One way to vary damage by weapon type is to classify weapons as either light, medium or heavy, then roll two six-sided dice, and select the lower or higher of the two values rolled depending on the classification. This approach changes the probabilities of rolling above or below the average roll.
For light weapons, you can roll two six-sided dice, and take the lower of the two values. The result is that you score a four to six 25% of the time, and a six 3% of the time.
For medium damage, you can roll one six-sided die. The result is that you score a four to six 50% of the time, and a six 17% of the time.
For heavy damage, you can roll two six-sided dice, and take the higher of the two values. The result is that you score a four to six 75% of the time, and a six 31% of the time.
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