• Craps Possible Combinations Meaning
• Craps Possible Combinations Games
• Craps Possible Combinations Game
• Craps Possible Combinations List

Chart on the possibility of each number being rolled.

The 36 Possible Combinations of Two Dice The odds are expressed as a ratio of the number of ways of rolling a certain number, divided by the total possible combinations. Examples: There is one possible combination of rolling 12, six/six. Thus the odds of 12 rolling is one in thirty-six or 1/36. Cheating at craps takes many forms. Most of the craps cheating methods include loaded dice or fixed dice, but that’s not the only way dice shooters gain an advantage over the casino. This guide to cheating at craps includes all the many ways to load dice. We also discuss other cheating methods, such as dice control or making late bets.

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.

It follows that the number of possible combinations is equal to 6 x 6 = 36 as each of the two dice used in craps has six sides. Each throw of the two dice will result in one of these eleven numbers coming out. Some numbers, however, are rolled more frequently as the number of combinations that add up to them is greater. You can use probability to figure out the odds of winning and losing in the popular casino dice game of craps. In the game of craps, on your first roll (called the come out roll), three outcomes are possible: Natural: Rolling a total of 7 or 11 — automatically wins. Craps: Rolling a total of 2, 3, or 12 — automatically loses.

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.

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.

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.

by Henry Tamburin

This is a controversial article because it is going to present a different view on how to determine what are the best bets on the crap layout. For example, if someone were to ask you to selectwhich of the four bets is the best bet, which one would you, pick?

1. $5 bet on the pass line.
2. $1 bet on the Field
3. $6 Place bet on the 6
4. $1 bet on Any Craps

Most players would pick bet number 1, the $5 pass line bet because “it has the lowest casino edge” compared to making bet 2, 3, or 4. Before we go on with our analyses let’s make sure youunderstand what the casino's edge is really all about and why it has its shortcomings.

We all know that casinos can’t depend upon luck to generate the income they need to pay their expenses and have a few bucks left over as profit in profit for their shareholders. To ensurethemselves a steady income they must have a mathematical advantage over every crap-shooter at all times. How do they create their advantage in the game of craps? They do it in two different ways but with the same result.

Take a bet on the pass line for example. Based on the rules for winning a pass line bet, for every 1,000 bets a player makes, he will win 493 on average and lose 507. In other words the rulesfavor the casino winning more bets than the player. How much more? If you bet a buck every time you would win $493 and lose $507 for a net loss of $14. Thus for every $1,000 worth of bets youmake on the pass line the casino stands to win $14 or 1.4% simply because the rules favor the casino winning more times than the player.

The casino creates its advantage on other crap bets a little differently. Take the bet on any seven whihc is a one-roll bet that the dice will show a 7. If you win that bet the casino will payyou $4 in winnings (4 to 1 payoff). That’s very nice that they give you $4 for only a dollar bet, but unfortunately it isn’t quite enough. You see the number 7 can be rolled in 6 different dicecombinations out of a possible 36 combinations. You can only roll the number 7 with a pair of dice when the following numbers show: 1,6; 2,5; 3,4; and the opposites 6,1; 5,2 and 4,3. Any otherdice combination – like 3,6 or 2,1 – will yield a non-7 number. There are in fact 30 combinations that yield a non-7 therefore the odds that a 7 will appear are 30 to 6 or by rounding 5 to 1.That is the true mathematical odds against rolling the dice and having a 7 show.

If the casino were to pay players at the same odds, namely 5 to 1, they wouldn’t make a penny profit on this bet. But being the smart business people that they are, they pay off a winning betnot at 5 to 1 odds but rather at 4 to 1 odds. By simply short changing the player one chip when he wins, the casinos have discretely created their edge on this bet. Frank Scoblete says it best:“when you lose a bet it’s lost; but when you win a bet you have a silent partner – the casino – who keeps a part of your winnings.”

Let’s be sure you also understand what the casino’s edge means in dollars and cents. The casino’s edge or advantage is usually written as a percentage. In the above example the casino’s edge onthe any seven bet is 16.7% which means a player can expect to lose 16.7% of all the money bet on any seven. It doesn’t matter whether your bets win or lose in the calculation of how much thecasino’s expect to win from you. All that’s required is that you bet and what the casino will earn day in and day out is 16.7% of what you bet. If you make a total of 25 one dollar bets on anyseven during the course of play the casino will expect to win from you about $4 for your action (16.7% times $25). Now most likely you will win or maybe lose a lot more than $4 but the moremoney you bet the closer your losses will come to the statistical 16.7% loss rate. The casinos bank on this fact day in and day out.

