 9 to 1, but only have a 9.09% chance of winning. The house edge for those two bets is 9.09%. It doesn’t seem like a bet bodes well for a player when the odds of winning equal the odds of the house advantage over the player.
Craps Rolling Odds
Buy Bets and Lay Bets
For players who like to use place bets but who don’t like the odds, the option exists to buy the points for a 5% house commission that reduces the house advantage to “fair odds.” Some casinos require that commission up front; others take the commission on winnings. Most players will advise staying away from Buy and Lay bets. Paying extra to level the odds is simply not worth it. However, some players do like to use these bets.
Buy bets have a standard 4.76% house edge on all three pairs of bets. The odds are:
- Buy four and Buy ten have 2 to 1 odds.
- Buy five and Buy nine have 3 to 2 odds.
- Buy six and Buy eight have 6 to 5 odds.
Lay Bets are the “Place to Lose” or wrong side lay odds commission bets. The lay bet odds are slightly different than the buy bet odds.
- Lay four and Lay ten have 1 to 2 odds with a house edge of 2.44%.
- Lay five and Lay nine carry odds of 2 to 3 and a house edge of 3.23%.
- Lay six and Lay eight have 5 to 6 odds and a 4% house edge.
Overall Craps Odds
Some players ask about their overall chances of winning or losing at craps. Honestly, with most games of chance players will do well to expect to lose more than what they win. Statistically, in a particular session the mathematical odds reinforce the odds of losing are slightly greater than the odds of winning.
The odds of breaking even are about 0.67%.
For a truly big picture perspective on the odds of playing craps, probabilities calculated from simulating 1,000,000 sessions of 100 come out rolls each leave a players odds of winning and losing overall at the following percentages:
- Winning $1 to $25: probability 28.64%
Losing $1 to $25: probability 30.06% - Winning $26 to $50: probability 14.43%
Losing $26 to $50: probability 16.36% - Winning $51 to $75: probability 3.91%
Losing $51 to $75: probability 4.64% - Winning $76 to $100: probability 0.564%
Losing $76 to $100: probability 0.65% - Winning over $100: probability 0.0418%
Losing over $100: probability 0.0422%
With so many calculations for craps odds and probabilities, the best way for a player to utilize this information is to remember the dice probabilities and the most beneficial bets to use. Craps tables list the payout odds for the higher bets as part of inviting players to spend money on bets that the house is more likely to win than the player. Seeing a 30 to 1 payout option makes some folks eager to bet there for the big return, but the savvy player will remember that the odds of that single two or twelve showing up on the next roll are 35 to 1. There are many more useful places to invest those bets. Strong players will use these odds and probabilities on craps to make guided decisions about where best to bet their hard earned money.