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Dice Combinations

A. Antonova (editor) |

The Many Combinations Dice Can Form

Dice CombinationsThe majority of casino games are known to offer either a low or a high house edge. Craps stands out from the crowd because it offers both. For one thing, this unique game features some of the best bets you can possibly make in a casino. For another, some of the more advanced, proposition bets in craps give the house a formidable edge over patrons that nearly reaches 17%!

Another distinctive trait of craps is that it is the only game of chance where players can actually bet something will not happen instead of backing the outcome they believe is most likely to occur, as is the case with Don’t Come and Don’t Pass bets.

These two features are what render this simple game of chance so unique and appealing in the eyes of millions of gamblers around the world.

As simple as craps seemingly is, you most definitely should take the time necessary to learn all the possible dice combinations along with their odds and probabilities before you invest any of your money in the game.

The purpose of this part of the guide is to introduce you to all dice combinations in craps and to help you make a distinction between true and casino odds. By the end, you will know whether dice control is effective in reducing the house edge and will be able to calculate your average expected losses at the craps tables.

Possible Dice Combinations in Craps

Possible Dice Combinations in CrapsAs we have previously explained in this guide, craps is a game of chance that plays with two six-sided dice, with each side having a different number of pips so as to represent numerical values 1 through 6. Each toss of the two dice can result in one of 11 possible numbers, namely numbers 2 through 12.

When two dice are in play, the number of possible dice combinations increases to 36 since each dice is practically a cube with six sides (6×6 = 36). Now, we want you to take a closer look at the table below and see whether you will be able to notice a trend.

Dice TotalNumber of Ways to Throw TotalPossible Combinations
321-2, 2-1
431-3, 3-1, 2-2
541-4, 4-1, 2-3, 3-2
651-5, 5-1, 3-3, 2-4, 4-2
761-6, 6-1, 2-5, 5-2, 3-4, 4-3
852-6, 6-2, 5-3, 3-5, 4-4
943-6, 6-3, 4-5, 5-4
1034-6, 6-4, 5-5
1125-6, 6-5

You have probably noticed the column with the possible combinations is diamond-shaped. From this shape, it becomes apparent the number of combinations that may result in a toss of 7 is the highest, which automatically means the probability of this number being tossed is the highest.

As many as 6 combinations result in a 7 which is the main reason why the majority of seasoned craps players favor the Pass Line where a come-out roll wins when 7 or 11 are tossed, with a total of 8 possible winning combinations (six for a toss of 7 and two more for a toss of 11).

We recommend you memorize the number of possible combinations for numbers 2 through 12. This knowledge would help you evaluate your chances of winning with a given wager, enabling you to approach betting at the craps tables smartly.

Do not be intimidated by the chart – there is one easy way for you to learn the combinations by heart. All you have to do is use 7 as a starting point and divide the remaining outcomes into groups of two. You can pair rolls of 6 and 8 since both outcomes have 5 possible combinations.

Next in line is the pair of 5 and 9, with each of these rolls having 4 possible combinations. The next pair comprises rolls of 4 and 10 with three dice combinations. Then you have 3 and 11 where the number of possible combinations drops with a unit to two.

The rolls of 2 and 12 are the easiest to memorize since there is only one possible dice combination for each of the two outcomes. Learning these combinations is essential because it helps you gain a better understanding of the odds and probabilities in craps. We tackle the subject in the next section.

Understanding the Odds and Probabilities of Craps Bets

Understanding the Odds and Probabilities of Craps BetsThis is the part most gamblers struggle with. Craps, like all other games of chance, is based on independent trials, which is to say the odds of the dice rolls remain constant and are not influenced by previous outcomes. This is easily the most important aspect of the game all craps players must understand. Yet, there are people who would invest their action in a given dice outcome simply because they have not seen it occur in a while.

Here it is important to draw a distinction between odds and probabilities. While interrelated, the two terms do not denote one and the same thing as many gamblers mistakenly presume. Probability is nothing more than the likelihood of an independent outcome occurring and is usually expressed either as a proper fraction or as a percentage.

