How to Calculate Dice Probabilities

By Michael Keenan

Calculating dice probabilities helps you determine the odds of different games. You can figure out whether certain bets are advantageous or if the odds are stacked against you. For example, rolling a five and rolling a seven are two possible outcomes when using two six-sided dice. A person requiring a roll of a five would be at a disadvantage because the probability of rolling the seven is greater. To calculate the probability of different rolls, you need to know the number of dice being used, the number of sides on each dice and the number of ways you can reach your desired outcome.

Write down the number of possible outcomes per set of dice. For example, if you use standard six-sided dice, there are six possible outcomes--one through six.

Write down the number of possible outcomes by raising the number of outcomes per set of dice to the number of dice used. Most games use two dice, so if you used two six-sided dice, you would raise six to the second power and get 36.

Write down the number of ways the desired result can occur. For example, if you want to roll a six, you could achieve that result five different ways: by rolling a one and a five, a two and a four, a three and a three, a four and a two, or a five and a one.

Divide the number of ways the desired result can occur by the total number of possible outcomes to calculate the probability of a result occurring. For example, the probability of rolling a six using two six-sided dice would be equal to five divided by 36, or 13.89 percent.

Tip

When determining how many ways an outcome can occur, be sure to count outcomes that use the same numbers in a different order as multiple possibilities. For example, if you were using three six-sided dice and wanted a total of five, you would count the combinations 1-2-2, 2-2-1 and 2-1-2 as three different ways to achieve your target outcome.

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."