Craps is some of the most fun you’ll have in the casino. However, if you want to be an educated craps player, you’ll need to understand some of the probability and odds involved with rolling a pair of dice.

Craps is always played with two dice, each of which is shaped like a cube less than an inch wide. Unlike the dice you’ll buy at your local game store for board games or RPGs, the dice used in craps have sharp edges and pointed corners.

Craps dice are also bigger than the dice you’ll find in a game like Yahtzee or Monopoly. Most of the time, a casino will imprint their logo on the dice they’re using, too. The dice are red, but they’re also translucent, so you can see that there are no weights attached.

Craps – Numbers 2, 3 and 12 on the come out roll. Crapless Craps – A type of Craps game offered at some casinos. When playing this version of craps, a roll of craps is not a loss at the come out. The number is instead marked as a point. Players may do this with hard way numbers and craps numbers as well. To calculate the ration, just divide your total number of 7s by the total number of rolls. The SRR is related to the actual true odds of rolling random numbers over the long term, so you have to have a large sample size to be accurate.

The shooter has just received the dice and is on his come-out roll. If he rolls any of the point numbers above on his come-out roll, that constitutes the 1-count. If he rolls a 2, 3, 7, 11, or 12 on the come-out, the count has not started yet. This type of craps dice sets is suitable for intermediate players and is good for hitting sixes, eights and inside numbers, which are characterised by lower house edge in comparison with outside numbers. To position the 3V set, you need to set three in the shape of a V on top of the dice. The faces will show eight or six.

Dice Numbers In Craps Games

Craps shooters often get on hot streaks. If a shooter gets on too hot a streak, the boxman will pause the game to examine the dice to make sure there’s no funny business going on.

The number of possible combinations on a pair of dice is what the game is built around. That’s also the subject of this post: how the dice combinations work in a game of craps.

What Combinations Are There?

Each die has six sides, and they’re numbered from 1 through 6, using dots. If you add the numbers on opposite sides of the dice together, you always get seven. So the 1 and the 6 are opposite each other, the 2 and the 5 are opposite each other, and the 3 and the 4 are opposite each other.

You have a total of 36 possible combinations – you have six possible combinations on one die and six possible combinations on the other die. Out of these 36 possible combinations, you have 11 possible totals.

Bristled dice are an old-fashioned way to cheat at craps. A person sticks a filament of some sort in one of the die’s numbers so that it protrudes and causes the die to slow down when it rolls over that side. Naturally, this eventually will cause the die to come to a stop on the bristled side.

Here are the possibilities:

1. A total of 2, which can be made up of only one combination: a 1 on each die
2. A total of 3, which can be made up of two different combinations: a 1 on the first die and a 2 on the second die; or a 2 on the first die and a 1 on the second die
3. A total of 4, which can be made up of three different combinations: 1 – 3, 2 – 2, 3 – 1
4. A total of 5, which can be made up of four different combinations: 1 – 4, 2 – 3, 3 – 2, 4 – 1
5. A total of 6, which can be made up of five different combinations: 1 – 5, 2 – 4, 3 – 3, 4 – 2, 5 – 1
6. A total of 7, which can be made up of six different combinations: 1 – 6, 2 – 5, 3 – 4, 4 – 3, 5 – 2, 1 – 6
7. A total of 8, which can be made up of five different combinations: 2 – 6, 3 – 5, 4 – 4, 5 – 3, 6 – 2
8. A total of 9, which can be made up of four different combinations: 3 – 6, 4 – 5, 5 – 4, 6 – 3
9. A total of 10, which can be made up of three different combinations: 4 – 6, 5 – 5, 6 – 4
10. A total of 11, which can be made up of two different combinations: 5 – 6, 6 – 5
11. A total of 12, which be made up of only one combination: a 6 on each die

If you look at this closely, you’ll notice that it makes a symmetrical bell curve. Also, the number of combinations that create a specific total can be divided by 36 to get the probability of getting that total.

A Note on Probability

Probability is a way to measure how likely it is that an event will occur. For our purposes, an event is a total on two dice.

Probability is just a ratio comparing the number of ways something can happen with the total number of possible events.

