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As you know, each die has six numbers on it, the numbers 1-6. When you throw a pair of dice, two combinations of the six numbers appear on the craps table, so there are a total of 36 different combinations. Some numbers can be made more times than others - for example, the seven can be made six ways, which makes it the most popular number. When we're using a pair of dice, we can make the following amount of combinations for the numbers that will roll-
| Seven |
6 |
| Six |
5 |
| Eight |
5 |
| Five |
4 |
| Nine |
4 |
| Ten |
3 |
| Four |
3 |
Three
|
2 |
Eleven
|
2 |
Two
|
1 |
Twelve
|
1 |
| Total 36 |
Both internet and land based casinos know this chart well, for it is what they base their house odds on, which is where their profits come from. They will offer you a much higher payoff if you bet on the 12 rather than the 7.
The reason for this is that the twelve's combination will roll only once compared to the seven's six times. In practical terms, you should realize that the seven will roll six times as much as the twelve. In 36 sample rolls, the seven will roll 6 times, while the twelve will roll only once.
For another example, let's look at the four (or ten) compared to the seven. In 36 sample rolls, the four will roll 3 times compared to six times for the seven. This means that for every one roll of the four, you will see two rolls of the seven. So the true odds of the four (or ten) is 2:1.
Using the same method we can see that the true odds of the five or nine (which rolls four times) compared to the seven (rolling six times) is 6:4 or 3:2. So for every three rolls of the seven, you should see two rolls of the five or nine.
Finally, the six or eight will roll five times compared to the seven's six times so the true odds are 6:5 - for every six rolls of the seven you should see five rolls of the six or eight.
A little more difficult method of calculation revolves around the casino's methods of calculating its casino edge.
For example, the casino's edge on a place bet on the six and eight is 1.52%. The casino pays 7:6 on this bet but the true odds are 6:5. What this really means is that in eleven decisions you will win five times and lose six times. So if you bet $12 you will win $70 ($14 x 5) and lose $72 ($12 x 6). This is a difference of $2. This $2 is divided by the total amount bet, or $132 ($12 x 11 decisions), and you get the casino edge of 1.52%.
To calculate the famous 1.4 casino edge for the pass line bet is even more difficult, as you must take into account all of the available numbers, both before and after the come-out roll.
By now you know that a pair of dice has 36 combinations. The 2 and 12 can roll one way, the 3 and 11 two ways, the 4 and 10 three ways, the 5 and 9 four ways, the 6 and 8 five ways, and the ubiquitous 7 can roll six ways.
On the pass line, you can win with the seven or eleven. The seven can be rolled six ways, and the eleven two ways, so you will win 8 of 36 times on the pass line, or, 2/9 of the time.
You will lose on the pass line with a 2, 3 (twice) or 12, so you lose 4 of 36 times, or 1/9 of the time.
This means that 1/3 of the time, the bet is decided without a point, as 1/9 (losing) plus 2/9 (winning) equals 3/9 or 1/3.
The other 2/3 of the time a point is established. There are six points - the 4, 5, 6, 8, 9 and 10, with 24 possible point rolls.
If the point is 4 (or 10), as an example, there are 3 ways to roll a 4 (or 10) but 6 ways to roll a 7. Thus, a four (or 10), which rolls three times, compared to the seven, which rolls six times, will roll 3/9 (or 1/3) of the time a seven does.
Similarly, with the five and nine, rolling four times, each is 4/10 (or 2/5) as likely to roll as the seven. The six and eight, rolling five times, is 5/11 as likely to roll as the seven.
To get the winning percentage then, we simply have to take how often you can possibly win with each point, and multiply it by how often each point occurs. The casino's edge is the losing percentage minus the winning percentage.
After the come-out, there are six point numbers which can be rolled 24 possible ways (4-3, 5-4, 6-5, 8-5, 9-4, 10-3). The four or ten will roll 3/24 (or 1/8) of the time. The five or nine will roll 4/24 (or 1/6) of the time. And the six or eight will roll 5/24 of the time.
The chance of winning the four or ten, then, is 1/3 of the time, but only comes up 1/8 of the time.
The chance of winning the 5 or 9 is 2/5 of the time, and comes up 1/6 of the time. And, the chance of winning the 6 or 8 is 5/11 of the time, and comes up 5/24 of the time.
So, for the 4 and 10, we multiply 1/3 x 1/8 x 2. For the five and nine, we multiply 2/5 x 1/6 x 2. And for the six and eight, we multiply 5/11 x 5/24 x 2. All this adds up to 67/165.
However, we know from before that an actual point is established only 2/3 of the time. 1/3 of the time you will win or lose without the point being established. And, when no point is established, you'll win 2/3 of the time and lose 1/3 of the time.
So, we need to take 2/3 of 67/165 and add it to 1/3 of 2/3, which is 244/495, or the winning percentage (which is 49.3%, or .493). Since the winning percentage is 49.3%, the losing percentage is 50.7% (or .507).
We can now finally find the house edge, in percentage, by subtracting the winning percentage (49.3%) from the losing percentage (50.7%). This is 1.4%, the house edge for the pass line with no odds.
You don’t need to know all of this information, but it is useful in knowing just how the game of craps actually works.
And remember - the more you know, the luckier you are!
And, as always, good luck at the tables!
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