Maths problem: fatigue vs critical hits
A DNR (Dominions random number) works like this:
Take a random number between 1 and 6. If the result is 6, take a random number between 0 and 5 and add it to the sum. If the result is a 5, repeat until the result isn't a 5.
What is the probability of getting a number of X or higher with 2 DRNs?
The manual lists comparisons, or chances of 2d6oe producing a value greater than 2d6 oe by a spesific amount. There comparisons are used for almost everything from attack to damage. There's only a single mechanic that I know of that uses 2d6oe value that ISN'T compared into another 2d6oe value, and that's the chance of a critical hit. Page 76 of the manual states the a critical hit happens if 2d6oe minus (fatigue/15) is less than 2.
For a single DRN, chance of results between 1-5 is 5/6. Chance of results larger than 5 is 1/6, result larger than 10 is 1/36, chance of result larger than 15 is 1/216 etc etc.
Any math students/professors/hobbyists want to try their hand at solving this?
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