Six divided by 36 is the same as 1/6, which is also the same at 16.67%.

When it comes to craps, it’s often useful to use odds as your preferred format for expressing probability. To do that, you just compare the number of ways something can’t happen with the number of ways it can. For example, the odds of rolling a 7 are 5 to 1. They’re actually 30 to six, but you reduce, just like you would a fraction.

You can compare the probability of winning a bet with the payout odds to see what kind of mathematical edge your land-based casino has on a specific bet.

This is the beginning of craps wisdom.

The Point Numbers

The point numbers are 4, 5, 6, 8, 9, and 10.

The 5 and the 9 have four possible combinations, and the 6 and the 8 have five possible combinations.

The odds of a 7 coming up before a 4 is easy to calculate. You have six possible combinations totaling 7 versus three possible combinations totaling 4.

That’s 2 to 1 odds.

The odds are the same for rolling a 10.

The odds of a 7 coming up before a 5 (or a 9) are six versus four, or 3 to 2 odds.

The odds of a 7 coming up before a 6 (or an 8) are six versus five, or 6 to 5 odds.

When the shooter makes a point, it’s his job to roll that point total again before rolling a 7.

Now, you know the odds that he’ll succeed.

Proposition Bets

One of the worst bets you can make at a craps table is a proposition bet. This is usually a bet on a specific total on the next roll. Depending on the number, the odds might look like the following examples.

If you’re looking at a 2 (snake eyes), the odds of winning are 35 to 1.

If you’re looking at a 12, you face the same odds.

If you’re looking at a 3, the odds of winning are 17 to 1. The same holds true for a total of 11.

If you’re betting on “any 7,” the odds of winning are 5 to 1.

If these bets paid off at those odds, you’d be facing a house edge of zero. If you played long enough, you’d break even or come close to tie.

But the casino isn’t in the business of breaking even. It’s in the money of making a profit.

That’s why they set the payouts for these proposition bets much lower than the odds of winning them.

Statistically, 36 bets of $100 each would mean losing $3500 on your 35 losing rolls and winning $3000 on your one winning roll.

Your net loss is $500.

Average that out by 36 rolls of the dice, and you’ve lost an average of $13.89 per bet or 13.89% of your action.

That’s the house edge, and it’s a huge number.

The “any 7” bet is another proposition bet which is always a one-roll bet, by the way. It’s a bet that the total will be 7 on the next roll.

The odds of winning this one are 5 to 1, but the payout is only 4 to 1.

You can calculate the house edge on this bet easily, too.

Assume six perfect rolls betting $100 each.

You’ll lose five of those bets for a total of $500 lost.

On the one bet you win, you’ll get a $400 payout.

Your net loss over six rolls of the dice is $100.

Divide that by six, and you can see that the house edge on the any 7 bet is 16.67%.

The pass line bet has a house edge of 1.41%.

On average, over enough rolls of the dice, you should lose $1.41 every time you place a $100 bet on the pass line.

But if you bet that same $100 on any 7, you’d lose $16.67.

Which one of those sounds like the better bet to you?

Conclusion

That’s as good an introduction to the dice combinations in craps as you’ll find. Once you understand the math in this blog post, you can figure out everything you need to know about every bet at the table.

For this exercise you will need a pair of casino dice. Used casino dice are available at most casino gift shops. You can also order new casino-quality dice on-line from a number of sources, including www.axispowercraps.com. Purchase several sticks (a set of five matching dice) in different colors to use when practicing your precision shooting.

Orient the dice in front of you as shown in graphic 2.1.

Graphic 2.1 – All Sevens Pre-Set

This is one of the most powerful pre-sets for the come out roll. It is called the All Sevens Set because the seven shows on all faces of the dice. It is also known as the 1-6/1-6 Axial set. This designation is derived from the numbers that appear on the left and right side or lateral faces of the dice. Another name for this set is the 4-2/3-5 set because the left die has the 4 up and the 2 facing the shooter and the right die has the 3 up and the 5 facing the shooter. Confusing? Just pick a term you can remember easily and go for it. The “All Sevens Set” will do fine.