To calculate the probability of rolling a certain value, you must know the number of dice combinations that result in it as well as the number of all possible dice combinations. For instance, the probability of tossing a 7 on the come-out roll is the highest at 16.67%. We can also say the probability is 6 in 36 because there are 6 winning combinations out of 36. This is called theoretical probability.

Odds, on the other hand, show you the ratio between winning and losing outcomes and are usually expressed as fractions. So for example, if you decide to make a Snake Eyes bet, which is a wager on a single roll of 2, the odds of winning will be 1 to 35 because there is only one winning combination for this roll while the remaining 35 combinations result in a loss. This corresponds to a theoretical probability of 2.78% because 1/36 = 0.02777 x 100 = 2.78%. Consult the table below to see the probabilities of rolling all two-dice totals in craps.

Two-Dice TotalProbability as a FractionProbability of Rolling the Total as a Percentage

The Difference between True Odds and Casino Odds

The Difference between True Odds and Casino OddsIt is of essential importance for you to understand there is a distinction between true odds and casino odds. It is the discrepancy between the two that gives the house the edge that eventually grinds the bankrolls of imprudent gamblers down to nothing.

If you hang around a casino for an hour or so, you are more than likely to hear (losing) players complaining about the games being rigged as they exit the venue with empty pockets. These players are, in fact, correct to a certain extent. The games are indeed rigged against them but not because the casino resorts to cheating. Why cheat your patrons when there is a perfectly legal way of extracting their money?

Another Example

Another ExampleThe main reason gamblers lose in the long term is the above-mentioned discrepancy between true odds and the odds the house pays you at when you win. The following example demonstrates how the house edge in craps works. Let’s presume you decide to make 36 consecutive Snake Eyes bets wagering a dollar on each. The mathematically correct odds for this bet are 35 to 1, which is to say 35 of all possible combinations result in a loss whereas only 1 combination (1-1) can lead to a win.

Now take a quick glance at the layout of the craps table. Can you see what it says? The payout for a one-roll Snake Eyes bet on 2 is 30 to 1 instead of being 35 to 1, as it should be. The same goes for a roll of 12 where again there is a single winning combination (6-6). This applies to all payouts in craps – they have all been reduced, making it possible for the house to extract consistent profits from its tables in the long term.

So you wager a dollar on Snake Eyes a total of 36 times in a row and the results are mathematically perfect, meaning that one of those 36 trials was indeed a winning one. Now, this is unlikely to happen in the short term but generally, the more you play, the closer your results get to the mathematical expectations for the game.

To sum it up, you would have wagered $36 in total but would have received only $30 for your winning Snake Eyes bet at odds of 30 to 1. The remaining $6 end up in the house’s coffers, giving it its edge. Similarly to probability, the house edge is also expressed as a percentage and in this instance, it stands at 13.89%. This percentage indicates you will be losing nearly $0.14 for every dollar you wager on the Snake Eyes bet.

Players can easily figure out what the house edge is for any available bet in craps as long as they know its true odds, its payout, and its probability. Let’s demonstrate how this works for the Any 7 bet. This wager wins on a roll of 7, regardless of which one of its six combinations occurs. The payout for a winning Any 7 bet is 4 to 1. The probability is 6 in 36 possible dice combinations.

The calculations will run in the following manner: (6/36) x 4 – (30/36) = (0.166 x 4) – 0.833 = 0.666 – 0.833 = (-0.166) x 100 = -16.67. The figures in the first brackets correspond to the probability of winning with an Any 7 bet, which is then multiplied by the casino’s payout of 4 units per unit wagered. You then subtract the probability of losing (the figures in the second brackets stand for 30 ways to lose out of 36 possible combinations) from the result and get a house edge of 16.67% for the Any 7 bet.

As you can see, you will lose $16.67 (hence the “-”) per every $100 wagered on the Any 7 bet. In other words, your expected return with this bet will be in the negative at -$16.67. If you are still struggling to understand this, we suggest you go back to the Craps House Edge article of this guide where you will be able to find further explanations on the matter along with the true and casino odds of all available craps bets.

