Dice Rolling Probability: The chances of rolling dice and its mathematical probability

Dice Rolling Probability basics

Dice Rolling Probability

Figuring out the mathematical probability of rolling two dice is a lot easier than you think.
If holding two dice in your hands, you'll probably figure this out on your own.
Lets make sense of things, and why the dice do what they do.

Dice Roll Odds

Understanding dice rolling probability isn't much different than a coin flip probability.
A coin has two sides.
If you flip a coin,probability dictates that either heads or tails have a 50% chance of coming up.
If you choose heads before the flipping of a coin, then there's 1 way of 2 that would happen.
It can be written as 1/2, 1 out of 2, or 50% (1 divided by 2).

Dice rolling probability is similar to a coins probability, only with more choices

Looking at a die (only one from a pair of dice), you'll see 6 sides.
The pips (the little white dots) are 1,2,3,4,5,6.

Take a trip back to high school and revisit fractions

An apple pie (my favorite) is cut into 6 slices, and one of these slices contains a $100 bill (eww) -
what would your chances be of grabbing that $100 bill?
Saying it out loud gives you the answer:
One slice out of the 6 slices has the $100.
Therefore, that's your odds of grabbing it - 1 out of 6, 1/6, or ~16.67% (1 divided by 6) chance.

That's exactly the probability of one side of a die coming up when you roll it.
The probability of at least one of the die coming up a 1,2,3,4,5, or 6 is exactly 1 out of 6.
rattan stick

Probability of rolling two dice

Craps actually has two dice, and not anymore complicated than the pie example.
There are 6 sides on each die. There are two of them.
Twist and turn each of the dice and you get 36 different variations.

Ever wanted to know the probability of rolling doubles with two dice?

A hardway,2 or 12 has exactly a dice rolling probability of 1 out of 36 possibilities.
Let's look at this chart, and see how it works.
I know it's everywhere, but you can't fight science...

Dice Rolling Probability Chart:

# on Dice
Ttl Combinations
Combinations/Permutations
211-1
321-2    2-1
431-3    2-2    3-1
541-4    2-3    3-2    4-1
651-5    2-4    3-3    4-2    5-1
761-6    2-5    3-4    4-3    5-2    6-1
852-6    3-5    4-4    5-3    6-2
943-6    4-5    5-4    6-3
1034-6    5-5    6-4
1125-6    6-5
1216-6
36 Total Combinations

7 has the most possibilities of coming up.
The dice rolling probability can never change in a random roll. It's the rules of probability.
The chances of rolling dice are confined to the above chart.
This is the reason 7 rolls more often then any number when you roll two dice randomly.
When playing Monopoly, you'll have approximately a 66.7% chance of moving 5-9 spaces (hopefully not into
another players' Boardwalk).
Why?
Because adding up the ways 5,6,7,8, and 9 can roll you get 24 different ways.
Since there's only 36 results the dice can roll - you're left with 24 out of 36 ways 5-9 come up.
That's 24 divided by 36, equaling .666666... Multiply by 100, and you have ~66.7%.
So if exaclty two squares away is the "Go To Jail" square, you don't have to worry much on landing there.
But there's always a chance of course (a 1 out of 36, or ~2.78% chance to be precise).

Since the 7 comes up more often than the rest, the casinos capitalize on this.
The more random the dice are, the more this is true.

rattan stick

An easy way to remember each numbers' combination

Looking at the chart, you see that there are pairs that have the same combinations:
2&12, 3&11, 4&10, 5&9,6&8.
Just memorize this, because I'm going to show you a cool trick.

By subtracting 1 from any number from 2 to 7, you get the total combinations:
Therefore the dice rolling probability of rolling a 6 with two dice is 5 out of 36 (Or 13.89%).

Knowing the pairs I just mentioned, helps you figure out any dice rolling probability.
Viola!

When playing craps, you should keep these combinations in mind

For example, most people play the 6 & 8 at the same time.
The 6 has 5 different ways of coming up on the dice, and so does the 8 - totalling 10 different permutations.
That's 10 out of 36 ways. Translation - ~27.8% chance of hitting the 6 or 8; and a ~16.7% chance of losing.
(dice rolling probability=6/36 ways the 7 can come out).

Others place bets on the "inside" - 5,6,8,9.
Using what you know so far, try and figure the chance of winning one of those bets on the next roll.
Did you get it?
It's 50% because 5&9 have 4 ways each 6&8 has 5, giving you 18 (4+5+5+4) out of 36 ways the dice can
come up.

I'm not saying whether these are good bets or bad ones, I'm just getting into the math right now.
For some betting strategies, check out How to Win At Craps on this website.

To know how setting the dice and dice control come into play with all this math,
check out dice setting & how to shoot craps.

Want to see something cool and be blown away?

Sign up to the newsletter, and I'll show you how 1 dice set, along with a certain type of throw,
increases the chances of 2 numbers to come up way more than the 7.
It's one of the cool "insider" tips I give to my readers.

Hope this gives you a headstart on understanding dice rolling probability.
Knowing this adds a new level to your craps play - or any dice game with two six sided dice.
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