Imagine you have your dice in this pre-set and there is a steel rod or axle running them as shown in Graphic 2.1. The axle runs through the center of the one-spots and prevents the dice from tumbling any way but forward and backward. If you could toss dice like this in the casino, what would be the results?

Graphic 2.1 – Forward Axial Rotation

With the axial model of dice control the number of possible combinations of the dice is reduced from thirty-six to sixteen. With 100% axis control there are only four faces that can come up on each die when rolled on axis. Additionally, under this model you would never hear the stick person call two, three, or twelve craps. Why? Because there are no ones or sixes showing when the dice are rolled on the All Sevens pre-set. The one and six are taken out of the equation, and without them you can’t roll a Craps.

Now take a moment to count the number of combinations of the dice that add up to seven when using this set. If you come up with four, you are absolutely correct. When rolled on axis the All Sevens Pre-Set yields a natural winner 25% of the time – with NO craps losers. That’s a powerful first step toward playing craps with a positive expectation.

Compare that to the random roll in which eight of the thirty-six combinations of the dice are naturals that add up to seven or eleven. Naturals will appear only 22% of the time. Net out the four combinations that result in come-out losers – the two, three, and twelve craps – and the percentage drops to 14%. So pre-setting to the All-Sevens and rolling on axis can equate to about an 11% advantage over a random Come-Out roll. And that goes a long way toward making craps a positive expectation game.

Here is the distribution of numbers that will appear when the All Sevens Pre-Set is rolled on axis:

Table 2-1 – All Sevens Pre-Set Number Distribution

By the way, the All Sevens pre-set contains ALL of the hardway numbers – a favorite and notoriously bad wager made by many precision dice shooters. Hardway numbers roll 6.25% of the time when the dice stay on axis. Compare that to the 2.8% performance random rollers experience and you’ll understand why these high vig bets are popular with some dice setters. In fact, often these players will arrange the dice on the 6-1/6-1 axis so that they are pre-set to the hardways. For example, they might set the 5-5 Hard Ten facing up. The hard four would be face down on the table. The hard eight and hard six would be facing up and down table, respectively. The axis numbers remain the same – 6-1/6-1. The hardway pre-set is simply another permutation of the All Sevens Axial Pre-Set. They are both part of the same “family” of pre-sets. Here’s what it looks like:

Graphic 2.2 – Hardway Set

Now let’s compare the All Sevens pre-set to another popular arrangement of the dice – The V-3 Hard Six set, also known as the 16/25 Axial pre-set. Some players refer to it as the 3-2/3-6 set, reading the top and front faces of the left die, then the right die. Here’s how it looks:

Graphic 2.3 – V-3 Hard Six Set

This is one of the most powerful pre-sets for use after the come out roll. Like the All Sevens pre-set, when rolled on axis there are only sixteen possible combinations of the dice instead of the random thirty-six. But unlike the All Sevens set, only two of these combinations add up to seven – the 3-4 and the 4-3. In other words, when rolled on axis the seven will only appear 12.5% of the time. Compare that to the random roller, who sees the seven on 16.7% of his rolls, and the potential power of this arrangement becomes abundantly clear.

Let’s examine the distribution of the remaining numbers utilizing this pre-set:

Table 2.4 – V-3 Hard Six Pre-Set Number Distribution

Look at the number of combinations that add up to six and eight. There are three ways to make each of these numbers, compared to two combinations that add up to seven. So the axis adjusted odds are 3-2 in favor of the six and eight, and the five and nine are even money. But since the five and nine place bets are paid off at 7-5, these wagers carry a positive expectation as well.

Like the All Sevens pre-set, the V-3 Hard Six has many permutations. While most players prefer to arrange the dice with the hard six on the top faces, some prefer to have the eleven facing up and the hard six and hard eight facing up and down table. Others will rotate one 180° on axis – presenting the eleven on the top faces, but arranging the dice so the 3-4 and 4-3 face up and down table. This variation is popular with many precision shooters on the come out roll. While these variations can be powerful and effective tools for the experienced precision shooter, initially we recommend that the beginner stick with the specific arrangements pictured in this book.