Distinguishing between “To” and “For” Odds

Distinguishing between “To” and “For” OddsThe trouble with most casual gamblers is that they are so engulfed in the action, they rarely pay any attention to anything else, including what’s in front of their eyes, right there on the table layout. If you take the time to carefully inspect craps layouts, you will undoubtedly notice there is something weird about the proposition bets section at some craps tables.

In some casinos, the layout states that you get 5 units “for” 1 unit wagered on Any 7 instead of the usual payout of 4 “to” 1. The same goes for proposition bets like the Hard 6 and the Hard 10 which pay 10 unit for each unit wagered instead of the usual 9 to 1. Many undiscerning gamblers are misled by this phrasing (that was the purpose in the first place) and are quick to assume their winning proposition bets return at enhanced odds. There is nothing of the kind, though.

The “for” payouts are basically the same since they include your initial stake. In contrast, the phrasing “to” distinguishes your net profits from your original bet. So in the case of the Any 7 bet, you get 4 units in net profits plus your original stake of 1 unit for a total of 5 units.

The wording of these payouts is no coincidence. Quite the contrary, the house uses this sly approach for the purpose of leading inexperienced craps players into believing they get higher payouts on the wagers with the steepest house edge when in reality, they are paid at standard casino odds. No matter what phrasing is used, we would like to remind you not to waste your money on proposition bets. The monstrous house edge you combat with these wagers is not worth it even if the payouts were indeed “enhanced”.

Figuring Out Your Expected Loss in Craps

Figuring Out Your Expected Loss in CrapsThis section is somewhat a continuation of the True Odds one. You are probably scratching your head wondering why on earth would we teach you how to calculate your expected losses. What you want to know is how to determine your hourly expected profits, right? We hate to break this to you but craps is a negative expectation game which is to say your expected value in the long run will always be in the negative due to the house edge, i.e. you will inevitably lose money to the casino in the long term.

It is important for you to learn to calculate your expected loss so that you know at what average rates you will lose money per hour. This depends on your action, the types of bets you make, and their house edge. The formula is quite simple – you must multiply the number of rounds you play per hour by the amount you wager, the house edge, and the number of hours you intend to play.

So, let’s suppose you play at a slower pace and go through 160 rolls, betting $5 on Any 7 for one hour. The calculations will look like this: 160 x $5 x 0.166 x 1 = $133 on average. This is the average rate at which you lose money with Any 7 wagers but you arrive at this amount after a gazillion of independent trials. In the short term, you might end up losing much more or far less within an hour. The bottom line is the longer you play, the closer you get to these expected loss figures.

Can Dice Control Influence the Probability of Rolling Certain Combinations?

Craps Dice CombinationsSome craps players would attempt to influence the outcome of the rolls by using an advanced technique, called dice setting or dice control. The main idea here is that you can skew the odds in your favor by tossing the dice in a specific manner. To achieve this, the shooter must toss the dice at the correct angle in order to allow them to produce the desired outcome.

The toss itself should be performed with as little hand movements as possible so that the dice do not tumble as much before they hit the back wall of the craps table. The dice must be picked in a particular way as well. The shooter’s wrist remains locked during the toss, i.e. there is no twisting motion when the dice are thrown. It makes sense this technique takes ages to master but the real question is does it really help you influence the outcome of the roll?

The efficacy of dice setting remains a hotly debated topic among gambling experts to this day. The trouble with this form of advantage play is that there simply is no definitive mathematical study to prove this actually works.

Renowned gambling author Stanford Wong is among the proponents of the efficiency of this technique and wrote extensively about it in his book Wong on Craps. The subject was also tackled by author Christopher Pawlicki in his 2002 book Get the Edge at Craps: How to Control the Dice. Some mathematicians and gambling experts are of the opinion the technique either does not work or is impossible to execute successfully in the casino environment.

Others are willing to give dice control some credence arguing that it might possibly work, provided that the dice do not hit the back wall of the craps table. Unfortunately, most casinos require the dice to hit the back wall in order for the roll to be considered valid. The bottom line is most members of the advantage play community still distrust the concept of overcoming the house edge in craps through dice control.