Advantage: Difference between revisions
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(added a quick summary to the math in "Effects on the average of dice rolls" near the top of the section for those who do not know/wish to know the actual math behind it.) |
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|8||65% ||87.75%||42.25% | |8||65% ||87.75%||42.25% | ||
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|9||60% ||84%|| | |9||60% ||84%||36% | ||
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|10||55%||79.75%||30.25% | |10||55%||79.75%||30.25% | ||
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A more general way of looking at advantage/disadvantage is calculating the effect on the average of dice rolls. On average, the bonus/penalty is +/-3.325. This makes it more broadly applicable than looking at specific rolls and makes it easier to compare to other bonuses and penalties which may apply to a roll. | A more general way of looking at advantage/disadvantage is calculating the effect on the average of dice rolls. On average, the bonus/penalty is +/-3.325. This makes it more broadly applicable than looking at specific rolls and makes it easier to compare to other bonuses and penalties which may apply to a roll. | ||
For this we first need to clarify the notations used below: D{{math|n}} represents an {{math|n}}-sided die, {{math|P(i)}} is the probability that a variable has value {{math| | For this we first need to clarify the notations used below: D{{math|n}} represents an {{math|n}}-sided die, {{math|P(i)}} is the probability that a variable has value {{math|i}}, {{math|\mathbb{E} }} denotes the average or expected value of a roll, and {{math|1=\textstyle\sum_{i=a}^b x_i}} denotes the sum of a series of numbers {{math|x}} over an index {{math|i}} with {{math|i}} going from {{math|a}} through {{math|b}}. | ||
The formula to calculate the expected value, {{math|\mathbb{E}[x]}}, of a variable {{math|x}} is equal to the sum of every possible value of {{math|x}} multiplied by the chance for {{math|x}} to have that value. | The formula to calculate the expected value, {{math|\mathbb{E}[x]}}, of a variable {{math|x}} is equal to the sum of every possible value of {{math|x}} multiplied by the chance for {{math|x}} to have that value. | ||