Dice Combinations

casino craps guideCraps is undoubtedly the most popular dice game of all time and a favorite of millions of players across the world. This game is based solely on chance but players should not be tricked by its apparent simplicity. Contrary to popular belief, craps is not only about rolling the dice. It can be a tricky game indeed, especially when one is not familiar with the dice rolling probabilities and the odds. However, these can be of crucial importance here as one cannot expect to turn a profit if they do not understand which numbers are more likely to come out. Because the game is played with two dice, players’ chances of throwing a given number depend on the number of different dice combinations that can eventually add up to the number they have placed their bet on.

Certain numbers are more likely to come out as the number of combinations that can add up to them is greater. Others are rolled less frequently since there is a single combination that can add up to them. Thus, the only possible combination that can add up to the number 2 is 1 plus 1, so this number is less likely to get rolled. On the other hand, if you place a bet on the number 7, your chances of winning are more substantial as there are more combinations to add up to the said number – 5 plus 2, 4 plus 3 and 6 plus 1. Moreover, the possible combinations for a number and the frequency at which it is rolled, determine the odds casinos offer for winning bets placed on the number in question.

If you want to emerge a winner the next time you decide to join the craps table, it is recommended to become better acquainted with the dice combinations and the probability of rolling the numbers.

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The Dice Rolling Probabilities

At first glance, understanding the mathematical probability of rolling two dice might seem a bit intimidating. However, there is absolutely no reason to stress over it as this turns out to be a lot easier than it originally seems. In fact, the dice rolling probability resembles to a great extent that of the coin flip. It is a common knowledge each coin has two sides so if one flips it, there are two possible outcomes – either heads or tails will come out. Each of the two has a 50% chance of coming out or in other words 1 to 2.

Determining the dice rolling probability is based on the same principle, the only difference is there are more possible outcomes. Each of the two dices used in a game of craps have six sides. Each side has small white dots or pips on it to represent the numbers from one to six. Allows us to demonstrate how dice probability works with the following example.

Imagine a cake is cut into six slices and someone has stuffed a $10 bill in one of the slices. What are the chances of you picking the one slice containing the $10 bill? That’s right, your chances of grabbing that particular slice are 1 to 6 or 1/6. Now, divide 1 by 6 and it turns out your chances of picking the $10 slice are equal to 16.67%. It is the same when you throw a single die with six sides – the probability of each of the numbers coming out is the same – 1 to 6 or 16.67%.

Things are not much different when one is rolling two dice; only the number of possible outcomes is greater. Each dice has six sides with numbers from 1 to 6, so the number of possible combinations, in this case, totals 36. However, some numbers tend to come out more frequently than others as there is a greater number of combinations that can add up to them.

The Dice Combinations

From this, it follows that if a player throws one die so that it falls at random, the chances of this one number, for instance 2, coming out are 1 out of 6. So the odds are 1 to 5. In other words, the chance of the number 2 being rolled is one as opposed to the five ways of losing. Provided that you use two dice, you can roll eleven different numbers, namely 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. 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. Thus, there is only one possible combination for numbers 2 (1 plus 1) and 12 (6 plus 6) as opposed to number 7, where 3 plus 4, 1 plus 6, 5 plus 2 and their respective permutations can all add up to its total. It would be best to illustrate the eleven totals and the dice combinations that add up to them with the following chart.

Number Number of Possible Combinations Combinations/Permutations
2 1 1 – 1
3 2 1-2, 2-1
4 3 1-3, 3-1, 2-2
5 4 1-4, 4-1, 3-2, 2-3
6 5 1-5, 5-1, 2-4, 4-2, 3-3
7 6 1-6, 6-1, 2-5, 5-2, 3-4, 4-3
8 5 2-6, 6-2, 3-5, 5-3, 4-4
9 4 3-6, 6-3, 4-5, 5-4
10 3 4-6, 6-4, 5-5
11 2 5-6, 6-5
12 1 6 – 6

The Relation between Dice Combinations and Odds

Why the number of combinations that add up to each of the eleven numbers is so important? The answer is quite simple, actually – it allows players to determine the “true” odds for each number coming out. Knowing the numbers’ “true” odds is essential in the game of craps as it enables one to better understand the likelihood of a specific number coming out before another one, which on its own will increase one’s chances of placing a winning bet. For example, if one is playing the Pass Line and a Point of 6 is established the chances of the number 6 being rolled before a seven-out occurs are more substantial than those of the number 4 with its three possible combinations. The odds, on the other hand, determine the payouts for the different types of bets in craps.

One very important aspect to consider in craps is that by its nature this game is extremely volatile since it is a negative expectation value game. Casinos never pay out winning players “true” odds if their number is rolled. Actually, it is the other way around – payouts are always less than the “true” odds indicate as casinos aim to gain an advantage over players and thus, turn a profit.

