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Hit Dice (HD)
Hit Dice represent a creature's general level of power and skill. As a creature gains levels, it gains additional Hit Dice. Monsters, on the other hand, gain racial Hit Dice, which represent the monster's general prowess and ability. Hit Dice are represented by the number the creature possesses followed by a type of die, such as “3d8.” This value is used to determine a creature's total hit points. In this example, the creature has 3 Hit Dice. When rolling for this creature's hit points, you would roll a d8 three times and add the results together, along with other modifiers
an 11th class level half celestial-human has 11d10 hitpoints, so does this mean he has 11 hit dice for purposes of his one per day racial ability to smite evil (which simply adds +HD (max 20) to damage on one attack against an evil creature)?
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Hit Dice (HD)Hit Dice represent a creature's general level of power and skill. As a creature gains levels, it gains additional Hit Dice. Monsters, on the other hand, gain racial Hit Dice, which represent the monster's general prowess and ability. Hit Dice are represented by the number the creature possesses followed by a type of die, such as “3d8.” This value is used to determine a creature's total hit points. In this example, the creature has 3 Hit Dice. When rolling for this creature's hit points, you would roll a d8 three times and add the results together, along with other modifiers
an 11th class level half celestial-human has 11d10 hitpoints, so does this mean he has 11 hit dice for purposes of his one per day racial ability to smite evil (which simply adds +HD (max 20) to damage on one attack against an evil creature)?
In that same light, does raising his HD through class levels give him access to the spell like abilities and higher defenses that are reserved for higher HD creatures?
Yes and yes.