We’ve just looked at the two most powerful pre-sets available to precision shooters. As you can see, using the correct pre-set at the correct time and adjusting your bets accordingly clearly puts the precision shooter in command of the game. Now that you grasp the concept, let’s take a look at all six of the basic axial pre-sets. Remember, there are many variants of each of these sets, but for now let’s stick with these:

Dice Numbers In Craps Machine

Graphic 2.5 – Dice Pre-Sets

The pre-sets shown on the top row are all seven-rich arrangements. They are the Straight Sixes, the Parallel Sixes, and the All-Sevens sets. When rolled on axis, each of these arrangements contains four combinations of numbers that add up to seven. For that reason they are often used when the shooter wants to toss sevens. Conversely, the pre-sets shown on the bottom row are point rich sets. There are only two combinations of numbers that add up to seven when these arrangements are rolled on axis, making these arrangements popular with controlled shooters once the point is established. When tossed on-axis each set has its own particular strengths and weaknesses.

Since we have already covered the All Sevens and the V-3 pre-set arrangements, let’s take a look at the number distribution tables for the other four basic dice sets. First on the list is the Straight Sixes – or the 34/34 Axial pre-set.

Table 2.6 – Straight Sixes Pre-Set Number Distribution

At first glance this looks like an excellent pre-set for the come out roll. There are four ways to win with the seven and two ways to win with the eleven. But further scrutiny reveals four ways to lose on the come out as well – the 2, 3, and 12. There is also a possibility of establishing the four or ten as the point – both difficult numbers to hit with any pre-set.

So who would use this set? While we don’t recommend the wager, this dice set arrangement is quite popular among players who bet the Horn or World prop bets on the come out roll. A skilled precision shooter might bet $25 on the pass line along with a $25 World bet. If he throws the seven he wins $25 and the World bet is a push, or tie. If he throws the eleven he wins $25 for his pass line bet and an additional $75 for the World Bet. The three-craps also pays $75, though the shooter would lose his $25 pass line bet. Should the shooter be skilled enough to toss a two or twelve his World bet will pay $150, less the losing $25 pass line bet. Since the housed advantage on the proposition bets is so high, this is not a strategy a true advantage player would use. On the other hand, it can provide an element of fun for casual dice setters who play primarily for the entertainment value of the game.

Dice Numbers In Craps Machines

Another wager you might see used in combination with this dice set arrangement is a Lay bet against the five and/or nine. Look at the chart once again. When tossed on-axis there are no fives or nines on this set. A $31 No Five bet would kick off a net $19 win if the shooter managed to toss a seven on the come out.

Next up is the Parallel Sixes, or 52-52 Axial pre-set. Here’s how the number distribution table shapes up for that arrangement:

Table 2.7 – Parallel Sixes Pre-Set Number Distribution

Looking at the numbers, it is plain that this pre-set leaves a lot to be desired. Yes, there are four ways to win with the seven, but there are also two losers – the two and twelve. Since there are four combinations that add up to seven, the smart precision shooter would not use this set once the point is established. Or would he?

You’ve probably heard the old story about how children are conditioned to “follow the rules” and “color inside the lines” when they are young – and how that can stifle creativity. To understand how to use this preset, you have to get outside the lines for a moment.

Remember that “No Five” bet we talked about a minute ago? Well, you could take it one step farther. Not all precision shooters shoot from the pass line. Some prefer to play the don’t pass. Should such a player end up with a don’t pass bet on a point of six or eight he might well switch to the Parallel Sixes pre-set. Why? There is only one combination of numbers that adds up to six or eight with this pre-set arrangement.

Now go a step further and look at the number distribution in relation to the other bets on the layout. See anything of interest? The Field Bet – a wager most smart players have learned to avoid – can be a winner with this pre-set. The Field is a winner on the 2, 3, 4, 9, 10, 11, and 12. There are eight combinations of the dice that add up to those points in the Parallel Sixes pre-set – compared with eight combinations that lose in the field. Even odds, right? But since the payoff is doubled on the 2 and 12 – and tripled on one or the other of those numbers in some casinos, that brings the total number of single unit wins to 10 or 11, depending on the layout – versus eight one-unit losers.