Now, let’s return to the coin toss example. As mentioned above, both heads and tails have a 50/50 chance of turning up. If you place a bet on tails and it comes out, you should be paid even money, at least if the payout reflects the “true” odds for this bet which are 1 to 1. Unfortunately, if you place a $10 bet with odds of 1 to 1 in a casino and win, you will not be paid another $10, you will receive only $9.96 because of the casino’s built-in advantage.

Another, more complex way to explain this is to define what the house edge actually is. As the house edge is meant to represent the ratio of players’ average loss to their initial bet, they can calculate how much they are going to lose by checking the casino’s built-in advantage for a specific bet in the game of craps. The house edge percentage varies in accordance with the type of bet you place. For instance, the house edge for a Pass Line bet amounts to 1.41%, which indicates you will lose about 28 cents per each winning $20 bet. The higher the house edge, the less money you will be paid even if you do win.

Thus, if your take your chances with a single bet of $10 on 11 or Yo-leven, where the house edge soars to 11.11% and the payout is 1 to 15, you will be paid out only $142.6 instead of $150. Moreover, the chances of you winning with a Yo-leven bet are smaller since only two dice combinations out of 36 add up to this number.

It is not hard to see numbers 2 and 12 have the worst odds as there are 35 ways to lose and only one way to win. The odds for numbers 3 and 11 are higher at 17 to 1, while those for numbers 4 and 10 are 11 to 1. So basically, the more combinations can add up to a given number, the higher its chances of coming up. Thus, 5 and 9 have odds of 8 to 1, while 6 and 8 have odds of 6 to 1. Since 7 has the highest number of 6 possible combinations, it also has the best odds of 5 to 1. Beginners should bear in mind that understanding and remembering (or calculating if you are good at math) the odds and the respective house edge is of crucial importance and needs to be done prior to joining the table.

However, there is one exception to this rule. The only way to avoid the built-in casino advantage is to place the so-called Free Odds bets where the house edge is nil. Note that Free Odds bet are accepted only when combined with another bet and the possible options are Pass, Don’t Pass, Come and Don’t Come bets.

How to Remember the Combinations

Memorizing all 36 possible dice combinations before you take your seat at the craps table is far from impossible, not to mention it is an absolute must if a given player aims at turning a profit at the end of their gaming session. Even more so when we consider the correlation between the dice combinations, their rolling probabilities and the respective payouts for each bet type.

However, there is an easier method which will enable you to memorize the combos without putting that much effort in it. The best way to go is to actually print the chart with the numbers, their combinations and permutations. Unfortunately, this is an option only for those who intend to play craps online from the comfort of their homes. Most likely you will not be permitted to openly use the chart at the craps table in a landbased venue. If such is the case, you can apply the following technique. One brief glance at the chart we provided above will suffice for you to discern there are certain pairs of numbers where the number of combinations coincides. Thus, 2 and 12 have only one combination, 3 and 11 have two, 4 and 10 have three, 5 and 9 have four, while five combinations add up to numbers 6 and 8. The following technique requires you to memorize the pairs of numbers only.

If you subtract 1 from numbers 2, 3, 4, 5, 6 and 7, you will get their total number of combinations. For instance, subtract 1 from 4 and the number of combinations is 3 here. As you can see, this corresponds to the number of combinations listed in the chart. So basically, the chance of you rolling the number 4 are 3 out of 36 possible combinations. Then, you can proceed by figuring out the probability percentage for this number being rolled by calculating what percentage is 3 from 36. The result is equal to 8.33%. There is no need to apply this technique to numbers 2 and 12 for obvious reasons. As for numbers 8, 9, 10 and 11, their number of combinations correspond to that of numbers 3, 4, 5 and 6.

Most Important Combinations to Remember

Bets on certain dice numbers are considered more volatile, so it would be best to consider some less risky options. When joining the craps table, many people opt for playing the numbers 6 and 8 at the same time by placing Place bets on them. As we can see in the chart, there are five combinations that add up to the number 6. The same applies for its pair mate 8, which makes for a total of ten permutations. So obviously the chances of 6 and 8 being rolled amount to 10 out of 36 which translates into 27.8% of you winning with Place bets on both numbers. As the odds of 7 being rolled are 6 out of 36, your chances of losing with your Place bets are equal to about 16.6%. As you can see, the volatility for this bet is relatively low.

Other players opt for placing the so-called Inside bets on the numbers 5, 6, 8 and 9. Let’s compare their volatility with that of Place bets on 6 and 8. The numbers 5 and 9 have four combinations and 6 and 8 have five which makes for a total of 18 possible combos (4+4+5+5=18). There are 18 out of 36 possible ways to win with such an Inside Bet which translates into 50% chance of winning.

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