Craps Possible Combinations Meaning

Table 1 ranks all the crap bets according to the casino’s edge. The pass/come/don’t pass/don’t come bets with odds clearly have the lowest casino’s edge compared to the other bets.

Table 1 - Ranking of Crap Bets by Casino’s Edge

But does comparing the worth of one bet to another solely based on the casino’s edge tell the whole story? Not really, because the number of times a bet wins or loses per unit of time has notbeen factored into the equation.

Think about it for a minute. Is the number of times you win or lose a pass line bet per hour the same or different then say a field bet? How about a bet on any craps or the place bet on the 6?In fact they are not the same. Which is why a meaningful comparison of the worth of different craps bets should be based on their “cost per hour” and not solely on their “casino’s edge”.

The cost per hour is just what its name implies. It’s what the casinos expect to earn or what it costs you per hour to make a bet. The equation to calculate the cost per hour is simply theamount of the bet times casino’s edge times number of decisions per hour.

Most casual players will typically bet $5 on the pass line. You can expect in most well run games the dice will roll about 100 times per hour. The number of pass line decisions that occur inthose 100 rolls is 30. Therefore the cost per hour is simply

$5 times 1.41% times 30 decisions per hour = $2 (rounded)

Craps Possible Combinations Games

By doing similar calculations for every bet you can compute each bet cost per hour and then rank them (Table 2).

Table 2 - Ranking of Crap Bets by Cost per Hour (rounded)
(assumes 100 rolls per hour)

What’s surprising when you scan the ranking of the bets in Table 2 is that several “bad bets” all of a sudden become better bets because they have a relatively lower cost per hour. Such isthe case with the hardway bet on the 6 and 8. Even though the bet is ranked low in Table 1 because of its high casino edge, it suddenly becomes a better bet when you look at its cost per hourranking in Table 2. Why is this? Simply because it’s possible to bet low amounts ($1) and the number of decisions per hour (30) is relatively low. Remember it’s the combination of casino’sedge and number of decisions per hour, which determines the ranking in Table 2.

Take a look at the hourly cost of some of the proposition bets in Table 2. If you are prone to making prop bets, you should confine your betting to the hardway 6 and 8 compared to say anycraps, any seven, or a bet on the 2/12 and 3/11 because the hourly costs are lower. If you like to bet the field, please do so in a casino which pays double on the 2 and triple on the 12. Yourhourly costs will decrease from $5.50 to $2.80. Also note how the place bet on the 6 and 8 ranks high in both tables. If you like betting on the numbers you better pay close attention to Table2. The numbers clearly show how much more it will cost you to buy a number vs. placing it.

Keep in mind that the cost per hour calculations and rankings in Table 2 is based on a specific bet size. If you bet only $1 on the pass line, for example, your cost per hour would be one fifththe figure in the Table 2 (40 cents vs. $2). Likewise if you decide to bet $5 in the field instead of $1 your hourly costs would jump from $2.80 to $14.00.

You must also keep the cost per hour rankings in perspective. Obviously one way to keep your hourly costs to as low as possible is to bet the smallest amount ($1) on a bet which doesn’t havemany decisions per hour. But that leads to a lot of rolls of the dice in which you would not be participating much and it won’t be fun playing.

Craps Possible Combinations Game

So what about the odds bet which is noticeably missing from Table 2? Shouldn’t it reduce the cost per hour for the pass/come/don’t pass/ don’t come wagers because it lowers the casino’s edgefor these bets (see table 1)? Well let’s see.

Craps Possible Combinations List

Table 2 tells us that the $5 pass line bettor’s hourly cost is $2. Suppose the player wagers doubles odds. The casino’s edge for the combined pass line plus double odds is reduced from 1.41% to0.61% and the number of decisions per hour stays the same. But, and it’s a big but, instead of making only $5 bets on the pass line the player betting double shells out another $10 on the oddsevery time a point number is thrown (about two thirds of the time). His average bet is about $11.67 per decision. If you multiply $11.67 times the 0.061% casino edge times the 30 decisions perhour, you arrive at an hourly cost of $2 - the same as the pass line player that doesn’t make the odds bet. Putting it another way, the casino’s edge on the odds bet is 0 so the hourly costsfor the pass line bet is the same as a pass line bet with odds assuming the same amount of money is riding on the pass line bet. Therefore whether you bet pass line or pass line with single,double, triple, even 100-times odds, your hourly cost for the basic $5 pass line bet is always $2.

Review the numbers in Table 2 before you hit the crap tables to determine what it is really costing you to play. And remember when it comes to playing craps, time is really money.