To take it to another level, a precision shooter who never learned to color inside the lines might go so far as to play the Don’t Pass line while utilizing this pre-set and bet the Field at the same time. It’s not a play we would recommend, but it works for some players.

We’ve already looked at the All Sevens set and its variant, the Hardway set, at the beginning of this chapter. Again, this is the most powerful pre-set for the come out roll and should be given strong consideration. The odds are good that the six or eight will be established as the point with this pre-set. A common strategy is to combine pass line play with all the hardways working on the come out. For example, by betting $10 on the pass line plus $2 each on all of the hardways – the player will still be guaranteed a small win if the seven is rolled. But if one of the hardways turns up, he picks up a quick fourteen to eighteen bonus dollars. Again, remember that proposition bets carry a huge housed edge you have to overcome with your toss. Most players will do well to avoid them.

Dice Numbers In Craps Odds

Now let’s look at the point-dominant pre-sets. These are the sets skilled players generally gravitate toward after a point is established. They are the Crossed Sixes, the Mini-V Hard Four, and the V-3 Hard Six arrangements. First on the list is the Crossed Sixes – or the 3-4 / 5-2 Axial pre-set. Remember, some dice setters refer to this as the 6-2/6-3 set, reading the dice from left to right. This set is extremely popular with precision rollers who enjoy playing all the numbers. A look at the distribution chart reveals why.

Table 2.8 – Crossed Sixes Pre-Set Numbers Distribution

When the dice are tossed on-axis using the Crossed Sixes pre-set the shooter has an axis adjusted odds advantage over the casino on all of the inside numbers. Ordinarily place betting the five and nine, which carries a 4% house edge, is not recommended. But placing the five and nine can be profitable with this arrangement. The frequent occurrence of Horn numbers on this axis prompts many recreational precision shooters to play the World or Horn bets on the come out roll with this pre-set. Others prefer to play the High-Low bet – the two and the twelve – on every roll. Can you profit from it? It depends on your skill level. On average, one of these numbers will show for every eight rolls of the dice. The winning wager pays 30-1.

The only Place Bet numbers that do not carry an on-axis advantage for the skilled shooter utilizing the Crossed Sixes pre-set are the 3, 4, 10, and 11. But on particularly long rolls these numbers will often appear in streaks. For that reason, many precision shooters play an up-and-out strategy. They press their inside bets to a pre-determined level, then add the four and the ten out of subsequent payoffs.

The next point-rich dice pre-set arrangement is the Mini-V Hard 4, or the 34/61 Axial pre-set, also called by some the 2-1 2-3 set. Next to the V-3, this is the most popular point-cycle pre-set arrangement among precision shooters. Why? Because it can yield powerful results on the outside numbers. A quick look at table 2.9 will tell you why:

Table 2.9 – Mini-V Hard 4 Pre-Set Number Distribution

By switching from the Crossed Sixes to the Mini-V the savvy precision shooter gives up the two and twelve in exchange for an advantage on the four and ten. In fact, the axis adjusted odds favor the precision shooter on all of the point numbers. For that reason, precision shooters often place all the inside numbers and buy the four and ten when using this pre-set. When playing in casinos that collect the commission after the win on Buy bets this is the most powerful pre-set arrangement you can use.

We’ve already looked at the V-3 Hard Six pre-set. In most instances is the preferred pre-set arrangement for experienced shooters. The precision shooter has an advantage over the casino on all the inside numbers. The fact that the six and eight are low vig bets to begin with means there is very little house edge to overcome – even with an off-axis roll. And, for recreational precision shooters this pre-set also offers ample opportunities to play the hard six and eight – often profitably.

Let’s take one more look at all of the pre-sets and the numbers distribution. These six dice arrangements are the cornerstone of precision shooting. Eventually you will commit the various sets and their application to memory. If you need help remembering, feel free to print a copy of Table 2.7 for your personal use.

Table 2.7 – Dice Pre-Set Number Distribution Chart

Each of the basic axial pre-sets has its own particular strengths and weaknesses. Master them all, then explore the various permutations each presents. The rewards for intelligent play will follow.

Copyright © by Axis Power Craps All Right Reserved.

Published on: 2005-07-03 (8157 reads)