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Research Topic: Six Sided Dice Result Distribution
By Ian Mander BSc, 19 February 1999, updated 15 August 1999.
Question: How do you work out how many ways there are of making any particular number when throwing a given number of [six sided] dice?
Answer: When one adds another die, each previous result has six new ways to be used. Therefore, one easy way to calculate the results is to use tables (such as a spreadsheet) to progressively sum for greater numbers of dice. The tables given below should be reasonably self-explanatory.
Each possible outcome total (for the number of dice being thrown - eg, you can throw anything from 2 to 12 inclusive for two dice) has a light blue background.
The number of ways of getting each outcome has a pale yellow background, and it's this line that's fed into the next table in six different positions for the six different ways the new die can be thrown.
Observation: The more dice one throws at one time, the closer the result distribution approximates a normal distribution. As can be seen by the graphs below, anything from three dice upwards gives a reasonably close approximation to a normal distribution.
One die:
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Two dice:
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Three dice:
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Four dice:
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