Dice probability for two 6 sided dice rolled together

Rolling two 6 sided dice

Rolling two 6 sided dice or 2D6 as many war gamers (warhammer springs to mind) and dungeon and dragons (other role playing games are available) players know is quite common. It is also present in board games such as monopoly or backgammon.

The intend of this hub is to give you some idea of the odds of getting a particular total on the sum of the two six sided dice. Using this information you can try to stack the odds more in your favour, remember though that luck is a fickle mistress and may desert you at any time regardless of how you may think the odds are stacked in your favour.

There are 36 potential combinations of number that you can roll on two 6 sided dice for this example we will use the total of the dice added together as it is used in most games.

The number of combinations that you can roll determine the odds that you get a particular total. For example take 2 as your total, when rolling two 6 sided dice there is only one combination possible that you can roll to get this total, that being double one or "snake eyes" as it is also known.


Probabilty for two 2 sided dice

Sum of the two dice
Number of different combinations/ fractional odds
Percential odds
2
1/36
2.778%
3
2/36
5.556%
4
3/36
8.333%
5
4/36
11.111%
6
5/36
13.889
7
6/36
16.667
8
5/36
13.889
9
4/36
11.111%
10
3/36
8.333%
11
2/36
5.556%
12
1/36
2.778%

Modern die theory

Veering away from mathematical probability for a moment, there is a theory that standard game die (the singular of dice) has a bias towards rolling higher numbers. This is because the standard "dots" or indentations used to represent the numbers remove a small proportion of the die's weight making the sides with lower numbers on fractionally more heavy then the higher numbers. This in turn causes the heavier sides to lie flat to the surface you are rolling on increasing the odds of rolling a higher number. You would have to roll a lot of dice however to prove this theory out.

Casinos and other establishments used specially crafted and weighted dice to ensure that every roll is fair and these are generally known as perfect or precision dice.

Fractional odds broken down even further

Sum of the two dice
Fractional odds
2
1/36
3
1/18
4
1/12
5
1/9
6
5/36
7
1/6
8
5/36
9
1/9
10
1/12
11
1/18
12
1/36

Conclusion

As you can see from the tables above the most likely outcome of rolling two 6 sided dice is rolling the sum of 7, the odds then pyramid down from here to either end of the spectrum. You can use this information even if you cannot remember the exact odds to help influence decisions you will make whilst playing games. For example you will know many rolls will be 6,7 or 8 whilst the chances of getting 2 or 12 are a lot slimmer indeed.

Never underestimate the element of chance whilst playing a game whilst a result may be "a dead cert" every once in a while (the odds even say so) a roll will go against your expectations!

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DDE profile image

DDE 3 years ago from Dubrovnik, Croatia

Dice probability for two 6 sided dice rolled together I learned so much more about dice. useful and interesting

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